report on sabbatical leave for dr. gerard p gilfoyle gerard p gilfoyle university of richmond

Report on Sabbatical Leave for

Dr. Gerard P Gilfoyle

Gerard P Gilfoyle

University of Richmond, Richmond, VA 23221

This document is the final report on the sabbatical leave of Dr. Gerard P Gilfoyle and de-scribes the work during the period of the sabbatical (September, 2009 - May, 2010). Dr. Gilfoylereceived support from the JSA/Jefferson Lab Sabbatical Research Leave Support Program to coverrelocation costs to Jefferson Lab during his leave. The amount of the award was $1,500/monthor $13,500 for the entire period. Below the research accomplishments of Dr. Gilfoyle during thistime are described, the value of the sabbatical support is assessed, and program enhancements arediscussed. A listing of papers, talks, and other contributions can be found in Appendices A-E.

The CLAS12 detector will be a new particle detector for nuclear physics and is to be builtin Hall B at Jefferson Lab to take advantage of the new physics opportunities after the 12 GeVUpgrade. An important part of collecting and publishing high quality data with low systematicuncertainties is a robust, modern, physics-based simulation of the detector. Work has begun onsuch a program called gemc, but there are still significant CLAS12 detector sub-systems that havenot been implemented in gemc. During the period of this sabbatical Dr. Gilfoyle wrote the code tosimulate the forward electromagnetic calorimeter (EC) in CLAS12. This task required developinga model of the EC in order to program the geometry of the EC, simulate the generation of thesignals, and the digitize those signals. Dr. Gilfoyle made three presentations during the sabbaticalperiod describing his progress and a draft of a CLAS Note is in preparation (see Appendix F).

The electromagnetic structure of the proton ground state has been mapped out for over 50years and with high precision and in a large range of Q2. However, only recently has it becomepossible to access the magnetic structure of the neutron with similarly high precision. A recentlypublished result [1] by Gilfoyle and the CLAS collaboration measured the magnetic form factorof the neutron using the ratio method on deuterium. The precision and coverage of these resultseclipse the world’s data on this elastic form factor in the Q2 range of 1.0− 4.8 GeV2. Dr. Gilfoyleis also spokesperson and contact person on another experiment (E12-07-104) that will extend thesemeasurements to higher Q2 during the 12-GeV era at Jefferson Lab [2] and was initially approvedin 2007, but without a scientific rating. During the period of this sabbatical, the Jefferson LabProgram Advisory Committee (PAC) was charged with rating the array of experiments that hadbeen approved for running after the 12 GeV Upgrade. Dr. Gilfoyle lead the effort to updatethe original proposal (E12-07-104) and made the PAC presentation. The experiment was given ascientific rating of A− and allocated 30 days of beam time. The report is in Appendix G.

During the same time period Dr. Gilfoyle was invited to make a contributed talk on the publishedGn

M measurement [1] at the fall meeting of the Division of Nuclear Physics of the American PhysicalSociety [3] and presented an invited talk on the PAC-approved, future Gn

M measurement (E12-07-104) at the Workshop on Exclusive Reactions at Large Momentum Transfer. The proceedings forthe latter presentation will be published and are shown in Appendix J.

There is still some analysis to be completed on the CLAS GnM measurement at low Q2. That

work has begun, but was interrupted by some of the tasks mentioned above. Happily, Dr. Gilfoyle’sgroup at the University of Richmond has received a grant of $162,000 from the National Science

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Foundation’s Major Research Instrumentation program to obtain a supercomputing cluster. Thecluster has been purchased and built at Advanced Clustering in Kansas City, Kansas. The systemis being hosted at the vendor temporarily and will be moved to Richmond in September, 2010.Good progress has been made to move the data and codes to the new system and it is expected tobe available for the low-Q2 Gn

M GnM analysis in the fall.

In the summer of 2009, Jefferson Lab administration encouraged Dr. Gilfoyle and Dr. DavidHeddle from Christopher Newport University to pursue funding from Jefferson Science Associatesto hold a workshop on the software developments for the new detector CLAS12 being built in HallB as part of the 12 GeV Upgrade. The pursuit was successful and in May, 2009 the CLAS12Software Workshop was held for two days at the University of Richmond. The first day consistedof speakers from outside the CLAS Collaboration and outside Jefferson Lab. See the program inAppendix I. The goal of the morning session was to learn about the state of the art in data analysisof large particle and nuclear physics experiments (see talks by M. Ernst from Brookhaven and E.Gerchtein from FermiLab) and to hear the perspective of the leadership in scientific computing atJefferson Lab (see talks by C. Watson and G. Heyes). In the afternoon session talks from CLASCollaborators working on the CLAS12 software were presented. About fifty people attended thefirst day of the workshop. On the second day of the workshop a series of tutorials was held in one ofthe teaching labs at the University of Richmond to introduce the attendees to some of the recentlydeveloped software systems. About twenty-five people attended the tutorials.

During the period of this sabbatical Dr. Gilfoyle made significant progress on the analysis ofdata from the Gn

M experiment (the E5 run period) to extract the fifth structure function fromthe 2H(e, e′p)n reaction. The goal of this project is to establish a baseline or benchmark for thehadronic model of nuclei to meet. This baseline is necessary so that we can more clearly map thetransition from hadronic to quark-gluon degrees of freedom at higher Q2. Dr. Gilfoyle completedthe extraction of the asymmetries associated with the fifth structure function and completed astudy of the effect of radiative corrections on those asymmetries. See Appendix ?? for a draft ofthe CLAS Analysis Note in preparation.

The JSA/Jefferson Lab Sabbatical Research Leave Support Program will be assessed here andrecommendations made for improving the program. The program has a high value. The fundingenabled Dr. Gilfoyle to be present at Jefferson Lab nearly every day during the period of hissabbatical. This was crucial for making progress on programming the the forward electromagneticcalorimeter in the CLAS12 simulation gemc. This code is still in the development stage and notyet well documented. The original author is Dr. M. Ungaro who is stationed at Jefferson Laband he was invaluable in collaborating with Dr. Gilfoyle to make progress on this project. It isalso worth noting that the procedure for being reimbursed for relocation expenses was easy andefficient. Ms. Elizabeth Lawson is to be commended for keeping the bureaucratic demands for thisprogram to a minimum. It is also worth noting that Ms. Lawson was similarly helpful when Dr.Gilfoyle organized the CLAS12 Software Workshop at Richmond in May, 2010. The only change tothe program would be to alert applicants and recipients about the tax implications of the programsooner and/or in a more obvious place like the program webpage. It was not clear until afterthe start of the sabbatical that the funds would be treated as salary for tax purposes instead ofa travel reimbursements. In all, JSA/Jefferson Lab Sabbatical Research Leave Support Programenhances the scientific productivity of Jefferson Lab by freeing visiting scientists from the worriesof relocation and allowing them to concentrate on the physics.

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References

[1] J. Lachniet, A. Afanasev, H. Arenhovel, W. K. Brooks, G. P. Gilfoyle, D. Higinbotham,S. Jeschonnek, B. Quinn, M. F. Vineyard, et al. Precise Measurement of the Neutron MagneticForm Factor Gn

M in the Few-GeV2 Region. Phys. Rev. Lett., 102(19):192001, 2009.

[2] G.P. Gilfoyle, W.K. Brooks, S. Stepanyan, M.F. Vineyard, S.E. Kuhn, J.D. Lachniet, L.B. Wein-stein, K. Hafidi, J. Arrington, D. Geesaman, R. Holt, D. Potterveld, P.E. Reimer, P. Solvignon,M. Holtrop, M. Garcon, S. Jeschonnek, and P. Kroll. Measurement of the Neutron MagneticForm Factor at High Q2 Using the Ratio Method on Deuterium. E12-07-104, Jefferson Lab,Newport News, VA, 2007.

[3] G.P. Gilfoyle et al. Precise Measurement of the Neutron Magnetic Form Factor in the Few-GeV2Region. In Bull. Am. Phys. Soc., Fall DNP Meeting, 2009.

Appendices

A Refereed Publications from the Period of the Sabbatical

1. M.E. McCracken et al. (CLAS Collaboration), ”Differential cross section and recoil polariza-tion measurements for the gamma p to K+ Lambda reaction using CLAS at Jefferson Lab”,Phys.Rev.C81:025201,2010.

2. Y. Ilieva et al. (CLAS Collaboration), ”Evidence for a backward peak in the gamma+d->pi0+d cross section near the eta threshold”, Eur.Phys.J.A43:261-267,2010.

3. S. Anefalos Pereira et al. (CLAS Collaboration), ”Differential cross section of gamma n –>K+ Sigma- on bound neutron with incident photons from 1 to 3.6 GeV”, Phys. Lett. B 688(2010) 289-293.

4. M. Williams et al. (CLAS Collaboration), ”Differential Cross Sections and Spin DensityMatrix Elements for gamma p -> p omega”, Phys. Rev. C 80, 065208 (2009).

5. M. Williams et al. (CLAS Collaboration), ”Partial Wave Analysis of the Reaction gamma p-> p omega and the Search for Nucleon Resonances”, Phys. Rev. C, 80, 065209 (2009).

6. I.G. Aznauryan et al. (CLAS Collaboration), ”Electroexcitation of Nucleon Resonances fromCLAS Data on Single Pion Electroproduction”, Phys. Rev. C 80, 055203 (2009).

7. M. Williams et al. (CLAS Collaboration), ”Differential Cross Sections for the Reactionsgamma p -> p eta and gamma p -> p eta-prime”, Phys. Rev. C 80, 045213 (2009). (2009).

8. M. Battaglieri et al. (CLAS Collaboration), ”Photoproduction of pi+ pi- Meson Pairs on theProton”, Phys. Rev. D 80, 072005 (2009).

9. G. Gavalian et al. (CLAS Collaboration), ”Beam Spin Asymmetries in DVCS with CLAS at4.8 GeV”, Phys. Rev. C 80, 035206 (2009).

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10. R. Nasseripour et al. (CLAS Collaboration), ”Photodisintegration of 4He into p+t”, Phys.Rev. C 80, 044603 (2009).

11. X. Qian et al. (CLAS Collaboration), ”The Extraction of phi-N Total Cross Section fromd(gamma,p K+ K-)n”, Phys. Lett. B 680, 417 (2009).

B Invited Talks and Panels from the Period of the Sabbatical

1. “Measuring the Magnetic Form Factor of the Neutron in CLAS12”, presented at the Workshopon Exclusive Reactions at High Momentum Transfer, Jefferson Lab, May 19, 2010.

2. “Putting the Genie Back in the Bottle: The Science of Nuclear Non-Proliferation”, presentedat the Joint Meeting of the New England Section and the New York State Section of theAmerican Physical Society, Modern Nuclear Applications, Union College, April 24, 2010.

3. Invited panelist for discussion on encouraging women and minorities in science and engineeringcareers, Women in Science and Technology Workshop at JLab, Nov 18, 2009.

C Other Talks and Presentations from the Period of the Sabbat-ical

1. “Simulation Results for CLAS12 From gemc”, CLAS12 Software Workshop, May 25, 2010.

2. “Nuclear Physics Working Group Report”, plenary session, CLAS Collaboration Meeting,March 19, 2010.

3. “CLAS12 Software”, plenary session, CLAS Collaboration Meeting, March 18, 2010.

4. “Recent progress implementing the electromagnetic calorimeter (EC) in the CLAS12 Geant4simulation (gemc)”, CLAS12 Software working group session, CLAS Collaboration Meeting,March 17, 2010.

5. “Update on Experiment E12-07-104, Measurement of the Neutron Magnetic Form Factor atHigh Q2 Using the Ratio Method on Deuterium”, JLab PAC35 review, January 29, 2010.

6. “Nuclear Physics Working Group Report”, plenary session, CLAS Collaboration Meeting,November 21, 2009.

7. “Recent software developments for the CLAS12 simulation gemc including adding the EC”,CLAS12 Software working group meeting, November 18, 2009.

8. G.P.Gilfoyle, J.Lachniet, W.K.Brooks, B.Quinn, M.Vineyard et al. (The CLAS Collabora-tion), “Precise Measurement of the Neutron Magnetic Form Factor in the Few-GeV2 Region”,Mini-Symposium on Electromagnetic Form Factors - from the Nucleon to Nuclei, Bull. Am.Phys. Soc., Fall DNP Meeting, BF.8 (2009).

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D Contributed Talks and Presentations by Students at NationalMeetings from the Period of the Sabbatical

1. M.Moog, G.P.Gilfoyle, and M.King, “Simulating the Neutron Detection of the CLAS12 De-tector”, Bull. Am. Phys. Soc., Fall DNP Meeting, GB.00086 (2009).

2. C.A.Copos and G.P.Gilfoyle, “Testing Analysis Algorithms for the 2H(e, e′p)n Reaction”,Bull. Am. Phys. Soc., Fall DNP Meeting, GB.00028 (2009).

3. M.Jordan and G.P.Gilfoyle, “Systematic Uncertainties of Out-of-Plane Measurements of theFifth Structure Function of the Deuteron”, Bull. Am. Phys. Soc., Fall DNP Meeting,GB.00059 (2009).

E Grant Applications and Other Proposals from the Period of theSabbatical

1. Proposal submitted for $7,500 from the JSA/SURA Initiatives Program to hold the CLAS12Software Workshop, August 24, 2009. Approved October, 2009.

2. Co-spokesperson on the beam time proposal entitled “Precision Measurement of the NeutronMagnetic Form Factor up to Q2 = 18.0 (GeV/c)2 by the Ratio Method” submitted to theJefferson Lab Program Advisory Committee, December 5, 2009.

3. Co-spokesperson on the beam time Letter-of-Intent entitled “The EMC Effect in Spin Struc-ture Functions” submitted to the Jefferson Lab Program Advisory Committee, December 5,2009, approved January 29, 2010

4. Co-spokesperson on the beam time Letter-of-Intent entitled “Nuclear Exclusive and Semi-inclusive Physics with a New CLAS12 Low Energy Recoil Detector” submitted to the JeffersonLab Program Advisory Committee, December 5, 2009, approved January 29, 2010

5. Travel grant proposal submitted for University of Richmond Faculty Research Committee,spring, 2010, Approved May 26, 2009.

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F Draft of CLAS Note on Programming the EC in gemc

Simulation of the Electromagnetic Calorimeter in

CLAS12

G.P. Gilfoyle1, M.Ungaro2, J. Carbonneau1, M. Moog1, and C. Musalo1

1 University of Richmond, Richmond, VA2 University of Connecticut, Storrs, CT

August 5, 2010

Abstract

We describe here the forward electromagnetic calorimeter (EC) that will be part ofthe base equipment for the CLAS12 detector in Hall B at Jefferson Lab. CLAS12 isbeing built to take advantage of the new physics opportunities opened by the 12 GeVUpgrade at Jefferson Lab. Robust, accurate simulations of the detector are essentialto keep systematic uncertainties low. We have developed a new, robust, physics-basedsimulation called gemc that uses the Geant4 package to simulate the interaction of par-ticle with matter. We describe here the implementation of the EC in gemc includingthe geometric model, how is was applied in gemc, simulation of raw signals, and digi-tization. We show results of tests of the package including comparisons with previoussimulations of the EC and measured properties.

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CLAS-NOTE 2010-Draft - August 5, 2010 2

1 Introduction

In this CLAS-Note we describe the implementation of the forward electromagnetic calorime-ter (EC) in gemc, the CLAS12 simulation package. The purpose of the EC is (1) detectionand triggering of electrons, (2) detection of photons (for reconstruction of other particleslike π0 and η), and (3) neutron detection. The information from the EC will be combinedwith data from the two threshold Cherenkov detectors (the high-threshold Cerenkov counter(HTCC) and the CLAS6 Cerenkov counter (CC)) to provide high electron detection efficien-cies and large hadron rejection factors. The EC is an electromagnetic sampling calorimeterthat consists of six, identical sectors and covers the forward region (5 < θ < 45) of eachCLAS12 sector. The CLAS6 forward electromagnetic calorimeter will be reused in CLAS12largely without modifications [1]. Relevant details can be found in Section 1.

Simulation of CLAS12 is an essential part of the design of the detector and is neededfor the analysis of CLAS12 data. The precision of many experiments will be be limited bysystematic uncertainties instead of statistical ones, so an accurate simulation is vital [2]. Arobust, maintainable simulation for CLAS12 gemc is now being developed [3]. In the paper,we will describe in broad terms the CLAS12 forward electromagnetic calorimeter and thenfocus in great detail on the EC geometry. We then describe how this geometric informationin implemented in gemc and our initial results measuring the features of the EC with thenew simulation (e.g. sampling fraction,...) and conclude with a summary.

2 Description of the Electromagnetic Calorimeter

The EC is an electromagnetic sampling calorimeter that covers the forward region (5 < θ <45) of each CLAS12 sector [4]. It is constructed from alternating layers of scintillator stripsand lead sheets, with a total thickness of 39 cm of scintillator and 8.4 cm of lead, for a totalthickness of 16 radiations lengths. The module construction is illustrated in Fig 1.

The lead sheets account for 90% of the 16 radiation length thickness. In each module,the scintillator/lead layers are contained in a volume having the shape of a nearly equilateraltriangle. Each module contains 39 layers consisting of 10−mm thick scintillator and 2.2 mmof lead. The module was designed using a projective geometry, pointed at the nominal CLAS6target position, such that the solid angle subtended by successive layers is approximatelyconstant for the CLAS6 configuration. The entire detector will be placed about 200 cmfurther away from the nominal CLAS12 target position than the CLAS6 target position.The azimuthal (φ) coverage ranges from about 50% at forward angles to approximately 90%at large angles. Each layer consists of 36 scintillator strips oriented parallel to one side ofthe triangle, with the strip orientation being rotated by 120 in each successive layer:ec1(labeled u, v, and w in Fig 1).

The three orientations (or views) of scintillator strips are labeled u,v and w. Each viewcontains 13 layers, which are subdivided into inner (5 layers) and outer (8 layers) stacks thatprovide longitudinal sampling. Each of the view/stack combinations are optically gangedand coupled to XP2262 PMTs via fiber optic cables. The optical readout of the EC isillustrated in Fig 2. The 1296 PMT channels are read out by FASTBUS crates containingLeCroy 1881M ADC and LeCroy 1872A TDC boards. Leading edge discriminators are used

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Figure 1: Exploded view of the electromagnetic calorimeter

to provide timing signals to the TDC.To reconstruct a hit in the EC in CLAS6, energy deposition is required in all 3 views of

either the inner or outer layers of the module. Adjacent strips are placed into groups in eachview if their energy deposit are above a software threshold. After grouping, the centroid andRMS for each group are computed. The intersection points of scintillator groups in differentviews are found. Intersections which contain groups from all 3 views correspond to hits. Theenergy deposit and time of the hit are calculated taking into account the path lengths fromthe hit location to the readout edge (to correct for signal propagation time and attenuation).If one group is involved in more than one hit, its energy is divided between hits with anappropriate weighting. A view of the CLAS6 EC showing reconstructed hits is shown in Fig3.

3 EC Geometry

In defining the CLAS12 EC geometry we draw on our experience with the CLAS6 version.Our description shares many features of the work of R. Minehart [5]. However, it is notidentical (although the actual detector is) to Ref. [5], because we generate the parametersused by Geant4 to build the detector simulation in gemc [6]. Geant4 is a toolkit for thesimulation of the passage of particles through matter and is one of the essential pieces of theCLAS12 simulation. We do use the same notation as Ref [5] when it is appropriate.

For each sector of the EC we define a coordinate system we call the G4 sector coordinatesystem. These coordinates are different from the usual sector coordinate system used in, say,

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Figure 2: Side view of EC module, showing optical connections.

the drift chamber geometry, but they are consistent with the local EC coordinate systemthat is centered on the individual detector and used in Geant4 to define the volume of thedetector. The z axis of the G4 sector coordinates is horizontal aong the beam line and inthe direction of the beam. The y axis is radially outward in the ideal midplane of the EC.The x axis is constructed to form a right-handed coordinate system. We define (for lateruse) the ‘perpendicular point’ P by a line drawn from the target point T at the origin (andnominal target center) to a point on the face of the first scintillator layer and perpendicularto that face. The G4 local EC coordinate system has its origin at the geometric center ofthe triangle formed by the three sides of the front face of the first scintillator (closest to thetarget) of the EC. The z axis of the G4 local EC coordinates is perpendicular to the faceof the detector (and hence parallel to the line from the target point T to the perpendicularpoint P ) and points away from the target. The negative y axis is parallel to the face ofthe first scintillator layer, passes through the origin, and passes through the vertex of thetriangle-shaped scintillator layer that is closest to the beam line (small polar angle θ). Thepositive y axis passes through the origin and through the center of the side of the trianglefarthest from the beam. It is also parallel to the face of the first scintillator layer. The x isoriented to form a right-handed coordinate system. The positive x axis points to the left asone is looking outward from the target and along the z axis of the G4 local EC coordinates.Note that the y axis for both the G4 sector coordinates and the G4 local EC coordinates liein the same plane.

The nominal distance from the target point T at the CLAS12 target center to P isL1 = 7217.23 mm. The front face (and all the layers)of the EC makes an angle θEC = 25 to

a line perpendicular to the beam line so we construct a vector ~L1 in the G4 sector coordinatesystem

~L1 = (0, L1 sin θEC , L1 cos θEC) = (0, 3050.13 mm, 6541.03 mm) (1)

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1

2 3

4

56

31 4

6

2

5

Figure 3: Event reconstruction in the EC. In sector 2,3,4,5 a single hit is found, while insector 1, multiple hits are reconstructed.

which goes from the target point T to P . Next, we construct a second vector ~S that goesfrom P to the geometric center of the face of the first EC scintillator (closest to the target)

~S = (0,−yPO cos θEC , yPO sin θEC) = (0,−861.79 mm, 401.86 mm) (2)

where yPO = 950.88 mm is the distance from the CLAS12 perpendicular point P to thegeometric center of the front face of the first scintillator. See Fig 4.

In the local coordinate system we treat the active area of each EC layer as a triangleand define this triangle in terms of a trapezoid in Geant4. The y position of the geometriccenter of layer L is at

ycent(L) = a1(L − 1)L (3)

where a1 = 0.0856 mm and the units of ycent(L) are mm. Note that for L = 1, the centerof the face of the scintillator is at the origin. The half-height in the y-direction (half thedistance from the vertex closest to the beamline to the center of the opposite side of thetriangle) is

∆y(L) = a2 + a3(L − 1) (4)

where a2 = 1864.65 mm, a3 = 4.627 mm, and the units of ∆y(L) are mm.We require the half-width in the x direction at the vertex of the triangle closest to the

beam (where it is zero) and the half-width in the x direction on the side of the trianglefarthest from the beam (∆x). The active triangular region is bounded by three lines:

y = ycent(L) − ∆y(L) + (− tan θo)x (5)

y = ycent(L) − ∆y(L) + (+ tan θo)x (6)

y = ycent(L) + ∆y(L) (7)

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Figure 4: Drawing of the active area of the front face of the first EC scintillator. The vectors~L1 and ~S determine the geometric center of the scintillator face. The G4 sector coordinatesystem is shown.

where tan θo = 1.95325 and θo = 62.889 is the angle between sides of the triangle on theoutside edge of the calorimeter (at large polar angle). Equations 5-6 define the left- and right-hand sides of the trianglular active area of the first scintillator (as one looks outward fromthe target) and Equation 7 defines the outer edge of the active area of the first scintillatorlayer (at large polar angle θ). The half-width in the x direction on the side of the triangledefined by Equation 7 (the side of the triangle farthest from the beam) is

∆x =2∆y

tan θo

(8)

where ∆y is defined in Equation 4. We also require the half-width in the z direction. Thethickness of each layer is constant at 12.38 mm so

∆z =12.38 mm

2= 6.19 mm . (9)

To define the geometry of the strips in each layer we start with the y coordinate of thelower edge of a U strip in layer number L given by

y = −a2 − a4(L− 1) + (U − 1)wu(L) (10)

where a2 is defined above, a4 = 4.3708 mm, and

wu(L) = a5 + a6(L− 1) (11)

is the strip width for the U strips in layer L and a5 = 103.655 mm and a6 = 0.2476 mm.Equation 10 is for the y coordinate for the lower edge of the U strip. The upper edge of thestrip is obtained by setting U = U + 1.

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The edges of the V strips are given by the equation

y = ycent(L) − ∆y(L) + wv(L)(37− n)2

√

1 + tan2 θo − tan θox (12)

and the edges of the W strips are given by

y = ycent(L) −∆y(L) + ww(L)(37− n)2

√

1 + tan2 θo + tan θox (13)

where n is the strip number (n = nmin = 1 is the shortest strip and n = nmax = 36 is thelongest). The widths of V and W strips are given by

wv = a7 + a8(L − 2) (14)

where a7 = 94.70 mm and a8 = 0.2256 mm and

ww = a9 + a8(L− 3) (15)

where a9 = 94.93 mm and a8 = 0.2256 mm. Each strip has a trapezoidal portion on itslight collection end that extends beyond the triangular region defined above. The trapezoidhas right angles at the end of the strip, and distance from the end to the triangular regionis given by two distances.

d2, d1 = d2 +w

2

(

tan2(θ) − 1

tan(θ)

)

(16)

where w is the width of the strip. For the first 15 layers

d2 = 36.4 mm, L ≤ 15 (17)

and for the remaining layers

d2 = 25.4 mm, L > 15. (18)

The z spacing between layers is (according to Cassim Riggs) 12.381 mm which is 2∆zso that the total depth of the detector along the z direction is

∆ztotal = 2(nmax − 1)∆z + 2∆zscint (19)

so the z coordinate of the front face of each layer of scintillator is

z(L) = −∆ztotal

2+ 2∆z(L − 1) (20)

The calorimeter can be subdivided into triangular stacks, each one directed back towardsthe target. A convenient labeling for these stacks is provided by the number N, where

N = U(U − 1) + V − W + 1 (21)

subject to the subsidiary condition for a valid combination that

S = U + V + W = 73 or 74 (22)

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With this numbering scheme, the cell #1 is at the vertex near the beam, with U = 1, V =W = 36, and S = 73. The final cell in this scheme is at U = V = 36, W = 1, for whichN = 362 = 1296. In general, if U + S = 2U + V + W is even(odd) the triangular cell pointstoward(away from)the beam. The center of the cell is at

y = −a2 − a4(L− 1) + (U − 0.5)wu(L) (23)

x tan θ = (W − V )wu(L) (24)

or

x =1

tan θo

(W − V )wu(L) (25)

.The parameters defined in the text above are summarized in Table 1 below.

Name Value Name ValueθEC 25 θO 62.88

a1 0.0856 a2 1864.6a3 4.627 a4 4.3708a5 103.66 a6 0.2476a7 94.701 a8 0.2256a9 94.926

Table 1: Table of coefficients for equations in text.

4 Adding the Forward Electromagnetic Calorimeter to

gemc

In this section we summarize the current, physics-based CLAS12 simulation program calledgemc, go through the steps required to add the EC to gemc and show some initial results.The physics-based CLAS12 simulation program gemc is a modern, object-oriented code. It isbased on the C++ programing language and Standard Template Libraries for constructingobjects. The parameters that define a particular simulation (geometry, materials, magneticfields, step size, etc.) are stored external to the code and most are saved in a mysql database.This enable users to rapidly change the parameters of the simulation without having torecompile the code. The factory method is used for the processing individual hits in CLAS12,for digitizing those hits to mimic the data stream, and for the defining the input/outputformats. We are using the Geant4 package from CERN for handling the passage of particlesthrough matter [6]. Geant4 (for GEometry ANd Tracking) performs this task using MonteCarlo methods and is the successor to GEANT3 mentioned above. It is the first such packageto use object oriented programming, is written in C++, and is well supported by CERN andthe international Geant4 Collaboration. Geant4 includes facilities for handling geometry,tracking, detector response, run management, visualization and user interface.

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The first step in adding the EC to gemc is to define the EC geometry using Geant4 andthe CLAS12 mysql database. Geant4 provides methods for defining the physical volumesthat make up the CLAS12 simulation and the information needed for a particular CLAS12component is read from the databse. For the EC we are using a generalized trapezoid(G4Trap method in Geant4) to represent the mother volume which encloses the entire ECmodule and to describe each scintillator or lead layer of the detector. The strips that makeup each scintillator layer are not defined until the digitization phase. The Geant4 parametersfor G4Trap are shown in Table 2 and Fig 5 shows the generalized trapezoid. We use the sameaxes definitions as Geant4 for our G4 local EC coordinate system. To define this geometry

Name Description Name DescriptionpDx1 Half x length of the side at y =

−pDy1 of the face at −pDzpDx2 Half x length of the side at y =

+pDy1 of the face at −pDzpDx3 Half x length of the side at y =

−pDy2 of the face at +pDzpDx4 Half x length of the side at y =

+pDy2 of the face at +pDzpPhi Azimuthal angle of the line joining

the centre of the face at −pDz tothe centre of the face at +pDz

pTheta Polar angle of the line join-ing the centres of the faces at±pDz

pDy1 Half y length at −pDz pDy2 Half y length at +pDzpAlp1 Angle with respect to the y axis

from the centre of the side (lowerendcap)

pAlp2 Angle relative to the y axisfrom the centre of the side (up-per endcap)

pDz Half z length

Table 2: Geant4 parameters for the G4Trap volume.

Figure 5: Geant4 generalized trapezoid.

a Perl script (ec build.pl in the area gemc/production/database io/clas12/geo/ec)

14


Name Index ???? ???? DescriptionETot 1 1 1 Total Energy Deposited< x > 2 1 1 Average global x position< y > 3 1 1 Average global y position< z > 4 1 1 Average global z position< lx > 5 1 1 Average local x position< ly > 6 1 1 Average local y position< lz > 7 1 1 Average local z position< t > 8 1 1 Average timepid 9 1 1 Particle IDvx 10 1 1 x coordinate of primary vertexvy 11 1 1 y coordinate of primary vertexvz 12 1 1 z coordinate of primary vertexE 13 1 1 Energy of the track at the entrance pointmpid 14 1 1 Mother Particle IDmvx 15 1 1 x coordinate of mother vertexmvy 16 1 1 y coordinate of mother vertexmvz 17 1 1 z coordinate of mother vertexsector 18 0 1 sectorstack 19 0 1 stackview 20 0 1 viewstrip 21 0 1 stripEC ADC 22 0 1 EC ADCEC TDC 23 0 1 EC TDC

Table 3: Contents of EC.bank which is used to define the EC banks.

generates a file containing the mysql code needed to modify the mysql database which iscalled by a shell script (go table).

The second step is to define the data banks that will be used by the EC and stored inthe mysql database. In the area gemc/production/database io/clas12/banks/bankdefs

a file EC.bank defines the quantities that will be generated in the simulation (see Table 3).Note that while we defined the geometry above in terms of layers, in the real detector, wedo not measure the properties of a track layer by layer. The first fifteen scintillator layersare ganged together to form the ‘inner’ calorimeter and the remaining twenty-four layersform the ‘outer’ calorimeter. This information (inner versus outer) is stored in the ‘stack’parameter in Table 3. We also record the orientation of the strips, the U , V , or W view, foreach hit. Recall Fig 1.

The file clas12 hits def.txt in gemc/production/database io/clas12/banks wasmodified to add the information necessary for the EC. Executing the shell scripts go table

followed by go hits puts the information in the mysql database. In the area gemc/production/hitprocess/we created the file EC hitprocess.cc (which contains the functions that process the hit)and the header file EC hitprocess.h (which declares those functions) to process the simula-

15


tion information and form hits. To add these functions to gemc we edited Clas12 HitProcess MapRegister.cc

After these steps gemc was recompiled.The last step in adding the EC to gemc is to digitize the signals produced in the

simulation. The geometry of each scintillator layer is one large sheet when it is really madeof separate strips. To determine which strip a particular track has struck consider Figure 6.The track has struck the layer at the point ~P = (x, y) (the hit). The corners of the triangle

strip

1r

2r

2r

A

CB

O

P

x

y

θ

V View from Target

Figure 6: Front view of V layer showing quantities needed to determine the strip of a hit atpoint P .

(points A, B, and C) can be written down in terms of the Geant4 parameters (see Table 2).

~A = (xA, yA) = (0,−pDy1) (26)

~B = (xB, yB) = (pDx2, pDy1) (27)

~C = (xC , yC) = (−pDx2, pDy1) (28)

With this information in hand we calculate ~r1 = ~P − ~C and construct the unit vector r2 sothat it is perpendicular to a vector going from A to B (i.e. ~B − ~A). Then

r2 =(yB − yA, xA − xB)

√

(yB − yA)2 + (xA − xB)2(29)

and

cos θ =~r1 · r2

|~r1|. (30)

We then calculate the length of the vector ~r2 in Figure 6 which is the distance to the hitperpendicular to the orientation of the V strips. This length is

|~r2| = |~r1| cos θ (31)

16


so the strip number is the following.

strip = ⌊|~r2|

36⌋ + 1 (32)

Once we have the strip number we can calculate the expected ADC signal and thephoton attenuation. For each hit we convert the deposited energy into photons at a rate3.5 photons/MeV and use this value to form a Poisson distribution. The number of photonsis chosen randomly from this Poisson distribution. The attenutation of the photons as theypropagate down the strip is calculated using the known attenuation factor λ0 = 3760 mmand the distance from the hit to the light guide on the end of each strip. The geometricquantity needed to calculate this distance is the length of the vector ~rV in Figure 7 whichgoes from the position of the hit at point P in a direction parallel to the line segment ABto the end of the strip. The vectors for the corners of the triangle, points A, B, C are the

strip

r 0r

Vrr1

A

CB

x

y

V View from Target

VO

P

Figure 7: Front view of V layer showing quantities needed to calculate the photon attentu-ation of a hit at point P .

same as those above. The equation for the line segment BC is the following.

y = yBC = pDy1 (33)

We want to get ~rV . The vector ~r1 can be written as

~r1 = ~r0 + lrV (34)

where

rV =~B − ~A

| ~B − ~A|. (35)

17


We can now set yBC = y1 and solve for l to obtain ~rV . Once we have accounted for the photonattenuation we calculate the expected PMT gain using (10 channels/MeV) and smear withthe PMT resolution using GSIM parameters. We also calculate the expected TDC signalusing 20 ns/channel.

We now show some initial results for the gemc simulation of the EC. Figure 8 shows theCLAS12 detector including the forward electromagnetic calorimeter in the left-hand paneland the same view of CLAS12 with a single electron event in the EC in the right-hand panel.Straight track results here.

Figure 8: The CLAS12 detector in gemc including the EC (left-hand panel) and with anelectron event (right-hand panel). Red tracks are negatively charged particles; green areneutrals; blue are positive; red dots are above-threshold hits; blue dots are below-thresholdhits.

5 EC Simulation Results

6 Summary

This work is supported by US Department of Energy grant DE-FG02-96ER40980 and Jef-ferson Science Associates.

18


References

[1] M. Amarian et al. Nucl. Inst. and Meth. A, 460:239, 2001.

[2] The CLAS12 TDR Editorial Board. The CLAS12 Technical Design Report. Technicalreport, Thomas Jefferson National Accelerator Facility, Newport News, VA, 2008.

[3] M. Ungaro. gemc Overview. http://clasweb.jlab.org/wiki/index.php/Gemc_overview,Jefferson Lab, 2008.

[4] E. Leader, A.V. Sidorov, and D.B. Stamenov. Phys. Rev., D73, 2006.

[5] R. Minehart. EC Geometry. http://www.jlab.org/~gilfoyle/CLAS12software/CLAS6ECgeometry.pdfUVa.

[6] A. Agostinelle et al. geant4: a simulation toolkit. Nucl. Instr. and Meth., A506:250–303,2003.

19


A Lead Sheet Dimensions

The lead sheets are on the average 2.387 mm thick. They are cut to cover the active triangulararea as well as the extension on the light collection side of the layer defined by the lengthd2. Layers 4,7,10 etc. have the vertex at the beam side clipped off. Their dimensions do notfollow a simple formula. On average, the z coordinate of the front surface of each layer oflead is 100.0 mm greater than the z coordinate of the front surface of the preceding layerof scintillator. In the following table layer 2 of the lead is between scintillator 1 and 2, etc.There is no layer 1 of lead. Measurements are from [5].

Layer Base Height Truncation2 152.096 147.264 03 152.454 148.890 04 152.948 149.372 1.4405 153.174 149.636 06 153.532 149.943 07 154.033 150.433 1.4488 154.252 150.007 09 154.610 150.996 010 155.118 151.492 1.45511 155.328 151.379 012 155.688 152.048 013 156.203 152.552 1.46214 156.406 152.750 015 156.766 153.101 016 156.820 153.153 1.0017 157.090 153.417 018 157.449 153.768 019 157.898 152.206 1.0020 158.168 154.470 0

Layer Base Height Truncation21 158.527 154.821 022 158.975 155.258 1.0023 159.246 155.523 024 159.605 155.873 025 160.054 156.311 1.0026 160.324 156.575 027 160.683 156.926 028 161.130 157.363 1.0029 161.400 157.628 030 161.760 157.979 031 162.208 158.415 1.0032 162.478 158.681 033 162.838 159.032 034 163.286 159.468 1.0035 163.556 159.733 036 163.916 160.084 037 164.364 160.521 1.0038 164.634 160.786 039 164.994 161.137 0

B Walls of the Containment Box

The side walls of the containment box can be represented by six planes of 1.5”thick aluminum.The vertices of the planes can be represented by 12 points at the rear of the box, six forthe outside and six for the insides surfaces. The labeling of these points is indicated in thefigure. The coordinates of the points in the local detector frame are shown in the next table.Measurements are from [5].

20


P1 2079.19 2076.73 0. P7 2259.10 2255.70 480.72P2 -2079.19 2076.73 0. P8 -2259.10 2255.70 480.72P3 -2139.49 1959.89 0. P9 -2319.43 2138.86 480.72P4 -65.02 -2092.05 0. P10 -65.02 -2264.50 480.72P5 65.02 -2092.05 0. P11 65.02 -2264.50 480.72P6 2139.49 1959.89 0. P12 2319.43 2138.86 480.72P1’ 2043.41 2036.06 0. P7’ 2223.31 2215.06 480.72P2’ -2043.41 2036.09 0. P8’ -2223.31 2215.06 480.72P3’ -2089.43 1946.89 0. P9’ -2269.36 2125.85 480.72P4’ -42.34 -2051.61 0. P10’ -42.34 -2224.05 480.72P5’ 42.34 -2051.61 0. P11’ 42.34 -2224.05 480.72P6’ 2089.43 1946.89 0. P12’ 2269.36 2125.85 480.72

The six surfaces can be characterized by the following outward pointing normal vectors:

n1 0 cos (20.42) − sin (20.42)n2 0.87848 -0.44975 -0.161259n3 -0.87848 -0.44975 -0.161259n4 0.79367 0.40978 -0.44693n5 -0.79367 0.40978 -0.44693n6 0 -0.94217 -0.33765

21

G Update for E12-07-104

Update for E12-07-104:

Measurement of the Neutron Magnetic Form Factor at High Q2

Using the Ratio Method on Deuterium

G.P. Gilfoyle∗†, W.K. Brooks∗, and K. Hafidi∗ for the CLAS Collaboration

1 Introduction

In JLab Experiment E12-07-104 we intend to dramatically extend the reach of our understandingof a fundamental feature of the neutron; its magnetic form factor Gn

M . The elastic electromagneticform factors(EEFFs) describe the distribution of charge and magnetization inside the nucleon atlow Q2 and probe the quark structure at higher Q2. This experiment is part of a broad program atJLab to measure the EEFFs, map the internal landscape of the nucleon, and test non-perturbativeQuantum Chromodynamics (QCD) and QCD-inspired models of the nucleon (see NSAC Long-Range Plan [1]). The measurement will cover the range Q2 = 3.5 − 14.0 GeV2 with systematicuncertainties less than 3%. Statistical uncertainties will be about 3% in the highest Q2 bin in thisrange and significantly less at lower Q2. The anticipated range and systematic uncertainties ofthe experiment are shown in Figure 1. The reduced magnetic form factor Gn

M/(µnGD) is plottedversus Q2 where µn is the neutron magnetic moment and GD = 1/(1 + Q2/Λ2)2 is the dipole formfactor with Λ2 = 0.71 GeV2. We used the recent parameterization of the world’s data on Gn

M inRef [10] to predict the reduced form factor. Also shown are selected world’s data for Gn

M including

∗Co-spokesperson†Contact person

2010-01-02 11:02:40 )2(GeV2Q

2 4 6 8 10 12 14

DG nµ/

MnG

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Solid - KellyDotted - Alberico et al.Squares - CLAS12 anticipatedGreen - Previous world data.Red - J.Lachniet et al.Blue, long-dashed - MillerBlue, dotted - Guidal et al.Blue, dashed - Cloet et al.

Anticipated error bars show systematic uncertainty.

Figure 1: Selected data [2, 3, 4, 5, 6, 7, 8, 9] and anticipated results for GnM for 56 days of running

with CLAS12 (black, filled squares) in units of µnGD as a function of Q2. The anticipated CLAS12results follow a fit to the world data on Gn

M that includes the recent CLAS6 GnM results [10]. The

red, open circles are the CLAS6 results. Other curves are described in the text.

122

the recent CLAS6 results (red, open circles)[2]. The proposed CLAS12 experiment (black, closedsquares) will nearly triple the upper limit of the previous CLAS6 measurement and provide precisedata well past any existing measurement. Other aspects of Figure 1 are discussed below.

To measure GnM we will use the ratio of quasielastic e − n to quasielastic e − p scattering on

deuterium. The ratio method is less vulnerable to systematic uncertainties than previous methodsand we will have consistency checks between different detector components of CLAS12 and anoverlap with our previous CLAS6 measurements. A liquid-hydrogen/liquid-deuterium, dual targetwill be used to make in situ measurements of the neutron and proton detection efficiencies. We takeadvantage of the large acceptance of CLAS12 and veto events with additional particles (beyonde−n and e−p coincidences) to reduce the inelastic background. We expect to limit the systematicuncertainties to 3% or less [11]. This experiment can be done with the base equipment for CLAS12and was approved by PAC32.

This experiment is part of a series to measure the elastic, electromagnetic form factors of thenucleon at JLab [11, 12, 13, 14, 15, 16]. The PAC has approved experiments in all three halls tomeasure the four EEFFs. That set includes E12-09-019 to measure Gn

M in Hall A over the sameQ2 as our experiment. Making both measurements will ‘allow a better control of the systematicerror on Gn

M ’ (see PAC 34 report [17]). In this update we discuss recent, relevant measurementsemphasizing developments in the last two years since E12-07-104 was approved. We also presentnew theoretical developments and analyses and connect this experiment with the Hall A one.

2 Experimental Status

New experimental results have been produced since PAC32. The CLAS6 measurement of theneutron magnetic form factor has been published [2]. The results are shown as the red points inFigure 2 and compared with several theoretical models and selected world data. The CLAS6 dataare surprisingly consistent with the dipole parameterization. This was unexpected because previousmeasurements show the reduced Gn

M decreasing at larger Q2 although with large uncertainties(Gn

M/µnGD = 0.62±0.15 at Q2 = 10 GeV2 [9]); see the green points in Figure 1 for Q2 ≥ 4.0 GeV2.

)2(GeV2Q0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

DG nµ/

MnG

0.6

0.8

1

1.2

1.4CLAS

Lung

Kubon

Bartel

Anklin

Arnold

Anderson

Green band - Diehl

Solid - Miller

Dashed - Guidal

Systematic Uncertainty

Figure 2: Results for GnM/(µnGD) from the CLAS6 measurement are compared with a selection of

previous data [3, 4, 5, 6, 7, 8] and theoretical calculations [18, 19, 20].

2

23

The solid, black curve in Figure 1 shows a fit by Kelly [21] to the world data without the CLAS6results, reflecting this drop with Q2. The dashed curve from Alberico et al. [10] is a fit that includesthe CLAS6 results which falls more slowly with Q2. The other curves shown in Figure 2 are fromDiehl et al. [18], Guidal et al. [19], and Miller [20] and are all constrained by the world’s previousdata without the CLAS6 results. The curves from Refs. [18] and [19] use generalized partondistributions (GPDs) to characterize the EEFFs at low Q2 and then extend their calculations tohigher Q2. Both fail to reproduce the CLAS6 data. In Miller’s calculation the nucleon is treatedusing light-front dynamics as a relativistic system of three bound quarks and a surrounding pioncloud (solid curve in Figure 2). The model gives a good description of much of the previous data(including the other three EEFFs) even at high Q2 and is consistent with the CLAS6 results.

Recent measurements [22] and planned ones [12, 13, 14, 15, 16] will reduce the systematicuncertainties on the proposed Gn

M measurement. Extracting GnM depends on precise knowledge of

the proton cross section and the neutron electric form factor GnE . The neutron electric form factor is

known to be small in this Q2 range and contributes at most about 0.7% to the anticipated systematicuncertainty [11]. Recent measurements of the ratio Gn

E/GnM [22] will improve our knowledge of this

quantity and drive down the uncertainty on its contribution. The proton cross section is well knowin this Q2 region and contributes at most about 1.5% to the anticipated systematic uncertainty [11].We expect this contribution to decline in the future because there is a planned 12 GeV experimentto precisely measure this quantity [13].

The broad effort at JLab to measure all four of the elastic electromagnetic form factors is in a Q2

region with significant discovery potential. All the EEFFs are needed to untangle nucleon structure[23]. For example, measuring the ratio of the proton electric to magnetic form factor Gp

E/GpM using

polarization observables revealed a striking difference from earlier measurements [24]. Instead ofbeing constant as expected this ratio fell linearly and appeared to be headed for a zero crossing atQ2 ≈ 8 GeV2. This has sparked a revival of interest in these form factors and dramatically changedour picture of the proton. Recent, preliminary results from the GEp(III) collaboration for Gp

E/GpM

using the recoil polarization method show a decrease with Q2, but with a shallower slope [25]. Theratio Gn

E/GnM was recently measured with greater precision and at higher Q2 than ever before [25].

Those researchers used the recent CLAS6 measurement of GnM to extract Gn

E . The preliminaryresults for the points at Q2 of 2.5 GeV2 and 3.5 GeV2 are 2-4 standard deviations away from theGalster parameterization; suggesting the onset of changes from the lower Q2 behavior. All of thesenew, intriguing results are in the same Q2 range as the proposed CLAS12 Gn

M measurement.

3 Theoretical Status

Progress has been made on the theory side of our understanding of the EEFFs. Mapping the internalgeography of the neutron is a central goal of the 12 GeV Upgrade [1]. The interpretation of theform factors in non-relativistic kinematics has long been in terms of the charge and magnetizationdensities of the nucleons with a positive, central core in the neutron and a negative region onits periphery. For the relativistic case where Q2 > M2

N this simple interpretation becomes modeldependent. Switching to the infinite momentum frame allows one to escape this model dependence,but apparently contradicts the traditional view [26]. Miller and Arrington [27] use a GPD modelto resolve this issue; demonstrating the importance of GPDs to understanding nucleon structure.

Another central goal of the 12 GeV Upgrade is to understand non-perturbative QCD and QCD-inspired models. Cloet et al. employ dynamically dressed quarks using the Dyson-SchwingerEquations in a framework that is fully Poincare’ covariant and symmetry preserving; an essentialfeature as we explore higher Q2 [28]. The degrees of freedom in this model are the three, dressed

3

24

quarks and nonpointlike quark-quark (diquark) correlations. The only free parameter in the modelis the diquark radius. Figure 3 shows the ratio of the neutron electric to magnetic form factors fortwo different values of the diquark radius (solid curve and long-dashed curve), data from Madey etal. [29], and the Kelly parameterization (dashed curve) [21]. The Cloet et al. prediction diverges

Figure 3: Result for the normalized ratio of Sachs electric and magnetic form factors for theneutron computed with two different diquark radii. Short-dashed curve: parameterization of Ref.[21]. Down triangles: data from Ref. [29].

dramatically from the data parameterization at Q2 ≈ 5 GeV2 and then bends over and crosseszero at Q2 ≈ 11 GeV2. This behavior marks this region of Q2 as one of potential discoveryvalue and lies well within the Q2 of our proposed experiment. To study this region further weshow some representative calculations in Figure 1. The blue curves are from Miller and Guidalet al., (described in Section 2) and extended to higher Q2 and Cloet et al. All three curves differmeasurably in magnitude and/or slope somewhere in the range Q2 = 6 − 14 GeV2. There isan opportunity here to distinguish among competing pictures of the neutron. We note here theuncertainties on the anticipated CLAS12 data are systematic ones. We expect the statistical onesto be about the same size (3%) in the highest bin and much smaller at lower Q2.

We also want to touch on truly ab initio calculations performed using lattice QCD. Thesecalculations are still limited in reach to Q2 ≈ 1 GeV2, but we expect that significant progress willbe made by the time the proposed experiment is complete. This is where the broad assault on theEEFFs at JLab is essential. The EEFFs can be formed into isovector and isoscalar combinationsthat are sensitive to different physical effects. The isovector combination is free of disconnectedcontributions which are notoriously difficult to compute on the lattice. This freedom will make theisovector form factor an early test of lattice QCD as the calculations reach higher Q2.

4 Experimental Method and Relationship To Existing Experi-

ments

We now outline the experimental technique and compare the CLAS12 procedures with others.More details are in Ref. [11]. We propose to use the ratio of quasielastic e− n to e− p scatteringfrom a deuterium target to measure Gn

M in the range Q2 = 3.5 − 14.0 GeV2. This technique

4

25

significantly reduces uncertainties associated with other methods and has been used by us [2] andothers [6, 30, 31, 32, 33] to measure Gn

M (see Figure 2). The method is based on the ratio

R =dσdΩ

(2H(e, e′n)QE)dσdΩ

(2H(e, e′p)QE)= a(Q2)

σnmott(G

nE

2 + τn

εn

GnM

2)(

11+τn

)

dσdΩ

(1H(e, e′)p)(1)

for quasielastic (QE) kinematics. The right-hand side is written in terms of the free nucleon formfactors and where τ = Q2/4M2 and ǫ = 1/[1+ 2(1+ τ) tan2(θ/2)]. Deviations from this ‘free ratio’assumption are parameterized by the factor a(Q2) which can be calculated from deuteron modelsand is close to unity at large Q2. The results of other measurements of the proton cross section andthe neutron electric form factor are used to extract Gn

M . The ratio R is insensitive to the luminosity,electron acceptance, electron reconstruction efficiency, trigger efficiency, the deuteron wave functionused in a(Q2), and radiative corrections [2, 34]. In the Hall A Gn

M experiment (E12-09-019) , theratio method is also used.

An essential step in applying the ratio method is selecting quasielastic (QE) events and reducingthe inelastic background. The selection criteria should be the same for e− p and e− n events (toavoid biasing the results) and we want to take advantage of the angular precision of CLAS12.Quasielastic neutron and proton events are chosen by applying a cut on θpq, the angle betweenthe nucleon 3-momentum and the momentum transfer ~q. Inelastic events tend to be emittedat large θpq while QE events are emitted along the direction of ~q. Next, we select events withW 2 = M2

N . In this Q2 regime, the width of the residual mass spectrum W 2 becomes large sothat contamination of the QE peak with inelastic events is a greater problem than at lower Q2.Figure 4 shows this kinematical effect and the impact of requiring θpq < 1.5 on the W 2 spectrumfor Q2 = 12.5 − 14.0 GeV2. The left-hand panel shows the results of a simulation of the reactiondescribed in the original proposal [11] for e − n coincidences at a beam energy of 11 GeV and inthe highest Q2 bin (Q2 = 12.5 − 14.0 GeV2) where we expect to have statistical precision equalto the anticipated systematic uncertainty of 3%. The red histogram shows the contribution of theQE events, the green one shows the inelastic events, and the black one is the total. The QE eventsare overwhelmed by the inelastic background in the left-hand panel. Requiring θpq < 1.5 for the

2009-12-31 21:54:49)2 (GeV2W

-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5

Co

un

ts

0

2000

4000

6000

8000

10000

12000

14000

16000

E = 11 GeVen eventsRed - QEGreen - InelasticBlack - total

2 = 12.5-14.0 GeV2Q

)2 (GeV2W-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5

Co

un

ts

0

500

1000

1500

2000

2500

E = 11 GeVen events

o < 1.5pqθ

No hermiticity cut2 = 12.5-14.0 GeV2Q

H(e, e’p)2

)2 (GeV2W-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5

Co

un

ts

0

500

1000

1500

2000

2500

E = 11 GeVen events

o < 1.5pqθ

Hermiticity cut ON2 = 12.5-14.0 GeV2Q

Figure 4: The impact of the hermiticity cut is shown. The left-hand panel displays the W 2 spectrafor simulated e−n events. In the middle panel, the neutrons are required to have θpq < 1.5. In theright-hand panel, we add the hermiticity cut. The number of events shown is not representative ofthe anticipated value.

5

26

neutron (middle panel) considerably reduces the inelastic background. Nevertheless, the QE eventsare still a shoulder on a larger inelastic peak. We now take full advantage of the large acceptanceof CLAS12. The inelastic events that emit nucleons and contaminate the QE spectrum have other,associated particles (pions, photons, etc.). CLAS12 will detect many of those associated particles.In the right-hand panel we have applied a multiparticle veto or hermiticity cut. Electron-protonevents that have a third particle and come from inelastic events (and are part of event samplein the other two panels) are rejected. This reduces the inelastic background by about a factor of4-5 here; the quasielastic peak now clearly rises out of the inelastic noise. We can then apply acut on W 2 to remove additional inelastic events. In the example shown, the contribution of thebackground in the region of the QE peak for W 2 < 1.2 GeV2 drops from 45% of the total in themiddle panel to 11% in the right-hand panel after applying the hermiticity cut. Notice also thereis no effect on the events in QE peak (red histogram going from the middle panel to the right-handone). We want to emphasize here that Figure 4 represents a worst case scenario. We simulated thereaction for the highest Q2 bin (12.5−14.0 GeV2) where we expect to obtain statistical uncertaintythat is equal to or less than our expected systematic uncertainty of 3%. The data at lower Q2

will have less kinematic spreading and inelastic contamination. See the E12-07-104 proposal forthe results of a simulation in the middle of the Q2 range of the proposed experiment [11]. Theapproved experiment in Hall A to measure Gn

M (E12-09-019) does not have a multiparticle veto.In that experiment the angular resolution and high luminosity of the Hall A spectrometers enablesone to place restrictive cuts on θpq to isolate the QE events.

The GnM measurement in CLAS12 has important consistency checks. Neutrons will be measured

in two subsystems of the forward detector. One of those subsystems, the forward calorimeter (FC),consists of the electromagnetic calorimeter (EC) used in CLAS6 (and the CLAS6 Gn

M measurement)and a new, pre-shower calorimeter (PCAL) which is located in front and and covers the face ofthe EC. The forward time-of-flight (TOF) system will consist of the same detectors used in CLAS6(thickness 25 mm) along with two new layers of scintillators (one is the same thickness and the otheris thicker at 30 mm). These two subsystems will enable us to make semi-independent measurementsof the e − n production in CLAS12 and provide a vital cross check on the measurement. Theapproved experiment in Hall A to measure Gn

M (E12-09-019) does not have an internal consistencycheck like this one. The CLAS6 measurement will also have a large overlap (Q2 = 3.5− 4.8 GeV2)with the previous CLAS6 Gn

M measurement (see Figure 1). Since we are reusing some of the samedetector subsystems that were used in the CLAS6 Gn

M experiment (the EC and one of the forwardTOF panels) this will provide another consistency check on our CLAS12 results.

An essential aspect of the neutron measurement in the TOF and FC systems is measuring theneutron detection efficiency. We will use the p(e, e′π+n) reaction as a source of tagged neutrons.Electrons and π+’s will be detected in CLAS12 and missing mass used to select candidate neutrons(found events). We then predict the position of the neutron in CLAS12 and search for it (if aneutron is found we call these reconstructed events). The ratio of reconstructed to found eventsgives us the detection efficiency. This will be done in CLAS12 with a unique, dual target. Co-linear,liquid hydrogen and deuterium cells will provide production and calibration events simultaneouslyand under the same conditions (in situ). This reduces our vulnerability to variations in detectorgains, beam properties, etc. The PAC32 report described this method as ‘elegant.’ In the Hall AGn

M experiment (E12-09-019), a radiator and a hydrogen target will be placed periodically in thebeam so the p(γ, π+)n reaction can be used to provide tagged neutrons [14].

In the CLAS6 measurement we used the same techniques described here to measure the neutronproduction and detection efficiency. To demonstrate the power of these methods we show Figure 5from Ref [2]. It shows Gn

M measured simultaneously with the CLAS6 TOF and EC subsystems (thatwill be reused in CLAS12). Two beam energies were used in the CLAS6 measurement so there are

6

27

four semi-independent data sets. The uncertainties are statistical ones only. The four measurementsare consistent within the statistical uncertainties, suggesting the systematic uncertainties are well-controlled and small. Any overall differences are within the 2-3% systematic uncertainty of theCLAS6 Gn

M experiment. In CLAS12 we will have similar internal consistency checks to validateour results for Gn

M and the systematic uncertainty.In Figure 6 we show the anticipated number of neutron and proton events as a function of Q2 (red

and blue points and left-hand scale) and the uncertainty on GnM (right-hand scale). Instead of using

the dipole approximation as we did in the original E12-07-104 proposal the cross sections for proton

2.6 GeV, TOF neutrons

2.6 GeV, EC neutrons

4.2 GeV, TOF neutrons

4.2 GeV, EC neutrons

2 (GeV/c)2Q1 1.5 2 2.5 3 3.5 4 4.5 5

D

G nµ/n M

G

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

Figure 5: Comparison of GnM measured with different CLAS6 subsystems (TOF and EC) and for

two different beam energies [2].

2009-12-26 21:56:59

)2(GeV2Q0 2 4 6 8 10 12 14 16

An

tici

pat

ed E

ven

ts

210

310

410

510

, 56 days of runningnMCLAS12 G

Red - Protons

Blue - Neutrons

Dotted - World data uncertaintyDashed - Anticipated CLAS12 statistical uncertaintyLong Dashed - Anticipated CLAS12 systematic uncertainty

nM/G

nM G

∆

-310

-210

-110

Figure 6: Run statistics for the CLAS12 GnM experiment (E12-07-104) for 56 days of running.

Proton cross sections were obtained using the Kelly fit [21]. Neutron cross sections were obtainedusing the Galster fit for Gn

E and the Alberico et al. [10] fit for GnM . The green, dotted line is

the current uncertainty on GnM for the world data, the green, short-dashed line is our anticipated

statistical uncertainty, and the green, long-dashed line is our goal of 3% systematic uncertainty.

7

28

events were calculated using the fits from Kelly [21] for the proton form factors. For the neutroncross sections the Galster fit was used for Gn

E , and the Alberico et al. fit for GnM [10] that includes the

recent CLAS6 GnM data. We also included the effect of a cut requiring W 2 < 1.2 GeV2. Bin sizes in

the low Q2 region where we overlap with the CLAS6 measurement match the CLAS6 ones and thenincrease gradually. The bin for the range Q2 = 12.5− 14 GeV2 will have statistical precision equalto the anticipated systematic uncertainty of 3%. Depending on the target position we can reachas far as Q2 = 15 GeV2, but with diminished statistical precision. This value of Q2 correspondsto the largest electron scattering angle we will measure in the forward detector in CLAS12. Atlower Q2 the statistical precision increases rapidly. Over the range Q2 = 3.5 − 14.0 GeV2 we havestatistical uncertainties at or below 3% (our goal for the upper limit on the systematic uncertainty)and typically much lower (green, dashed line in Figure 6). These uncertainties are far below thecurrent precision on Gn

M (green, dotted line). The Hall A measurement (E12-09-119) will havebetter statistical precision across the full Q2 range (3.5− 14.0 GeV2) than the CLAS12 one. Bothexperiments will be limited by systematic uncertainties.

We have set a goal of 3% as the upper limit on the systematic uncertainty (long-dashed linein Figure 6). Based on our CLAS6 experience, the largest contributors to the systematic uncer-tainty will be the parameterization of the neutron detection efficiency (NDE) for the TOF and ECsystems, the uncertainty on the proton cross section, and the uncertainty on Gn

E . We estimatedthose contributions to have maximum values of 0.75% (NDE parameterization), 1.2% (proton crosssection), and 1.4% (Gn

E) (see Section 3.5 of Ref [11]). The uncertainties on the proton cross sectionand Gn

E are lower over most of the Q2 range and will shrink with future measurements. We alsoestimated the systematic uncertainty due to the inelastic background subtraction using the highestQ2 bin with good statistics (12.5−14.0 GeV2) again as a worst-case scenario. In this bin 11% of theneutron events and 12% of the proton events in the range W 2 < 1.2 GeV2 are inelastic background.We expect to determine that value within 20%; giving us a systematic uncertainty of 2% in theratio R and 1% in Gn

M . We added all these contributions in quadrature including weighting theeffect of the TOF NDE measurement less (because the TOF efficiency is about one-sixth of the ECefficiency). We obtain an estimate of the maximum anticipated systematic uncertainty of 2.4%;this result determined our goal of 3% for the systematic uncertainty. In the Hall A experiment(E12-09-119) the anticipated systematic uncertainties on Gn

M are in the range of 1.2%-2.9%We also note here that like CLAS6, CLAS12 will have an electron trigger so a wide range of

data will be collected. Experiments with different physics requirements can use the same dataset. The CLAS12 experiment will make efficient use of beam time by allowing other experimentsto run concurrently with E12-07-104. Experiments E12-09-007 and E12-09-008 will study nucleonstructure using semi-inclusive deep inelastic scattering. They have been approved and will runconcurrently with us [35, 36].

To summarize, the scientific motivation for measuring the neutron magnetic form factor is morecompelling than when E12-07-104 was approved. The dipole form of Gn

M has returned to prominencefor Q2 = 1.0−4.5 GeV2. At higher Q2 (5−13 GeV2) we have observed new, surprising behavior inthe other form factors (a possible zero crossing in Gp

E/GpM ), developed QCD-inspired models that

diverge widely, and predictions for a zero crossing in GnE . To explore this new territory JLab will

measure all of the EEFFs. The CLAS12 experiment will use a tested method for measuring GnM and

push the frontier of our understanding of the neutron magnetic form factor up to Q2 = 14 GeV2

and with high precision. The ability to veto multiparticle final states dramatically reduces thebackground from inelastic events that contaminate the QE peak. We will use a dual-cell target forprecise, in situ measurements of the neutron detection efficiency as demonstrated in the CLAS6experiment. Finally, with CLAS12 we have several important consistency checks using differentdetector subsystems of CLAS12 (TOF and EC) to validate our results.

8

29

References

[1] Nuclear Science Advisory Committee. The Frontiers of Nuclear Science. US Department ofEnergy, 2007.

[2] J. Lachniet, A. Afanasev, H. Arenhovel, W. K. Brooks, G. P. Gilfoyle, D. Higinbotham,S. Jeschonnek, B. Quinn, M. F. Vineyard, et al. Precise Measurement of the Neutron MagneticForm Factor Gn

M in the Few-GeV2 Region. Phys. Rev. Lett., 102(19):192001, 2009.

[3] W. Bartel et al. Nucl. Phys. B, 58:429, 1973.

[4] G. Kubon et al. Phys. Lett. B, 524:26–32, 2002.

[5] A. Lung et al. Phys. Rev. Lett., 70(6):718–721, Feb 1993.

[6] H. Anklin et al. Phys. Lett. B, 428:248–253, 1998.

[7] B. Anderson et al. Phys. Rev. C, 75:034003, 2007.

[8] R. G. Arnold et al. Measurements of transverse quasielastic electron scattering from thedeuteron at high momentum transfers. Phys. Rev. Lett., 61(7):806–809, Aug 1988.

[9] S. Rock et al. Measurement of Elastic Electron-Neutron Cross Sections up to Q2 = 10(GeV/c)2. Phys. Rev. Lett., 49(16):1139–1142, Oct 1982.

[10] W. M. Alberico, S. M. Bilenky, C. Giunti, and K. M. Graczyk. Electromagnetic form fac-tors of the nucleon: New fit and analysis of uncertainties. Phys. Rev. C (Nuclear Physics),79(6):065204, 2009.

[11] G.P. Gilfoyle, W.K. Brooks, S. Stepanyan, M.F. Vineyard, S.E. Kuhn, J.D. Lachniet, L.B. We-instein, K. Hafidi, J. Arrington, R. Geesaman, D. Holt, D. Potterveld, P.E. Reimer, P. Solvi-gnon, M. Holtrop, M. Garcon, S. Jeschonnek, and P. Kroll. Measurement of the NeutronMagnetic Form Factor at High Q2 Using the Ratio Method on Deuterium. E12-07-104, Jeffer-son Lab, Newport News, VA, 2007.

[12] E.J. Brash, M.K. Jones, Punjabi V., et al. GpE/Gp

M with an 11 GeV electron beam. E12-09-001,Jefferson Lab, Newport News, VA, 2009.

[13] S. Gilad et al. Precision Measurement of the Proton Elastic Cross Section at High Q2. E12-07-108, Jefferson Lab, Newport News, VA, 2007.

[14] B. Quinn, B. Wojtsekhowski, R. Gilman, et al. Precision Measurement of the Neutron MagneticForm Factor up to Q2 = 18.0 (GeV/c)2 by the Ratio Method. E12-09-119, Jefferson Lab,Newport News, VA, 2009.

[15] B.D. Anderson, J. Arrington, S. Kowalski, R. Madey, B. Plaster, A.Yu. Semenov, et al. TheNeutron Electric Form Factor at Q2 up to 7 (GeV/c)2 from the Reaction 2H(e, e′n)1H viaRecoil Polarimetry. E12-09-006, Jefferson Lab, Newport News, VA, 2009.

[16] B. Wojtsekhowski et al. Measurement of the Neutron Electromagnetic Form Factor RatioGn

E/GnM at High Q2. E12-09-016, Jefferson Lab, Newport News, VA, 2009.

[17] JLab Physics Advisory Committee. PAC34 Report. Technical report, Jefferson Laboratory,2009.

9

30

[18] M. Diehl et al. Eur. Phys. J. C, 39:1, 2005.

[19] M. Guidal et al. Phys. Rev. D, 72:054013, 2005.

[20] G.A. Miller. Phys. Rev. C, 66:032201, 2002.

[21] J. J. Kelly. Simple parametrization of nucleon form factors. Phys. Rev. C, 70(6):068202, Dec2004.

[22] Seamus Riordan. Measurements of the electric form factor of the neutron at high momentumtransfer. AIP Conf. Proc., 1149:615–618, 2009.

[23] M. Diehl, Th. Feldmann, R. Jakob, and P. Kroll. Eur. Phys. J. C, 39:1, 2005.

[24] M. K. Jones et al. GpE/Gp

M Ratio by Polarization Transfer in ~ep → e~p. Phys. Rev. Lett.,84(7):1398–1402, Feb 2000.

[25] Kees de Jager. The Super Bigbite Project: a Study of Nucleon Form Factors. 2009.

[26] Gerald A. Miller. Charge densities of the neutron and proton. Phys. Rev. Lett., 99(11):112001,2007.

[27] Gerald A. Miller and John Arrington. The neutron negative central charge density: aninclusive- exclusive connection. Phys. Rev., C78:032201, 2008.

[28] I. C. Cloet, G. Eichmann, B. El-Bennich, T. Klahn, and C. D. Roberts. Survey of nucleonelectromagnetic form factors. Few Body Syst., 46:1–36, 2009.

[29] R. Madey et al. Phys. Rev. Lett., 91:122002, 2003.

[30] C.E. Hyde-Wright and K.deJager. Electromagnetic Form Factors of the Nucleon and ComptonScattering. Ann. Rev. Nucl. Part. Sci., 54.

[31] H. Anklin et al. Phys. Lett. B, 336:313–318, 1994.

[32] G. Kubon et al. Phys. Lett. B, 524:26–32, 2002.

[33] E. E. W. Bruins et al. Measurement of the neutron magnetic form factor. Phys. Rev. Lett.,75(1):21–24, Jul 1995.

[34] J.D. Lachniet, W.K. Brooks, G.P. Gilfoyle, B. Quinn, and M.F. Vineyard. A high precisionmeasurement of the neutron magnetic form factor using the CLAS detector. CLAS AnalysisNote 2008-103, Jefferson Lab, 2008.

[35] K. Hafidi et al. Studies of partonic distributions using semi-inclusive production of Kaons.E12-09-007, Jefferson Lab, Newport News, VA, 2009.

[36] K. Hafidi et al. Study of the Boers-Mulders Asymmetry in Kaon Electroproduction withHydrogen and Deuterium Targets. E12-09-008, Jefferson Lab, Newport News, VA, 2009.

10

31

H Proceedings for Workshop on Exclusive Reactions at High Mo-mentum Transfer

July 27, 2010 16:25 WSPC - Proceedings Trim Size: 9in x 6in gilfoyleProc

1

Measurement of the Neutron Magnetic Form Factor at High Q2

Using the Ratio Method on Deuterium

G.P. Gilfoyle∗, W.K. Brooks, and K. Hafidi et al. for the CLAS Collaboration

∗E-mail: [email protected]

The 12-GeV Upgrade at Jefferson Lab will create an opportunity to dramati-cally extend our knowledge of the magnetic form factor of the neutron (Gn

M)

and the other elastic, electromagnetic form factors. We describe here an ap-proved experiment that will cover a Q2 range (3.5− 14 GeV2) with significantdiscovery potential. Different theoretical approaches (generalized parton dis-tributions, Dyson-Schwinger equations, etc) diverge is this region and existingdata cannot distinguish among them. The proposed measurement will be per-formed in Hall B with the CLAS12 detector and will have statistical and sys-tematic uncertainties below 3%. It is based on the ratio of electron-neutron toelectron-proton scattering that was successfully applied in the CLAS detectorat Jefferson Lab.

Keywords: Form factors; Proceedings; World Scientific Publishing.

1. Introduction

The 12 GeV Upgrade at the Thomas Jefferson National Accelerator Facility

(JLab) has begun and will double the beam energy and open new physics

opportunities. The new physics program at JLab will dramatically extend

the reach of our understanding of a fundamental feature of the neutron; its

magnetic form factor GnM . The elastic electromagnetic form factors(EEFFs)

describe the distribution of charge and magnetization inside the nucleon at

low Q2 and probe the quark structure at higher Q2. A broad program is

planned at JLab to measure the EEFFs, map the internal landscape of

the nucleon, and test non-perturbative Quantum Chromodynamics (QCD)

and QCD-inspired models of the nucleon (see NSAC Long-Range Plan and

others[1–7]). The measurement we discuss here will be performed with the

new CLAS12 detector in Hall B (Experiment E12-07-104 [2]) at JLab which

will replace the current and similar CLAS6 detector. CLAS12 is a large

acceptance spectrometer consisting of layers of silicon counter, drift cham-

bers, time-of-flight scintillators, electromagnetic calorimeters, and Cerenkov

32


2

counters. The forward part is based on a toroidal magnet and there is a

central detector for particles emitted at large angles based on a solenid

magnet. The proposed measurement we describe here will cover the range

Q2 = 3.5− 14.0 GeV2 with systematic uncertainties less than 3%. Statisti-

cal uncertainties will be about 3% in the highest Q2 bin in this range and

significantly less at lower Q2. The anticipated range and uncertainties of

the experiment are shown in Figure 1. The reduced magnetic form factor

GnM/(µnGD) is plotted versus Q2 where µn is the neutron magnetic moment

and GD = 1/(1 + Q2/Λ2)2 is the dipole form factor with Λ2 = 0.71 GeV2.

We used the recent parameterization of the world’s data on GnM in Ref

[16] to predict the reduced form factor. Also shown are selected world’s

data for GnM including the recent CLAS6 results (red, open circles)[8]. The

proposed CLAS12 experiment (black, closed squares) will nearly triple the

upper limit of the previous CLAS6 measurement and provide precise data

well beyond any existing measurement. In this paper we discuss the current

experimental and theoretical situation and our method for measuring GnM

with CLAS12.

2. Experimental Status

Figure 1 shows the world data for GnM up to Q2 = 14 GeV2. For Q2 >

4.5 GeV2 the data are sparse and have large uncertainties. In the range Q2 <

2010-05-18 00:10:02 )2(GeV2Q2 4 6 8 10 12 14

DG nµ/

MnG

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Red - J.Lachniet et al.Green - Previous World DataBlack - CLAS12 anticipated

AnticipatedStatistical uncertainties only

Miller

Guidal et al.

Cloet et al.

Fig. 1. Selected data [8–15] and anticipated results for GnM

for 30 days of running withCLAS12 (black, filled squares) in units of µnGD as a function of Q2. The anticipatedCLAS12 results follow a fit to the world data on Gn

Mthat includes the CLAS6 Gn

M

results [16] (red, open circles). Curves are described in the text.

33


3

4.5 GeV2, the situation is much better especially with the addition of the

CLAS6 measurement [8] (red, open circles). The CLAS6 measurement was

performed using largely the same method we propose here for CLAS12. The

CLAS6 data are surprisingly consistent with the dipole parameterization.

This was a unexpected because previous measurements show GnM decreasing

at large Q2 although with large uncertainties (green points in Figure 1 for

Q2 ≥ 4.5 GeV2.

The broad effort at JLab to measure the EEFFS is in a Q2 region

with significant discovery potential. All these form factors are needed to

untangle nucleon structure [17]. Measuring the ratio of the proton electric

to magnetic form factor GpE/Gp

M using polarization observables revealed a

striking dropoff contradicting previous measurements [18]. On the neutron

side the ratio GnE/Gn

M was recently measured with greater precision and at

higher Q2 than ever before [19]. Those researchers used the recent CLAS6

measurement of GnM to extract Gn

E . The preliminary results for the points

at Q2 of 2.5 GeV2 and 3.5 GeV2 are 2-4 standard deviations away from the

Galster parameterization; suggesting the onset of changes from the lower

Q2 behavior. All of these new, intriguing results are in the same Q2 range

as the proposed CLAS12 GnM measurement.

3. Theoretical Status

Progress has been made on the theory side of our understanding of the

EEFFs. The interpretation of the form factors in relativistic kinematics

has proven more challenging than expected and has required a new picture

based on generalized parton distributions (GPDs) [20,21]. To understand

non-perturbative QCD Cloet et al. employ a Dyson-Schwinger Equation

approach and assume two of the valence quarks form a di-quark. Figure

2 shows the ratio of the neutron electric to magnetic form factors for two

different values of the diquark radius (solid curve and long-dashed curve),

data from Madey et al. [22], and the Kelly parameterization (dashed curve)

[23]. The Cloet et al. prediction diverges dramatically from the data pa-

rameterization at Q2 ≈ 5 GeV2 and crosses zero at Q2 ≈ 11 GeV2. This

behavior marks this region of Q2 as one of potential discovery value and

lies well within the Q2 range of our proposed experiment. The prediction

of GnM by Cloet et al. for Gn

M is shown in Figure 1 along with two other

calculations. In Miller’s calculation the nucleon is treated using light-front

dynamics as a relativistic system of three bound quarks and a surrounding

pion cloud [24]. The model gives a good description of much of the previous

data (including the other three EEFFs) even at high Q2 and is consistent

34


4

Fig. 2. Result for the normalized ratio of Sachs electric and magnetic form factors for theneutron computed with two different diquark radii. Short-dashed curve: parameterizationof Ref. [23]. Down triangles: data from Ref. [22].

with the CLAS6 results. The curve from Guidal et al [25] uses GPDs to

characterize the EEFFs at low Q2 and then extend their calculations to

higher Q2, but fails to reproduce the data at low Q2. All three curves differ

measurably in magnitude and/or slope in the range Q2 = 6 − 14 GeV2.

There is an opportunity here to distinguish among competing pictures.

We also want to touch on truly ab initio calculations performed using

lattice QCD. These calculations are still limited in reach to Q2 ≈ 1 GeV2,

but we expect that significant progress will be made by the time the pro-

posed experiment is complete. This is where the broad assault on the EEFFs

at JLab is essential. The EEFFs can be formed into isovector and isoscalar

combinations that are sensitive to different physical effects. The isovector

combination is free of disconnected contributions which are notoriously dif-

ficult to compute on the lattice. This freedom will make the isovector form

factor an early test of lattice QCD as the calculations reach higher Q2.

4. Experimental Method

We now outline the experimental technique (more details are in Ref. [2]).

We will use the ratio of quasielastic e−n to e−p scattering from a deuterium

target to measure GnM . This technique reduces uncertainties associated with

other methods and has been used by us [8] and others [12,26–29] (see Figure

35


5

1). The method is based on the ratio

R =dσdΩ

(2H(e, e′n)QE)dσdΩ

(2H(e, e′p)QE)= a(Q2)

σnmott(G

nE

2 + τn

εn

GnM

2)(

1

1+τn

)

dσdΩ

(1H(e, e′)p)(1)

for quasielastic (QE) kinematics. The right-hand side is written in terms

of the free nucleon form factors and where τ = Q2/4M2 and ǫ = 1/[1 +

2(1+ τ) tan2(θ/2)]. Deviations from this ‘free ratio’ assumption are param-

eterized by the factor a(Q2) which can be calculated from deuteron models

and is close to unity at large Q2. The results of other measurements of the

proton cross section and the neutron electric form factor are used to extract

GnM . The ratio R is insensitive to the luminosity, electron acceptance, elec-

tron reconstruction efficiency, trigger efficiency, the deuteron wave function

used in a(Q2), and radiative corrections [8].

We will first select quasielastic (QE) events by applying a cut on θpq,

the angle between the nucleon 3-momentum and the momentum transfer ~q.

Nucleons from inelastic events nucleons tend to be emitted at large θpq while

QE nucleons are emitted along ~q. Analyzing protons and neutrons the same

way avoids biasing the results. Next, we select events with W 2 = M2N , but at

high Q2 the width of the residual mass spectrum W 2 and contaminates the

the QE peak. The top panel of Figure 3 shows the results of a simulation

for such high-Q2 e − n events. The red histogram shows the QE events,

the green one shows the inelastic events, and the black one is the total.

The QE events are overwhelmed by the inelastic background. Requiring

θpq < 1.5 for the neutron (lower-left-hand panel) considerably reduces the

inelastic background, but the QE events are still a shoulder on a larger

inelastic peak. We now take advantage of the large acceptance of CLAS12.

The inelastic events emit additional particles (pions, photons, etc.). and

CLAS12 will detect many of those particles. In the lower-right-hand panel

we have applied a hermiticity cut; rejecting events with a third particle. The

quasielastic peak now clearly rises out of the inelastic noise. We emphasize

here that Figure 3 is a worst case scenario. We simulated the reaction for

the highest Q2 bin (12.5 − 14 GeV2) where the inelastic contamination

is largest. The data at lower Q2 will have less kinematic spreading and

inelastic contamination.

The CLAS12 GnM measurement has important consistency checks. Neu-

trons will be measured in two subsystems of CLAS12: the forward electro-

magnetic calorimeter (FC) and the forward time-of-flight (TOF). These two

subsystems will enable us to make semi-independent measurements of the

e−n production and provide a cross check. The CLAS12 measurement will

36


6

also have a large overlap (Q2 = 3.5− 4.8 GeV2) with the previous CLAS6

GnM one (see Figure 1).

An essential aspect of the neutron measurement in the TOF and FC

systems is measuring the neutron detection efficiency. We will use the

p(e, e′π+n) reaction as a source of tagged neutrons. Electrons and π+’s will

be detected in CLAS12 and missing mass used to select candidate neutrons

(found events). We then predict the position of the neutron in CLAS12 and

search for it (if a neutron is observed we call these reconstructed events).

The ratio of reconstructed to found events is the detection efficiency. This

will be done in CLAS12 with a unique, dual target. Co-linear, liquid hy-

drogen and deuterium cells will provide production and calibration events

simultaneously and under the same conditions (in situ). This reduces our

vulnerability to variations in detector gains, beam properties, etc. In the

)2 (GeV2W-1 -0.5 0 0.5 1 1.5 2 2.5 3

Cou

nts

0

2000

4000

6000

8000

10000

12000

14000

16000

E = 11 GeVenX eventsRed - QEGreen - InelasticBlack - total

2 = 12.5-14.0 GeV2Q

)2 (GeV2W-1 -0.5 0 0.5 1 1.5 2 2.5 3

Cou

nts

0

500

1000

1500

2000

2500

E = 11 GeVenX events

o < 1.5pqθ

No hermiticity cut2 = 12.5-14.0 GeV2Q

H(e, e’p)2

)2 (GeV2W-1 -0.5 0 0.5 1 1.5 2 2.5 3

Cou

nts

0

500

1000

1500

2000

2500

E = 11 GeVen events

o < 1.5pqθ

Hermiticity cut ON2 = 12.5-14.0 GeV2Q

Fig. 3. The impact of the hermiticity cut is shown. The top panel displays the W 2

spectra for simulated e−n events. In the lower-left-hand panel, the neutrons are requiredto have θpq < 1.5. In the lower-right-hand panel, we add the hermiticity cut. Thenumber of events shown is not representative of the anticipated value.

37


7

2010-05-18 10:39:38)2(GeV2Q

0 2 4 6 8 10 12 14

n M/G

n MG∆

-210

-110 World’s Data Uncertainty

CLAS12 Anticipated Statistical Uncertainty

CLAS12 AnticipatedSystematic Uncertainty

Fig. 4. Run statistics for the CLAS12 GnM

experiment (E12-07-104) for 30 days ofrunning. The blue, solid curve is the current uncertainty on Gn

Mfor the world data, the

green, dashed line is our anticipated statistical uncertainty, and the red, solid curve isour goal of 3% systematic uncertainty.

CLAS6 measurement we used the same techniques and found the different

data sets were consistent within the statistical uncertainties [8].

In Figure 4 we show the anticipated uncertainty on GnM (red, solid line).

Proton cross sections came from Ref [23] and neutron cross sections from

Galster (GnE) and Alberico et al. (Gn

M ) [16]. We included the effect of a cut

requiring W 2 < 1.2 GeV2 that reduces residual inelastic contamination.

Over the range Q2 = 3.5−14.0 GeV2 we have statistical uncertainties at or

below 3% (green, dashed line) and typically much lower. These uncertainties

are far better than the current precision on GnM (blue, solid line).

5. Summary

To summarize, the scientific motivation for measuring the neutron magnetic

form factor is compelling. At higher Q2 (5 − 13 GeV2) we have observed

new, surprising behavior in the other form factors and developed QCD-

inspired models that diverge widely. To explore this new territory JLab

will measure all of the EEFFs. The CLAS12 experiment will use a tested

method for measuring GnM and push the frontier of our understanding of

the neutron magnetic form factor up to Q2 = 14 GeV2 and with high

precision. The ability to veto multiparticle final states dramatically reduces

the background from inelastic events that contaminate the QE peak. We

will use a dual-cell target for precise, in situ measurements of the neutron

38


8

detection efficiency as demonstrated in the CLAS6 experiment. Finally,

with CLAS12 we have several important consistency checks using different

detector subsystems of CLAS12 (TOF and EC) to validate our results.

References

1. Nuclear Science Advisory Committee, The Frontiers of Nuclear Science (USDepartment of Energy, 2007).

2. G. Gilfoyle et al., Experiment E12-07-104, Jefferson Lab (Newport News,VA, 2007).

3. E. Brash et al., Experiment E12-09-001, Jefferson Lab (Newport News, VA,2009).

4. S. Gilad et al., Experiment E12-07-108, Jefferson Lab (Newport News, VA,2007).

5. B. Quinn et al., Experiment E12-09-119, Jefferson Lab (Newport News, VA,2009).

6. B. Anderson et al., Experiment E12-09-006, Jefferson Lab (Newport News,VA, 2009).

7. B. Wojtsekhowski et al., Experiment E12-10-005, Jefferson Lab (NewportNews, VA, 2010).

8. J. Lachniet, A. Afanasev, H. Arenhovel, W. K. Brooks, G. P. Gilfoyle, D. Hig-inbotham, S. Jeschonnek, B. Quinn, M. F. Vineyard et al., Phys. Rev. Lett.102, p. 192001 (2009).

9. W. Bartel et al., Nucl. Phys. B 58, p. 429 (1973).10. G. Kubon et al., Phys. Lett. B 524, 26 (2002).11. A. Lung et al., Phys. Rev. Lett. 70, 718(Feb 1993).12. H. Anklin et al., Phys. Lett. B 428, 248 (1998).13. B. Anderson et al., Phys. Rev. C 75, p. 034003 (2007).14. R. G. Arnold et al., Phys. Rev. Lett. 61, 806(Aug 1988).15. S. Rock et al., Phys. Rev. Lett. 49, 1139(Oct 1982).16. W. M. Alberico, S. M. Bilenky, C. Giunti and K. M. Graczyk, Phys. Rev. C

(Nuclear Physics) 79, p. 065204 (2009).17. M. Diehl, T. Feldmann, R. Jakob and P. Kroll, Eur. Phys. J. C 39, p. 1

(2005).18. M. K. Jones et al., Phys. Rev. Lett. 84, 1398(Feb 2000).19. K. de Jager (2009).20. G. A. Miller, Phys. Rev. Lett. 99, p. 112001 (2007).21. G. A. Miller and J. Arrington, Phys. Rev. C78, p. 032201 (2008).22. R. Madey et al., Phys. Rev. Lett. 91, p. 122002 (2003).23. J. J. Kelly, Phys. Rev. C 70, p. 068202(Dec 2004).24. G. Miller, Phys. Rev. C 66, p. 032201 (2002).25. M. Guidal et al., Phys. Rev. D 72, p. 054013 (2005).26. C. Hyde-Wright and K.deJager, Ann. Rev. Nucl. Part. Sci. 54.27. H. Anklin et al., Phys. Lett. B 336, 313 (1994).28. G. Kubon et al., Phys. Lett. B 524, 26 (2002).29. E. E. W. Bruins et al., Phys. Rev. Lett. 75, 21(Jul 1995).

39

I Program of the CLAS12 Software Workshop

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CLAS12 Software Workshop

May 25-26, 2010

Physics Department

University of Richmond

Program

Tuesday, May 25, 2010 - Gottwald Center for the Sciences Auditorium (Chair: David Heddle, CNU)

9:00-9:20 Welcome and Summary of the 12 GeV Upgrade Jerry Gilfoyle (Richmond)

9:20-10:10 Big Science in an Era of Large Datasets - BNL Experience

and Perspective in Nuclear and Particle Physics Data

Analysis

Michael Ernst (BNL)

10:10-10:50 Scientific Computing at Jefferson Lab: Petabytes,

Petaflops, and GPUs

Chip Watson (JLab)

10:50-11:10 Break

11:10-12:00 The Offline Analysis Framework at CDF Elena Gerchtein (FNAL)

12:00-12:30 JLab Data Analysis Coordination, Planning and Funding Graham Heyes (JLab)

12:30-2:00 Lunch

2:00-2:20 Overview of the CLAS12 Software Enterprise Dennis Weygand (JLab)

2:20-2:50 CLARA: Service oriented architecture based PDP

application development framework

Vardan Gyurjyan (JLab)

2:50-3:10 The JANA Reconstruction Framework Dave Lawrence (JLab)

3:10-3:30 Event Reconstruction - The Big Picture Mac Mestayer (JLab)

3:30-3:50 Socrat - CLAS12 Electron Reconstruction Sebastien Procureur

(Saclay)

3:50-4:10 Break

4:10-4:30 Reconstructing CLAS12 events using JANA Maurizio Ungaro (UConn)

4:30-4:45 gemc - A Modern Simulation for CLAS12 Maurizio Ungaro (UConn)

4:45-5:00 Simulation Results for CLAS12 From gemc Jerry Gilfoyle (Richmond)

5:00-5:20 CED12 - Seeing Tracks Through Thick and Thin Dave Heddle (CNU)

5:20-5:40 Code Sharing and the EVIO Package Elliott Wolin (Jlab)

5:40-6:00 Data Storage Format for CLAS using HDF5 Gagik Gavalian (ODU)

6:00-8:00 Reception in the Gottwald Atrium

Wednesday, May 26, 2010, Room D-115, Gottwald Center for the Sciences

9:00-12:00 Morning (lab session) Tutorials on CLAS12 Software.

1. Building and using gemc for CLAS12 simulation. Jerry Gilfoyle

2. Building and using Socrat/JSocrat for event

reconstruction.

Maurizio Ungaro

Dennis Weygand

3. Running CLARA. Vardan Gyurjyan

4. Running CED12. Dave Heddle

A DVD will be available for all participants with all the relevant software.

Jefferson Lab - CLAS12 Software Workshop http://conferences.jlab.org/CLAS12Software/prog...

1 of 2 08/05/2010 11:23 AM40

J Draft of CLAS Analysis Note on Measuring the Fifth StructureFunction

Measurements of the Fifth Structure Function of theDeuteron

G.P. Gilfoyle, W.K. Brooks, J.D. Lachniet,B.P. Quinn, and M.F. Vineyard

August 5, 2010

Abstract

We have measured the fifth structure function of the deuteron σLT ′ using the re-action D(~e, e′p)n and the helicity asymmetry in quasi-elastic kinematics with CLAS.The hadronic model of nuclear physics is not well-developed in the GeV region and thetheoretical mixture of relativistic corrections, final-state interactions, meson-exchangecurrents, and isobar configurations is unknown. These data will provide a baselinefor conventional nuclear physics to meet so that deviations from the hadronic modelat higher Q2 can be attributed to quark-gluon effects with greater confidence. Thestructure function was extracted by measuring the moments of the out-of-plane pro-duction in CLAS. This analysis was performed on the E5 data set that covers the rangeQ2 = 0.2−5.0 (GeV/c)2. It is part of a CLAS Approved Analysis entitled ‘Out-of-PlaneMeasurements of the Structure Functions of the Deuteron’

41

CLAS-Analysis-NOTE 2010-Draft - August 5, 2010 1

Contents

1 Introduction 3

2 Necessary Background 3

3 Previous Measurements 5

4 Experimental Details 5

4.1 Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54.2 Dual-Cell Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

5 Event Selection of D(~e, e′p)n 8

5.1 Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85.2 Run Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85.3 Electron Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95.4 Proton Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115.5 Neutron Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

6 Corrections 13

6.1 Momentum Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136.2 Beam Charge Asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166.3 Beam Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166.4 Radiative Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

7 Experiment Results 17

7.1 Extracting Asymmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177.2 Results for Asymmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197.3 Consistency Checks of the Analysis . . . . . . . . . . . . . . . . . . . . . . . 20

7.3.1 Asymmetry at pm ≈ 0 . . . . . . . . . . . . . . . . . . . . . . . . . . 217.3.2 Extracting A′

LT by Fitting the φpq Dependence . . . . . . . . . . . . . 227.3.3 Effect of Fiducial Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . 237.3.4 Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . . 267.3.5 Radiative Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

7.4 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287.5 Final Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

A Electron Fiducial Cuts 34

B Electron Fiducial Fits 37

C Proton Fiducial Cuts 43

D Proton Fiducial Fits 47

42


E Acceptance Effects in 〈sin φpq〉± 53

F Monte Carlo Simulation of Quasielastic Scattering in Deuterium 55

G Systematic Uncertainties 58

H Radiative Corrections 62

43


1 Introduction

This CLAS Analysis Note presents the results of a measurement of the fifth structure functionσLT ′ of the D(~e, e′p)n reaction in quasi-elastic kinematics. The motivation of the measure-ment is to study the transition from a description of nuclei based on hadronic degrees offreedom to one based on quarks and gluons. To quantitatively understand that transitionrequires a solid understanding of the hadronic model to identify where its breakdown willoccur. The structure functions are an essential meeting ground of theory and experimentand this measurement of the so-called ‘fifth’ structure functions extracts one this little-known component of the deuteron in a model-independent way. This is also the first resultof a broader program to extract other structure functions (σLT and σTT ) using the uniqueout-of-plane capabilities of CLAS and to explore other kinematic regions.

Understanding the deuteron tests our ability to construct a ‘consistent and exact de-scription’ of few-body nuclei (2H, 3H, 3He, 4He) [1]. For example, it is an open questionwhether a single interaction or current operator can account for the attributes of all thesenuclei. Calculations using hadronic effects like meson-exchange currents (MEC), isobar con-figurations (IC), and final-state interactions (FSI) are under development, but have yet tobe fully challenged by data in the GeV region [1, 2]. The influence of relativity is also beingstudied [1, 2, 3, 4, 5]. Previous results at lower Q2 reveal the onset of many of these effectsso a complete, modern calculation is needed to compare with data across the full range ofQ2 to test and understand the hadronic model in this region. These issues were raised as‘Key Questions’ at the Jefferson Laboratory PAC14 Few-Body Workshop [1].

Improvements in the hadronic model will enable us to clearly map out the transitionto quark-gluon degrees of freedom; an essential goal of nuclear physics [1, 6]. The basicidea is that if we cannot describe observations with all of the pieces mentioned above, thenwe would see genuine quark-gluon effects in the nucleus. Clearly, we cannot make thatleap without getting firm control of the calculations using the hadronic degrees-of-freedom.It is expected the transition may occur in the GeV region or higher and some expect theregion 1 (GeV/c)2 < Q2 < 6 (GeV/c)2 to be an ideal one for investigating this transition[2, 6, 7, 8]. The mixture of physics effects that influence the different structure functionsdepends on the transferred energy in this energy region. For quasi-elastic (QE) scattering,FSI and relativistic corrections are important for the structure functions, but MEC and ICare less so [9].

In this CLAS Analysis Note we first present some necessary background defining anasymmetry used as the main analysis tool and describe the context of other measurementsof the fifth structure function of the deuteron. We then describe the experiment performedand how events were selected from the data set. Corrections to the first-pass analysis arediscussed and then the results are shown including uncertainties. An Appendix containsmany details so we could use the main text to focus on the physics.

2 Necessary Background

We now develop some of the necessary background for our discussion of the structure func-tions. The fivefold differential cross section for the quasielastic D(~e, e′p)n reaction can be

44


Figure 1: Kinematic quantities used in this analysis.

written as [10]

d3σ

dQ2dpmdφpqdΩedΩp

= σ± = c[ρLfL + ρT fT + ρLT fLT cos(φpq)+

ρTT fTT cos(2φpq) + hρLT ′fLT ′ sin(φpq)] (1)

where the superscript on σ± refers to the helicity, φpq is the angle between the plane definedby the incoming and outgoing electron momenta and the plane defined by the ejected protonand neutron (see Figure 1), the ρi’s depend only on the electronic kinematics, fi are thehadronic structure functions, and h is the helicity of the electron beam (h = ±1). Theconstant c is

c =αE ′

6π2EQ4(2)

where α is the fine structure constant, E is the beam energy, E ′ is the scattered electronenergy, and Q2 is the square of the 4-momentum transfer. The kinematic quantities areshown in Figure 1. For compactness we write the cross section as

d3σ

dQ2dpmdφpqdΩedΩp

= σL + σT + σLT cos φpq + σTT cos 2φpq + hσLT ′ sin φpq (3)

where the σi’s are the partial cross sections for each component. Consider the helicityasymmetry [10]

Ah(Q2, pm, φpq) =

σ+ − σ−

σ+ + σ−(4)

where the superscripts refer to the helicity of the electron beam and pm is the missingmomentum defined as

~pm = ~q − ~pp (5)

45


where ~q is the momentum transfer and ~pp is the measured proton momentum. If we pickφpq = 90 the asymmetry becomes (see Section 7.1)

Ah(Q2, pm, φpq = 90) = Afa

LT ′ =σ+

90 − σ−90σ+

90 + σ−90=

σLT ′

σL + σT − σTT

. (6)

where we call Afa

LT ′ the fixed-angle asymmetry. This form of the asymmetry is used inprevious experiments discussed below and is often called simply ALT ′. However, we haveused a slightly different form of the helicity asymmetry that enables us to take full advantageof the large acceptance of CLAS. It is the following (see Section 7.1).

A′

LT =σLT ′

σL + σT

(7)

The difference between Equations 6 and 7 is only in the subtraction of σTT in the denominatorof Equation 6 which is usually small. Within the uncertainties in our measurement the twoare identical.

3 Previous Measurements

Existing measurements of σLT ′ and its associated amplitude fLT ′ are sparse. For quasi-elastickinematics they have only been made at Q2 = 0.22 (GeV/c)2 and Q2 = 0.13 (GeV/c)2 atBates [9, 11, 12]. An example of the results is shown in Figure 2. The bottom panelshows the dependence of the amplitude fLT ′ on θpq the angle between the transferred 3-momentum ~q and ~pp the ejected proton momentum (bottom scale) or the magnitude of themissing momentum ~pm (top scale). The middle panel shows the results for the asymmetryALT ′ which is equivalent to fixed-angle asymmetry Afa

LT ′ in Equation 6. The top panelshows Σ which is is the non-beam-helicity-dependent part of the cross section. That workdemonstrated the feasibility of out-of-plane measurements and the calculations show thatrelativity already plays a significant role even at this low value of Q2 [5]. The effect offinal-state interactions is dramatic and can be seen in the bottom and middle panels ofFigure 1. The double-dot-dashed lines at fLT ′ = 0 and ALT ′ = 0 are from a Plane-WaveBorn Approximation calculation which does not include FSI. In general, Afa

LT ′ and A′

LT arenon-zero only in the presence of final-state interactions. The other calculation (solid curve)does include FSI and is significantly different from zero in the bottom and middle panelsof Figure 2. Unfortunately, the large uncertainties of the measurements prevent one fromdistinguishing among different phenomena like relativistic corrections, MEC, FSI, and IC orbetween different potentials. The success of the Bates work at low Q2 is an invitation toextend the measurements with CLAS.

4 Experimental Details

4.1 Data Sets

We are investigating the d(~e, e′p)n reaction by detecting the scattered electron and theejected proton with CLAS and using missing mass to identify the neutron. The data were

46


Figure 2: Measurements of fLT ′ and its associated cross section and asymmetry from Refer-ence [9] at Q2 = 0.13 (GeV/c)2.

collected during the E5 run period (spring, 2000) and consist of runs 24020–24588 at twobeam energies: 2.56 GeV and 4.23 GeV. About 2.3 billion triggers were collected under threesets of run conditions shown in Table 1 where normal polarity refers to inbending electronsand reversed polarity is for outbending electrons. We focus most of our attention on the two

Data Set Beam Energy (GeV) Torus Current (A) Polarity1 4.23 3375 normal2 2.56 2250 normal3 2.56 2250 reversed

Table 1: Running conditions for E5.

2.6-GeV data sets because the statistics for A′

LT are limited at 4.2 GeV.

4.2 Dual-Cell Target

The target for each data set was dual, co-linear, liquid hydrogen-deuterium cell which enabledus to collect calibration data simultaneously with production data. We used the proton targetto check the beam helicity sign, measure the beam charge asymmetry, and to determine

47


momentum corrections. The deuterium cell was 6 cm long and located upstream from thenominal CLAS target position. The hydrogen cell was also 6 cm long and centered on thenominal CLAS target position. There were 3 cm between the cells. Figure 3 is an engineeringdrawing of the target. The cells were constructed of aluminum with thin (20 micron) windows

Figure 3: An engineering drawing of the E5 dual-cell cryotarget.

on each end. Figure 4 shows the z-component of the electron (black) and proton (red) vertexpositions and the clear separation of the deuterium and hydrogen cells.

Figure 4: Position of the electron and proton vertex along the beamline for the e5 target forep events.

48


5 Event Selection of D(~e, e′p)n

5.1 Event Reconstruction

The reconstruction of the E5 data is described in [13]. We summarize that material here. Theanalysis of the E5 data was performed with a modified version of the CLAS reconstructionsoftware, derived from the ‘release-4-3’ code. The detectors were calibrated (EC timing andenergy, SC timing and energy, DC drift time to drift distance conversion) using the standardpackages. Because of the unique, dual-cell target, a set of special ‘road files’ generated for theE5 target and magnetic field configurations was used as an input template to the RECSISevent reconstruction code. RECSIS returned particle charge, momentum, and position valuesfor charged particles in the drift chamber. Details of the tracking code can be found in [14].Information from other detector packages, such as hit locations and times in the EC and SC,were matched to the DC tracks by the SEB package. The SEB package was modified to writesummary information to a MySQL database after processing each file. The reconstructedevents were written to BOS files, along with some of the raw event information, to the JLabtape silo.

5.2 Run Selection

Run files were selected for analysis by examining the ratio of protons to electrons originatingin the hydrogen target cell, and the ratio of time-based tracks to hit-based tracks. The cutswere selected to remove files in which either of these quantities differed too much from theaverage. See [13]. Figure 5 shows a sample of those two ratios for the 2.6 GeV, normal-torus-polarity data sets from Ref [13].

Figure 5: The ratio of the number of protons to the number of electrons for events originatingin the hydrogen target versus run number is shown in the left-hand-side panel. The data arefrom the 2.6-GeV normal-torus-polarity data set. The cuts applied are shown in red. Theratio of the number of time-based tracks to the number of hit-based tracks versus run numberis shown in the right-hand-side panel. The data are from the 2.6-GeV, normal-torus-polaritydata set. The cuts applied are shown in red. Both plots are from Ref [13].

49


5.3 Electron Identification

Electrons were identified as negative tracks from the EVNT bank (produced by SEB) in co-incidence with hits in the Cerenkov counters, the TOF scintillators, and the electromagneticcalorimeter. A cut on the number of photo-electrons of greater than 2.5 from the Cerenkovcounters was imposed to reduce the number of negative pions mis-identified as electrons[15]. The deuterium target was selected by requiring the electron vertex vz lie in the range−11.5 cm < vz < −8.0 cm. See Figure 4. A summary of the criteria for identifying electronsis shown in Table 1. More details can be found in [13].

Description of cut Parameters

Good CC, EC, SC status cc > 0, ec > 0, sc > 0, stat > 0

Energy-momentum match 0.325pe − 0.13 < Etotal < 0.325pe + 0.06

Reject pions ec ei ≥ 0.100 and nphe ≥ 25

EC track coordinates fiducial |dc ysc| ≤ 165(dc xsc− 80)/280

EC fiducial No tracks within 10 cm of the end of a strip

Egiyan threshold cut pe ≥ (214 + 2.47 · ec threshold) · 0.001

Quasi-elastic scattering 0.89 GeV ≤ W ≤ 0.99 GeV

Select deuterium target −11.5 cm < vz < −8.0 cm

Table 2: Electron Identification Parameters.

We have studied the D(~e, e′p)n reaction in quasielastic kinematics. To select thosekinematics for each CLAS torus polarity setting we first calculated W , the mass of theresidual hadron left behind by the scattered electron. The W spectrum for the 2.6-GeV,normal torus polarity data is shown in the left-hand panel of Figure 6. The quasielasticpeak centered at W equal to the nucleon mass is clearly visible. To select the W range toisolate quasielastic kinematics, we studied the asymmetry A′

LT for different regions of W byapplying cuts represented by the different colors as shown in the right-hand panel of Figure6. The central-W asymmetry (0.89 GeV < W < 0.99 GeV) shows a prominent dip aroundpm ≈ 0.25 GeV/c and goes to zero for pm = 0. The statistics for the W regions above(blue points in the right-hand panel of Figure 6 and 1.04 GeV < W < 1.14 GeV) and below(red points, 0.70 GeV < W < 0.89 GeV) are limited, but the results are consistent withthe 0.25 − GeV/c dip disappearing. Notice also for the high-W region near pm = 0 theuncertainty in the asymmetry is large which hints at the presence of non-quasielastic effects.For higher-lying, residual masses above the quasielastic peak, events where the proton comesout in the same direction as ~q become increasingly rare so we expect few events and a large,statistical uncertainty. See Section 7.3.1 for a discussion on the behavior of A′

LT at pm = 0.The cut used to select quasielastic events (0.89 GeV < W < 0.99 GeV) is shown by the redlines in the left-hand panel of Figure 6. The results for the same analysis of the 2.6-GeV,reverse torus polarity data are shown in Figure 7. These data show similar behavior for A′

LT ;a dip at pm ≈ 0.25 GeV/c in the central W region which disappears outside this W range.At pm = 0 and high-W there are few events. The asymmetry here is off scale (0.9 ± 0.7)with a very large uncertainty because of the small number of events. The dip in A′

LT isclearly connected to quasielastic scattering and the high and low-W regions show different

50


2009-11-27 11:05:49

W (GeV)0.7 0.8 0.9 1 1.1 1.2 1.3

Cou

nts

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

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polaritye-p events

2009-11-27 11:07:56 (GeV/c)

mp

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

LTA

’

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08 2.6 GeV, normal torus polarityBlack - 0.89 < W < 0.99 GeVRed - 0.70 < W < 0.89 GeVBlue - 1.04 < W < 1.14 GeV

Figure 6: Spectrum of the residual mass W for the 2.6-GeV, normal polarity data (left-handpanel) and the helicity asymmetry A′

LT for W ranges at the quasielastic peak and the regionsabove and below the peak.

2009-11-27 14:20:08

W (GeV)0.7 0.8 0.9 1 1.1 1.2 1.3

Cou

nts

0

50

100

150

200

250

300

350

400

450

310×

2.6 GeV

Reversed toruspolarity

e-p events

2009-11-27 14:08:47 (GeV/c)

mp

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

LTA

’

-0.04

-0.02

0

0.02

0.04

0.06

2.6 GeV, reversed torus polarityBlack - 0.89 < W < 0.99 GeVRed - 0.70 < W < 0.89 GeVBlue - 1.04 < W < 1.14 GeV

Figure 7: Spectrum of W for the 2.6-GeV, reversed torus polarity data set and the helicityasymmetry A′

LT for different W regions.

behavior so we have focused on this central W region. The position of the cut used forthese data is shown by the red lines in the left-hand panel of figure 7 (same range as thenormal-torus-polarity data).

We generated fiducial cuts for the electron sample to restrict the acceptance to regionswhere is is expected to be well-behaved. The azimuthal part of the electron solid angleis determined by the range of the electron’s azimuthal angle φe in each sector. These φe

51


limits are, in turn, defined by the drop in efficiency in the optical collection of the Cerenkovdetector mirrors. See Figure 8 for an example of the φe dependence. To focus our analy-

Figure 8: Electron azimuthal dependence for sector 3, 2.6-GeV, normal polarity run. Theelectron’s polar angle θe is written on each plot. The black curve is the result a fit to atrapezoidal function described in Appendix A.

sis on the regions of uniform proton acceptance we have largely followed the technique ofD.Protopopescu, et al. in [16] and summarize the method in Appendix A. One of the benefitsof the procedure described below is to make the fiducial cuts smoothly varying functions ofparticle momentum and position and reduce the chances of experimental artifacts appearingin the analysis. An example of the final CLAS electron acceptance is shown in Figure 9 forthe 4.2-GeV data set.

5.4 Proton Identification

Proton candidates were selected from positively-charged tracks in the EVNT bank in co-incidence with a good electron. An additional mass cut 0.90 GeV < mp < 1.05 GeV wasrequired where mp is the proton mass derived from tracking and two more cuts were appliedto the electron and proton track vertices. The proton vertex vz(p) was required to lie in thesame range as the electron −11.5 cm < vz(p) < −8.0 cm (see Figure 4) and the electron andproton vertices were required to be within 1.5 cm on one another |vz(e)− vz(p)| ≤ 1.5 cm.

Proton fiducial cuts are necessary to eliminate e−p coincidences where the proton is ina region near the cryostat holding the wire coils used to generate the CLAS magnetic field.The field in these regions is sensitive to the distance from the coils and not as well-known asthe field in the more central region between the coils. We have largely followed the methoddescribed in [17] which is analogous in approach to the technique used to determine theelectron fiducials. The details of the method are described in Appendix C and the finalhadron acceptance is shown in Figure 10.

52


Figure 9: CLAS acceptance for electrons at E = 4.2 GeV with fiducial cuts turned on (redpoints) and off (blue points).

Figure 10: Final hadron sample.

5.5 Neutron Identification

Neutrons were identified in e − p coincident events using the missing mass method. Figure11 shows the square of the missing mass (MM2) versus the missing momentum pm

~pm = ~q − ~pp (8)

53


where ~pp is the ejected proton momentum and ~q is the 3-momentum transfer. In the plane-wave impulse approximation this missing momentum is the opposite of the initial momentumof the proton. Figure 11 shows the distributions for both sets of running conditions. The

Figure 11: Missing mass versus pm for eD → e′pX for 2.6 GeV, reversed torus polarity (leftpanel), 2.6 GeV, normal torus polarity (right panel.

ridge at the square of the missing mass of the neutron (0.88 GeV2) is clearly visible, wellseparated from higher MM2 events, and extends to pm = 0.7 GeV.

To isolate neutrons we placed a cut on the square of the missing mass (MM2). TheMM2 distribution for the 2.6-GeV, normal-torus-polarity data set is shown in the left-handpanel of Figure 12. The neutron is clearly visible. We explored the dependence of A′

LT onthe position and width of this cut. The results for the 2.6-GeV, normal field data are shownin in the right-hand panel of Fig 12. It shows A′

LT as a function of missing momentum pm

in three regions: below the neutron peak (red, open boxes), centered on the neutron peak(black, filled boxes), and above the neutron peak (blue, filled circles). There is a clear dip inA′

LT for the MM2 range centered on the neutron peak. The statistics in the ranges aboveand below the neutron peak are limited, but the results are consistent with the 0.25-GeV/cdip disappearing. The final cut (0.84 GeV2 < MM2 < 0.92 GeV2) is shown as the red linesin Figure 12.

The results for the 2.6-GeV, reversed-torus-polarity data are shown in Figure 13. TheMM2 distribution is shown in the left-hand panel along with vertical lines marking the finalfit. As with the normal-torus-polarity data, there is a large dip in the central MM2 regionof A′

LT in the right-hand panel which goes away (within the rather poor statistics) in theMM2 regions above and below the neutron peak.

6 Corrections

6.1 Momentum Corrections

Misalignments of the CLAS drift chambers and uncertainties in the magnetic field producedby the CLAS torus can lead to inaccuracies in measuring the momentum of charged particles.

54


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(GeV/c)m

p0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

LTA

’

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.082.6 GeV, normal torus polarity

2 < 0.92 GeV2Black - 0.84 < MM2 < 0.84 GeV2Red - 0.70 < MM

2 < 1.1 GeV2Blue - 0.92 < MM

Figure 12: The distribution of the square of the missing mass is shown in the left-hand panelfor the 2.6-GeV, normal-torus-polarity data. The results for ALT ′ for the 2.6-GeV, normaltorus polarity data for different ranges in MM2 are shown in the right-hand panel. The finalcut used is shown as the red lines in the left-hand panel.

2 (GeV2XM

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

Cou

nts

0

100

200

300

400

500

310×2.6 GeVReversed torus

polarity, e’p)XeH(2

2009-11-27 20:05:37

(GeV/c)m

p0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

LTA

’

-0.04

-0.02

0

0.02

0.04

0.062.6 GeV, reversed torus polarity

2 < 0.91 GeV2Black - 0.83 < MM2 < 0.83 GeV2Green - 0.70 < MM

2 < 1.1 GeV2Blue - 0.91 < MM

Figure 13: The distribution of the square of the missing mass is shown in the left-hand panelfor the 2.6-GeV, reversed-torus-polarity data. The results for ALT ′ for the 2.6-GeV, reversedtorus polarity data for different ranges in MM2 are shown in the right-hand panel. The finalcut used is shown as the red lines in the left-hand panel

To correct for these inaccuracies, we used the method described by J.Lachniet in Ref [13] andpioneered by Volker Burkert. This technique relies on elastic scattering from the proton inthe E5, dual target. For elastically scattered electrons we determine θe for the electron andcalculate W 2, the square of the mass of the residual object, a proton here. The differencebetween W 2 and the square of the proton mass is minimized to determine a correction factor

55


Sector Uncorrected (GeV2) Corrected(Lachniet) (GeV2)〈W 2〉 ∆(W 2) 〈W 2〉 ∆(W 2)

1 0.866 0.023 0.879 0.0282 0.853 0.027 0.875 0.0323 0.829 0.043 0.866 0.0184 0.860 0.027 0.877 0.0275 0.861 0.025 0.877 0.0246 0.864 0.025 0.876 0.029

Average 0.855 0.029 0.875 0.027

Table 3: Effect of momentum corrections on the average value and width of W 2 peak for epelastic scattering for the 2.6-GeV, reversed-torus-polarity data.

to the electron momentum as a function of the electron θe and phie and for each data set.The correction factor is a function of θ and φ and for each data set.

The effect of the momentum corrections on the 2.6-GeV, reversed-torus-polarity data onthe centroid and width of the proton peak in the W 2 spectrum is shown in Table 3. The firstfeature of Table 3 to notice is the E5 data are well calibrated to start. The uncorrected protonpeak is, on average, 3% below the expected value. Applying the momentum corrections, theproton peak moves to 0.6% below the expected value. The Lachniet method reduces thewidth of the proton peak by 7%.

The effect of the momentum corrections on the 2.6-GeV, normal-torus-polarity dataon the centroid and width of the proton peak in the W 2 spectrum is shown in Table 4.Again, the E5 data is well calibrated; the uncorrected proton peak is only about 1% below


1 0.870 0.034 0.879 0.0282 0.839 0.045 0.877 0.0273 0.887 0.033 0.881 0.0284 0.872 0.030 0.879 0.0285 0.874 0.031 0.879 0.0296 0.889 0.029 0.881 0.030

Average 0.871 0.034 0.879 0.028

Table 4: Effect of momentum corrections on the average value and width of W 2 peak for epelastic scattering for the 2.6-GeV, normal-torus-polarity data.

the expected value. The Lachniet method improves the agreement with the proton mass to0.2% and reduces the width of the distribution by about 18%.

For completeness we show the results for the 4.2-GeV data set in Table 5. As we showlater, we found the statistical uncertainty on the fifth structure function asymmetry ALT ′ ispoor. The E5 data is well calibrated; the uncorrected proton peak is only about 2% belowthe expected value. The Lachniet method improves the agreement with the proton mass to0.8% and reduces the width of the distribution by 25%.

To conclude, we find the E5 data set is well calibrated at the start. The Lachniet method

56



1 0.849 0.048 0.874 0.0332 0.832 0.053 0.865 0.0333 0.893 0.037 0.877 0.0344 0.858 0.041 0.873 0.0305 0.864 0.042 0.872 0.0306 0.885 0.035 0.875 0.031

Average 0.863 0.043 0.873 0.032

Table 5: Effect of momentum corrections on the average value and width of W 2 peak for epelastic scattering for the 4.2-GeV, normal-torus-polarity data.

reduces the discrepancy with the proton mass in the W 2 spectrum from 1-3% depending onwhich data set is used down to 0.8% or less. The width of the proton peak in the W 2

distribution is reduced by 7-25%.

6.2 Beam Charge Asymmetry

To measure the helicity-dependent charge asymmetry of the electron beam we used the ratioof inclusive, elastic ep scattering from the E5 proton target to measure the quantity

AQ =N+

N−(9)

where N± is the number of elastic scattering events from the proton target for each helicity.The inclusive cross section has no helicity dependence and is more reliable than the Faradaycup readings [18]. All electron selection cuts were applied except the fiducial cuts. We showlater that our results for ALT ′ are largely independent of applying the electron or protonfiducial cuts. We selected elastic events by requiring that 0.92 GeV < W < 1.0 GeV andtook the ratio of the results for the different beam helicity states. The results are shown inTable 6. The half-wave plate which determines the beam helicity was fixed during the E5

Data set AQ

2.6-GeV, reversed torus polarity 0.9936± 0.00072.6-GeV, normal torus polarity 0.9954± 0.00074.2-GeV, normal torus polarity 0.9987± 0.0009

Table 6: Beam charge asymmetries for different helicity states for the E4 data set.

run period and, as expected, no shifts were observed in the helicity during the run.

6.3 Beam Polarization

The fraction of the beam polarization was monitored during the E5 run using the Hall BMoeller polarimeter. The polarization is measured by observing asymmetries in the yields

57


2 = 0.15-2.0 GeV2

0.0017, Q±>= -0.0154 LT<A’

2=0.4-0.7 GeV2

0.0009, Q±>= -0.0158 LT<A’

= 0.8ν/2χ 0.0019, ± from fit: -0.0150 LTA’

Run Number

24520 24530 24540 24550 24560 24570 24580

LTA

’

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

Run Number

24520 24530 24540 24550 24560 24570 24580

LTA

’

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

2 = 0.15-2.0 GeV2

0.0017, Q±>= -0.0154 LT<A’

2=0.4-0.7 GeV2

0.0009, Q±>= -0.0158 LT<A’

= 0.8ν/2χ 0.0019, ± from fit: -0.0150 LTA’(this work)

(Joo and Smith)

Figure 14: Comparison of helicity asymmetry for p(~e, e′p)π0 measured previously in CLAS(left-hand panel) by Joo and Smith ([19]) and during the E5 run (right-hand panel)

of beam electrons scattered from electrons in a polarized iron target with polarization com-ponents parallel and anti-parallel to the beam direction. This method was used seven timesduring the E5 run and an average polarization Pe = 0.736± 0.017 was obtained.

To check the sign of the beam helicity we extracted the helicity asymmetry ALT ′ fromthe p(~e, e′p)π0 reaction from the proton target. This reaction has a large asymmetry andhas been measured in CLAS [19] so it serves as a clear test of understanding of the sign ofthe helicity. The results are shown in Figure 14. Our results agree with the ones from Jooand Smith in sign and magnitude.

6.4 Radiative Corrections

7 Experiment Results

7.1 Extracting Asymmetries

In this section we discuss in more detail the method for extracting the asymmetry ALT ′

discussed in the Section 1. The method we use is based on measuring weighted moments ofthe data to take full advantage of the acceptance of CLAS. Recall that we wrote the fivefolddifferential cross section for the quasielastic D(~e, e′p)n reaction as

d3σ

dQ2dpmdφpqdΩedΩp

= σ± = σL + σT + σLT cos φpq + σTT cos 2φpq + hσLT ′ sin φpq (10)

where the superscript on σ± refers to the helicity, φpq is defined in Figure 1, and the σi’sare the partial cross sections for each component. First, we want to make contact with theform of the asymmetry used in Ref [9, 12, 11, 20] and shown in Figure 2. Recall the helicityasymmetry.

Ah(Q2, pm, φpq) =

σ+ − σ−

σ+ + σ−(11)

58


Substituting Equation 10 into Equation 7.1 one obtains the following result.

Ah(Q2, pm, φpq) =

σLT ′ sin φpq

σL + σT + σLT cosφpq + σTT cos 2φpq

(12)

If we then pick φpq = 90 we obtain the fixed angle asymmetry discussed in Section 2.

Ah(Q2, pm, φpq = 90) = Afa

LT ′ =σ+

90 − σ−90σ+

90 + σ−90=

σLT ′

σL + σT − σTT

. (13)

This is the form of the asymmetry used in Ref [9, 12, 11, 20] and shown as ALT ′ in Figure2. It depends on measurements at a few select angles. With CLAS we want to take fulladvantage of the large acceptance so we take a different approach.

Consider taking the sin φpq moment of the distribution for the two different choices ofhelicity.

〈sin φpq〉± =

∫

2π

0σ± sin φpqdφpq∫

2π

0σ±dφpq

(14)

=

∫

2π

0(σL + σT + σLT cos φpq + σTT cos 2φpq + hσLT ′ sin φpq) sin φpqdφpq∫

2π

0(σL + σT + σLT cos φpq + σTT cos 2φpq + hσLT ′ sin φpq)dφpq

(15)

By the orthogonality of sines and cosines all of the terms disappear except for the σLT ′ termin the numerator and the φpq-independent terms in the denominator. The result is

〈sin φpq〉± =±σLT ′

2(σL + σT )≈ ±

AfaLT ′

2(16)

where we have used h = ±1, and made the approximation that σTT is small compared to σL

or σT as has been observed [11, 21, 22]. We now redefine the asymmetry A′

LT in the followingway. where the denominator differs from the one in Refs [9, 12, 11, 20] by neglecting theadditional σTT term. For practical purposes as we will show later, there is no significantdifference between the two definitions. To extract A′

LT we will use the sin φpq-weightedmoments of the data corrected for the beam polarization Pe and beam charge asymmetryAQ so

ALT ′ =1

PeAQ

(

〈sin φpq〉meas+ − 〈sin φpq〉

meas−

)

(17)

and 〈sin φpq〉meas±

is defined by Equation 14 and subject to the cuts described in Section 5.To determine 〈sin φpq〉± from the data for a given bin in Q2 and pm or θcm

pq one uses

〈sin φpq〉± =1

N±

N±∑

i=1

sin φi (18)

where the sum is over the φpq distribution of the data, i’s refer to individual events, and N±

refers to the number of events of each helicity.We now discuss an interesting bonus of using the sin φpq-weighted moments of the data

to reduce acceptance effects. In Equation 16, σLT ′ depends on Q2, pm or θpq, but as a function

59


h=+1

h=-1

pm HGeVL

XsinΦ

pq\

Figure 15: Schematic drawing showing the possible results for 〈sin φpq〉± with no acceptance

effects.

of pm one expects to see behavior like that shown in Figure 15 below. The curve for onehelicity is the opposite of the curve for the other helicity. However, acceptance effects candistort the expected distributions of Equation 16 if the CLAS acceptance has a componentthat varies as sin φpq. In such a case this experimental artifact will survive the integrationin Equation 15 when it is multiplying the constant portion of the cross section (σL and σT

terms in Equation 15). Such an acceptance effect is additive and shifts 〈sin φpq〉± up or down,so

〈sin φpq〉meas±

= ±σLT ′

2(σL + σT )+ α (19)

where α is the additive acceptance correction. See Appendix E for more details. If one hasmeasured this sin φpq moment for each helicity then the results can be combined so

〈sin φpq〉meas+ − 〈sin φpq〉

meas−

=σLT ′

σL + σT

(20)

and〈sin φpq〉

meas+ + 〈sin φpq〉

meas−

2= α . (21)

The asymmetry ALT ′ is extracted with reduced sensitivity to acceptance corrections and thesin φpq-dependent acceptance effects have been measured from the data. This technique hasbeen used by others for the p(~e, e′π+)n and p(~e, e′p)π0 reactions [23, 19].

7.2 Results for Asymmetries

In Fig 16 we show our results for the asymmetry ALT ′ for all three sets of running conditionsfrom the E5 running period. The data are integrated over the full Q2 range for each setof running conditions to get adequate statistics so we have included the Q2 distribution inparallel with the asymmetry for each data set. The 2.6-GeV, reversed torus field data showa very clear dip to ALT ′ ≈ −0.03 at pm near 0.25 GeV followed by a rise back to or possibleabove zero at larger missing momentum. The same general features are seen in the 2.6-GeV,normal torus field data at higher Q2 with a deeper dip in the same pm region. The 4.2-GeV

60


2009-10-22 22:56:58

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

LTA

’

-0.1

-0.05

0

0.05

0.1E=2.6 GeVNormal torus polarity

(GeV/c)m

p0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

LTA

’

-0.4

-0.2

0

0.2

0.4 E=4.2 GeVNormal torus polarity

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

LTA

’

-0.04

-0.02

0

0.02

0.04

,e’p)neD(

E=2.6 GeVReversed torus polarity

2008-09-20 22:42:23

0 0.5 1 1.5 2 2.5 3 3.5 4)3

10

×C

ount

s (

50

100

150

200

250

300

10×

E=2.6 GeVNormal torus polarity

2 (GeV/c)2Q0 0.5 1 1.5 2 2.5 3 3.5 4

Cou

nts

05000

1000015000200002500030000350004000045000 E=4.2 GeV

Normal torus polarity

0 0.5 1 1.5 2 2.5 3 3.5 4

Cou

nts

5000

1000015000

200002500030000

3500040000

D(e ,e’)X

E=2.6 GeVReversed torus polarity

Figure 16: The left-hand column shows the results for A′

LT for the 2.6-GeV, reversed toruspolarity data (top panel), the 2.6-GeV, normal torus polarity data (middle panel), and the4.2-GeV, normal torus polarity data (bottom panel). The right-hand column shows the Q2

spectrum for each data set. The asymmetries were summed over all Q2. The uncertaintiesare statistical only.

has large statistical uncertainties over most of the pm range and so there are few conclusionsto be drawn from these data.

In Figure 17 we show our results for the background asymmetry α defined in Equation21. The background asymmetries are about the same size as the magnitude of the features inthe ALT ′ distributions which emphasizes the importance of the use of the helicity asymmetry.It enables us to eliminate this significant background in a clean way.

7.3 Consistency Checks of the Analysis

We now present the results of a series of consistency checks of our results to test our analysisalgorithms.

61


2008-09-20 23:09:41

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

LTA

’

-0.15-0.1

-0.050

0.050.1

0.15 E=2.6 GeV, Normal torus polarity

(GeV/c)m

p0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

LTA

’

-0.4

-0.2

0

0.2

0.4 E=4.2 GeV, Normal torus polarity

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7LT

A’

-0.04

-0.02

0

0.02

0.04

,e’p)neD(

E=2.6 GeV, Reversed torus polarity

Figure 17: The background asymmetry α for the 2.6-GeV, reversed torus polarity data(top panel), the 2.6-GeV, normal torus polarity data (middle panel), and the 4.2-GeV,normal torus polarity data (bottom panel). The asymmetries were summed over all Q2. Theuncertainties are statistical only.

7.3.1 Asymmetry at pm ≈ 0

The first one we study is the behavior of A′

LT at small missing momentum or small θpq. Weexpect the asymmetry to go to zero in this region. To understand this consider A′

LT at somenonzero pm. For fixed Q2, W 2, and pm, the only kinematic dependence is on sin φpq and thisdependence will disappear if one averages over all φpq. Consider now A′

LT at small pm. Thesinusoidal dependence is now compressed into a small cone around the 3-momentum transfer.In the limit of small pm and the finite resolution of our detector, we will be averaging overthe sin φpq part which will go to zero. Since we are taking the difference between 〈sin φpq〉for different beam helicities, the low pm behavior is a good test of the accuracy of the beamcharge asymmetry.

Our data are consistent with this behavior. See Figure 16 and focus on the first binin each distribution of A′

LT (left-hand column). In Table 7 we list the results in that firstbin. All are consistent with zero within the statistical uncertainties. To study this issue

62


Data Set A′

LT

2.6 GeV, reversed polarity 0.0008± 0.00142.6 GeV, normal polarity −0.0040± 0.00434.2 GeV, normal polarity −0.003± 0.019

Table 7: Asymmetry in the first pm bin for each data set. In each case this bin covers therange pm = 0.0− 0.05 GeV.

more carefully we studied A′

LT in finer steps at small pm for the 2.6-GeV, normal toruspolarity data set. The results are shown in Figure 18. At the smallest pm, we have limited

(GeV/c)m

p0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03 2.56 GeV, normal polarity2all Q

0.92 < W < 1.0 GeV

’LTA

Figure 18:

statistics, but clearly the small pm behavior is consistent with zero within the experimentaluncertainties. More data points are at negative asymmetry than positive, but recall the fulldistribution for A′

LT is going negative at higher pm. Within the experimental uncertaintiesthe asymmetry A′

LT shows the correct behavior near pm = 0.

7.3.2 Extracting A′

LT by Fitting the φpq Dependence

We investigated another method for extracting A′

LT that takes advantage of the large accep-tance of CLAS. Recall the expression for Ah(Q

2, pm, φpq) (see Equation 12). The numeratorin Equation 12 is proportional to sin(φpq) and the denominator is approximately constantas long as σLT and σTT are small. If one forms the ratio of different helicities

A(Q2, pm, φpq) =σ+ − σ−

σ+ + σ−=

N+ −N−/AQ

N+ + N−/AQ

=σ′LT sin φpq

σL + σT + σLT cosφpq + σTT cos 2φpq

(22)

where AQ is the beam charge asymmetry, then the distribution should have a sinusoidaldependence on φ if σLT and σTT are small relative to σT and σL. We have calculated

63


this ratio and results are shown in Figure 19 for four different angle bins in the rangeQ2 = 0.8− 1.0 (GeV/c)2 for the 2.6-GeV, normal torus polarity data set. The distributions

-150 -100 -50 0 50 100 150-0.1

-0.05

0

0.05

0.1 / ndf 2χ 6.335 / 8

p0 0.007435± 0.01406

o-10o = 0cmpqθ, pqφ) vs. -+N

+)/(N--N

+(N

/ ndf 2χ 6.335 / 8

p0 0.007435± 0.01406

-150 -100 -50 0 50 100 150-0.3

-0.2

-0.1

0

0.1

0.2

0.3 / ndf 2χ 12.4 / 8

p0 0.0154± -0.002363


+)/(N--N

+(N

/ ndf 2χ 12.4 / 8

p0 0.0154± -0.002363

-150 -100 -50 0 50 100 150-0.3

-0.2

-0.1

0

0.1

0.2

0.3

/ ndf 2χ 10.49 / 8p0 0.03903± -0.112


+)/(N--N

+(N

/ ndf 2χ 10.49 / 8p0 0.03903± -0.112

-150 -100 -50 0 50 100 150-0.3

-0.2

-0.1

0

0.1

0.2

0.3 / ndf 2χ 7.363 / 8p0 0.06975± 0.01035


+)/(N--N

+(N

/ ndf 2χ 7.363 / 8p0 0.06975± 0.01035

Figure 19: Results for φ dependence of A′

LT using the helicity ratio technique.

were fitted with a sine curve and the results are shown on the figure. The fits all haveacceptable reduced χ2. We also tried fitting a more complex function that included thecos φpq and cos 2φpq terms in the denominator of Equation 12. We found the contributionsfrom σLT and σTT were consistent with zero and there was no significant improvement tothe fit.

We compared the two different methods for measuring A′

LT and show the results inFigure 20. The top panel shows the angular distribution in θcm

pq measured using the sin φpq

moments of the distribution and the lower panel is from the fits to A(Q2, θpq, φpq). The resultsin Figure 20 are for the range Q2 = 0.8− 1.0 (GeV/c)2. The two panels are very consistentwith each other. The values of A′

LT in each angle bin agree for both methods as well as thesize of the uncertainties in each angle bin. It is worth noting how A′

LT goes from small andpositive for θcm

pq = 0 − 10 to large and negative for θ′pq = 20 − 30. This is clearly seenin the shapes of the φpq distributions in Figure 19 in the upper-left and lower-left panels.We expect the sin φpq moments and the A(φpq) methods to be consistent; they representthe same quantity extracted from the same data set. We conclude that these methods areconsistent and the sin φpq moments analysis and the fit to A(φpq) are equivalent methods.We have used the sin φpq moments analysis throughout this analysis note.

7.3.3 Effect of Fiducial Cuts

We studied the effect of the electron and proton fiducial cuts on A′

LT . In our definition of theasymmetry (Equation 17-18) we count the number of events of a particular helicity and in aparticular Q2 and pm bin weighted by sin φpq. We then divide that number by the numberof events of that helicity in the same Q2 − pm bin. Since we are using a ratio we expectthat many acceptance and efficiency effects will cancel. When we make fiducial cuts we

64


Figure 20: Comparison of A′

LT extracted using different analysis techniques. The calculationis not corrected for the CLAS acceptance.

are restricting our measurements to regions in CLAS where the acceptance is well-behaved.This is essential for measurements of cross sections, but in this measurement we can considerdropping the fiducial cuts since the acceptance corrections should cancel. Recall Equation7.3.2. Any acceptance correction to N± would cancel in the ratio since we are consideringthe same bin in Q2, pm, and φpq in both numerator and denominator. The advantage wegain by turning off the fiducial cuts is to improve our statistics. We found our fiducial cutsthrew away one-third or more of the final event total mainly due to low-Q2 events at smallscattered electron angles where the CLAS acceptance is rapidly shrinking and is not well-behaved. In Figure 21 we show A′

LT with the electron and proton fiducial cuts on and offfor the reversed-torus-polarity data. In taking the difference between A′

LT with and withoutthe fiducials cuts turned on, we cannot simply add the uncertainties in quadrature becausethe two data sets are not statistically independent (the events that lie within the fiducialcuts are in both samples). Instead we re-analyzed the data and divided the sample intotwo parts: (1) events that pass all other cuts and lie within the electron and proton fiducialregion and (2) events that pass all other cuts and lie outside the electron and proton fiducialcuts. In this way we can recover the ’no-fiducial-cut’ sample and still have two statisticallyindependent data sets. Uncertainties can then be calculated using standard methods and areshown in the right-hand panel of Fig 21. The uncertainties on the difference are still largeand the weighted average is negative. However, the average is small and it is only 2σ away

65


2009-10-22 23:32:59 (GeV/c)

mp

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

LTA

’

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04 2.6 GeVReversed torus polarityBlue - No fiducial cutsRed - Fiducial cuts on

’LTA

2009-10-22 23:38:29 (GeV/c)

mp

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

LT A

’∆

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.042.6 GeVReversed torus polarity

0.001±> = -0.002 LT A’∆<

Figure 21: The results for A′

LT for the 2.6-GeV, reversed torus polarity data with electronand proton fiducial cuts on and off are shown in the left-hand panel. The difference betweenA′

LT with the electron and proton fiducial cuts on and off is shown in the right-hand panel.

from zero which is not compelling evidence that the fiducial cuts have a significant effect.For the normal torus polarity data, the results are shown in Fig 22. The analysis is

2009-10-06 13:28:14 (GeV/c)

mp

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

LTA

’

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.082.6 GeVNormal torus polarity

Red - Fiducial cuts onBlue - No fiducial cuts

2009-10-06 13:35:41

(GeV/c)m

p0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

LT A

’∆

-0.08

-0.06

-0.04

-0.02

0

0.02

0.042.6 GeVNormal torus polarity

0.0024±> = -0.0015 LT A’∆<

Figure 22: The results for A′

LT for the 2.6-GeV, normal torus polarity data with electronand proton fiducial cuts on and off are shown in the left-hand panel. The difference betweenA′

LT with the electron and proton fiducial cuts on and off is shown in the right-hand panel.

the same as above. Here the difference between A′

LT with the fiducial cuts off is clearly notstatistically significant. We will show these results for A′

LT with the fiducial cuts turned offin the rest of this analysis note since they have better statistics.

66


7.3.4 Monte Carlo Simulations

We have tested our analysis codes in simulation using GSIM. We started with the eventgenerator QUEEG [13] which includes elastic scattering and the effect of the Fermi motionof the nucleons in deuterium. The code is described in Appendix F. We modified the originalcode to include a part that depended on sin φpq with an amplitude controlled by the user.The goal here is to control the size of the sin(φpq) dependent part of the D(e, e′p)n crosssection so we can compare the value used in the event generator with the final results of theanalysis chain. First, we summarize how QUEEG generates events.

1. The magnitude of the Fermi momentum of the proton is picked from the Hulthendistribution and given a random direction in the laboratory frame.

2. Transform to the (now moving) rest frame of the proton and calculate a new beamenergy for the incoming electron relative to this new rest frame of the proton.

3. The angle of the scattered electron is selected based on the cross section for elasticscattering at this new electron energy.

4. The angle of the scattered electron is transformed from the proton rest frame into thelab frame.

5. Determine the scattered electron energy for the D(e, e′p)n reaction using the knownmomentum of the neutron (i.e. the negative of the Fermi momentum of the protonchosen in step 1 above).

6. Calculate ~q (3-momentum transfer) and pp (proton 3-momentum) in the lab for thisquasi-elastic scattering.

7. Randomly select the lab azimuthal angle (φ) and rotate the 3-vectors for the momentumtransfer, proton, and scattered electron momenta.

The modifications we have made have been to change the angle φpq, the angle betweenthe scattering plane (defined by the incoming and outgoing electron 3-momenta) and thereaction plane (defined by the proton and momentum transfer 3-vectors) (see Figure 1). Thedirection of the momentum transfer, the magnitude of the proton 3-vector, and the angle θpq

are unchanged. The modifications are made to step 7 above. They are described below.

1. The missing momentum is calculated based on the known momentum of the beam,scattered electron and proton. This is the same as the neutron momentum mentionedin step 5 above.

2. The coordinates are rotated so that the z-axis is now in the direction of the 3-momentumtransfer ~q. The y-axis stays the same for this new coordinate system and the lab sys-tem.

3. A new φpq is randomly generated based on a sinusoidal distribution with an amplitudethat depends on the magnitude of the missing momentum. The amplitude is a functionof pm derived from a fit to the measured asymmetry A′

LT .

67


4. A new missing momentum 3-vector is calculated with the same magnitude as in part1, but with a different φpq using the result of part 3.

5. The coordinate system is now rotated back to the lab coordinate system with the z-axisalong the beam.

6. A new, proton 3-vector is calculated using momentum conservation and the originalbeam, target, and scattered electron momenta and the modified neutron momentum.

Figure 23 below shows the results from using this modified version of QUEEG and ex-tracting A′

LT from simulated events analyzed with the same codes used for the data analysis.The expectation is that by using a ratio to extract 〈sin φpq〉 and A′

LT it should be independentof acceptance corrections. To test this we have used fits A′ in

LT to the measured asymmetries(the red curves in each panel of Figure 23) as input for A′

LT in the simulation and thencompared the results extracted from the simulation with that original function (the black‘data’ points in Figure 23). To make a better comparison between the input to GSIM and

2009-10-02 23:27:27 (GeV/c)

mp

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

’LT

A

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.122.6 GeV, reversed torus polarity

GSIM results

Blue - bin averaged input curve

Red - input curve

2009-10-02 23:29:16 (GeV/c)

mp

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

’LT

A

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.122.6 GeV, normal torus polarity

GSIM results

Blue - bin averaged input curve

Red - input curve

Figure 23: Comparison of GSIM-simulated A′

LT with ‘true’ asymmetry used as input to thecode for 2.6-GeV, reversed torus polarity (left panel) and 2.6-GeV, normal torus polarity(right-hand panel). The red curve is the input function derived from a fit to the measuredA′

LT . The blue points calculated with the same input function and averaged over the bins.The black points are the product of the simulation.

the simulated results, we averaged the input function over the same bins used in the analysisso

〈A′ inLT 〉 =

∫

binA′ in

LT (pm)dpm

∆pm

(23)

where A′ inLT in the input function derived from a fit to the measured A′

LT . The bin-averagedasymmetries are the blue points in Figure 23. There is good agreement over the range of pm

within the statistical uncertainties of the Monte Carlo calculation between the bin-averagedinput asymmetry and the asymmetry extracted from the simulation; validating our methodand analysis codes.

68


7.3.5 Radiative Corrections

The measurements of the D(~e, e′p)n reaction in this proposed analysis are subject to radiativecorrections. We are using a version of the program EXCLURAD written by Afanasev, et al.

and modified for the D(~e, e′p)n reaction to perform those calculations [24]. This code appliesa more sophisticated method than the usual approach of Mo and Tsai or Schwinger and takesinto account the exclusive nature of our measurements [25, 26]. This work is described inAppendix H. The effect on A′

LT is small.

7.4 Systematic Uncertainties

We now consider systematic uncertainties in our extraction of A′

LT . This asymmetry can bewritten as

A′

LT = A′

LT (~f) (24)

where ~f is the set of parameters defining our extraction of A′

LT and we assume all dependon Q2. The standard propagation of uncertainties is used so

(∆A′

LT )2

=∑

i

(

∂A′

LT

∂fi

)2

(δfi)2 (25)

where the index i is over the parameter set. The primary contributions to the systematicuncertainty are shown in Table 8 along with the value of that uncertainty or the maximumvalue if it varies with Q2. Additional cuts like the electron EC fiducial cut and the Egiyanelectron momentum threshold had no effect on the final value of the helicity asymmetry.Below we discuss in more detail how we arrived at those results.

Row Quantity δA′

LT /A′

LT

1 Beam Polarization 0.017%2 Electron Track Fiducial < 0.007%3 W cut < 0.0054 MM2 cut < 0.0055 Number of Photoelectrons < 0.004%6 EC pion threshold < 0.002%7 EC sample fraction < 0.002%8 Proton mass cut < 0.0069 e− p vertex cut10 Beam charge asymmetry 0.0007%

Table 8: Main contributions to the systematic uncertainty and their values (maximum mag-nitudes for Q2-dependent quantities).

The results in rows 2-9 Table 8 were determined by changing the position of the cutby ±10% (e.g, the EC pion threshold and number of photoelectrons) or by increasing anddecreasing the width of a cut by ±10% (e.g., the W cut used to select quasielastic events

69


or the MM2 cut used to select neutrons). The final uncertainty was determined by thefollowing expression.

δA′

LT =A′

LT (1.1× fi)− A′

LT (0.9× fi)

2(26)

The results for each of the quantities as a function of Q2 are listed in Table 8 are shownin Appendix G. The systematic uncertainties for each element in Table 8 were summed inquadrature and the results are shown in Figure 24. The systematic uncertainty is everywhere

Red - Normal torus polarity

Blue - Reversed torus polarity

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.000

0.002

0.004

0.006

0.008

0.010

0.012

pm HGeVcL

DA

LT

’

Systematic uncertainty, 2.6 GeV

Figure 24: Systematic uncertainty on A′

LT as a function of Q2 for the normal torus polaritydata (red) and the reversed polarity data (blue).

less than 10−2 and is typically much less than the statistical uncertainty. This feature of thedata is shown in Figure 25 where the ratio of the systematic uncertainty to the statisticaluncertainty is plotted. At each point the statistical uncertainty is larger than the systematicone.

7.5 Final Results

Final results with statistical and systematic uncertainties are shown in Figure 26 and Figure27.

This work is supported by US Department of Energy grant DE-FG02-96ER40980 andJefferson Science Associates.

70


(GeV/c)m

p0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

’(sta

t)LT

Aδ’(s

yst)

/LT

Aδ

0

0.1

0.2

0.3

0.4

0.5

0.6

Red - Normal torus polarityBlue - Reversed torus polarity

2.6 GeV

Figure 25: Ratio of systematic uncertainty on A′

LT to statistical uncertainty as a function ofQ2 for the normal torus polarity data (red) and the reversed polarity data (blue).

References

[1] JLab Physics Advisory Committee. PAC14 Few-Body Workshop. Technical report,Jefferson Laboratory, Williamsburg, VA, 1998.

[2] S. Jeschonnek. Phys. Rev. C, 63:034609, 2001.

[3] S. Jeschonnek and T.W. Donnelly. Phys. Rev. C, 57:2438, 1998.

[4] S. Jeschonnek and J.W. Van Orden. Phys. Rev. C, 62:044613, 2000.

[5] F. Ritz, H. Goller, Th. Wilbois, and H. Arenhoevel. Phys. Rev. C, 55:2214, 1997.

[6] DOE/NSF Nuclear Science Advisory Committee. Opportunities in nuclear science: Along-range plan for the next decade. Technical report, US Department of Energy andNational Science Foundation, Washington, DC, 2002.

[7] M. Sargsian. Int. J. Mod. Phy., E10:405–458, 2001.

[8] P. Rossi et al. Onset of asymptotic scaling in deuteron photodisintegration. Physical

Review Letters, 94(1):12301, 2005.

[9] S. M. Dolfini et al. Out-of-plane measurements of the fifth response function of theexclusive electronuclear response. Phys. Rev. C, 60(6):064622, Nov 1999.

[10] S. Boffi, C. Giusti, F.D. Pacati, and M. Radici. Electromagnetic Response of Atomic

Nuclei. Oxford Science Publications, Oxford University Press, Walton St., Oxford, 1stedition, 1996.

[11] S. Gilad, W. Bertozzi, and Z.-L. Zhou. Nucl. Phys., A631:276c, 1998.

71


(GeV/c)m

p0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

’ LTA

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08,e’p)neH(2

2.6 GeV

Reversed torus polarity

Figure 26: Final results for helicity asymmetry A′

LT for the 2H(e, e′p)n reaction at 2.6 GeVwith reversed torus polarity.

[12] S. Dolfini et al. Out-of-plane quasielastic scattering from deuterium using polarizedelectrons. Phys. Rev. C, 51(6):3479–3482, Jun 1995.

[13] J.D. Lachniet. A High Precision Measurement of the Neutron Magnetic Form Factor

Using the CLAS Detector. PhD thesis, Carnegie Mellon University, 2005.

[14] J.W.C. McNabb. Photoproduction of Λ and Σ0 hyperons off protons in the nucleon

resonance region using CLAS at Jefferson Lab. PhD thesis, Carnegie Mellon University,2002.

[15] C. Hadjidakis. private communications.

[16] D. Protopopescu, F.W. Hersman, M. Holtrop, and S. Stepanyan. Fiducial cuts forelectrons in the clas/e2 data at 4.4 gev. Technical Report CLAS Note 2000-007, JeffersonLaboratory, Newport News, VA, 2000.

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(GeV/c)m

p0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

’ LTA

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08,e’p)neH(2

2.6 GeV

Normal torus polarity

Figure 27: Final results for helicity asymmetry A′

LT for the 2H(e, e′p)n reaction at 2.6 GeVwith normal torus polarity.

[17] R. Nyazov and L. Weinstein. Fiducial cut for positive hadrons in clas/e2 data at 4.4gev. Technical Report CLAS Note 2001-013, Jefferson Laboratory, Newport News, VA,2001.

[18] M. Anghinolfi, M. Battaglieri, A. Bersani, R. DeVita, M. Ripani, and M. Taiuti. Aboutthe error estimation in charge assymetry measurements - a montecarlo simulation. Tech-nical Report CLAS Note 2001-020, Jefferson Laboratory, Newport News, VA, 2001.

[19] K. Joo and C. Smith. Measurement of polarized structure function σ′LT for p(e, e′p)π0

in the delta(1232) resonance region. CLAS Analysis Note 2001-109, 2001.

[20] Z.-L. Zhou et al. Relativistic Effects and Two-Body Currents in 2H(e[over → ], e′

p)nUsing Out-of-Plane Detection. Phys. Rev. Lett., 87(17):172301, Oct 2001.

[21] T. Tamae, H. Kawahara, A. Tanaka, M. Nomura, K. Namai, M. Sugawara, Y. Kawazoe,H. Tsubota, and H. Miyase. Out-of-plane measurement of the d(e, e

′

p) coincidence crosssection. Phys. Rev. Lett., 59(26):2919–2922, Dec 1987.

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[22] M. van der Schaar, H. Arenhovel, H. P. Blok, H. J. Bulten, E. Hummel, E. Jans,L. Lapikas, G. van der Steenhoven, J. A. Tjon, J. Wesseling, and P. K. A. de Witt Hu-berts. Longitudinal-transverse interference structure function of 2h. Phys. Rev. Lett.,68(6):776–779, Feb 1992.

[23] H. Avakian. CLAS Analysis Note 2002-101, 2002.

[24] A. Afanasev, I. Akushevich, V. Burkert, and K. Joo. Phys. Rev., D66:074004, 2002.

[25] L.W. Mo and Y.S Tsai. Rev. Mod. Phys., 41:205, 1969.

[26] J. Schwinger. Phys. Rev., 76:898, 1949.

[27] M.N. Rosenbluth. Phys. Rev., 79:615, 1959.

[28] M. J. Moravcsik. Nucl. Phys, 7:113, 1958.

[29] E.J. Brash, A. Kozlov, S. S.Li, and G.M. Huber. 2H(e, e′

p)n Reaction at High RecoilMomenta. Phys. Rev., C66:051001, 2002.

[30] K. Aniol and J. Cornejo. radiative corrections, external and internal bremsstrahlungfactors. Technical report, Cal State, LA, 2003.

74


A Electron Fiducial Cuts

To focus our analysis on the regions of uniform proton acceptance we have largely followed thetechnique of D.Protopopescu, et al. in [16]. One of the benefits of the procedure describedbelow is to make the fiducial cuts smoothly varying functions of particle momentum andposition and reduce the chances of experimental artifacts appearing in the analysis.

1. Two-dimensional histograms of φe versus θe in momentum bins of 100 MeV/c areextracted first. This was done starting with a three-dimensional histogram in ROOTof pe versus θe versus φe for electron singles events and then projecting out the φe − θe

histogram for each electron momentum bin. Figure 28 is a sample of the φe − θe

distribution for pe = 2.2− 2.3 GeV/c and a beam energy of 4.2 GeV.

2007-03-08 13:17:02

(deg)eθ0 50 100 150 200 250 300

(de

g)eφ

10

15

20

25

30

35

40

45

50

55

60

helectron_fiducials_xy

Entries 1.108776e+07

helectron_fiducials_xy

Entries 1.108776e+07

_xye

vs. peθ vs. e

φD(e,e’)X, E = 4.23 GeV

Figure 28: Distribution of φe versus θe for electrons for all sectors and E = 4.2 GeV.

2. A series of one-dimensional histograms of φe in one-degree bins in θe are projected outfor each electron momentum bin. These distributions are then fitted with a trapezoidalfunction. We refer to these fits as first generation fits. Some typical results are shownin Figure 29.

3. The edges of the central, flat region of the φe distribution for each θe bin at this valueof the electron momentum are extracted from the fits and plotted versus θe. See Figure30. The distribution is then fitted with a function that can be asymmetric about thecentral φe angle of the sector. The function used for the upper branch in Figure 30 is

φedge = φmid + blt

(

1−1

1 + (θe − tl0)/alt

)

(27)

75


Figure 29: Electron azimuthal dependence for sector 3, 2.6-GeV, normal polarity run. Theelectron’s polar angle θe is written on each plot. The black curve is the result a fit to atrapezoidal function described in the text.

Figure 30: Fits to the position of the edges of the plateau of the trapezoids used in the thefirst generation fits.

where blt, φmid, tl0, and alt are fit parameters. For the lower branch in Figure 5, we use

φedge = φmid − brt

(

1−1

1 + (θe − tl0)/art

)

(28)

76


where brt, φmid, t0, and art are fit parameters. The average of φmid is taken from theseparate fits to each branch and then the fits are done again with φmid fixed. Anexample of the results is shown as the black curve in Figure 30 . These curves arecalled second generation fits.

4. The last step in generating the electron fiducial cuts is to take the results of the secondgeneration fits to the φe versus θe distributions as a function of electron momentum pe

and fit these results for each sector. The parameter t0 is fitted with a power functionand the other fit parameters (alt, blt, art, brt) are fitted with a fifth-order polynomial.These curves are third generation fits. Plots of these fits for all sectors are shown inAppendix B. An example of the final CLAS electron acceptance is shown in Figure 31for the 4.2-GeV data set.

Figure 31: CLAS acceptance for electrons at E = 4.2 GeV with fiducial cuts turned on (redpoints) and off (blue points).

77


B Electron Fiducial Fits

Third Generation Fits, 2.6 GeV, normal polarity.

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83


C Proton Fiducial Cuts

The procedure we used to produce the proton fiducial cuts is described here. First, one has tolocate the region of flat acceptance in the center of each region to perform the first-generation,trapezoidal fits to the azimuthal distribution. This proved more of a challenge here thanfor the electron fiducials. Figure 44 shows the CLAS acceptance for protons that are incoincidence with electrons. Much of the acceptance is flat except for a rounded ‘peninsula’

Figure 44: CLAS acceptance for protons in coincidence with electrons.

in the range θp = 50−70. This feature distorts the flat acceptance of CLAS and makes ourtrapezoidal fit (see Appendix A) unusable. This feature is a product of quasielastic eventswhere the proton is strongly correlated with the electron and the forward angle electronacceptance of CLAS; forward-angle, quasielastic electron events have a large-angle proton.Thus, the proton ‘peninsula’ reflects the shape of the forward-angle electron acceptance inCLAS. The protons in the peninsula come from e − p coincidences where the electron isdetected in the forward portion of the opposite sector (i.e. an electron in sector 4 will havea correlated proton in sector 1). The shape of the azimuthal distribution is produced bythe CLAS, forward-angle, electron acceptance in the opposite sector. To demonstrate thiseffect more clearly we eliminated all electron events with θe < 40, but only in sector 4. Ifour explanation is correct, then the protons correlated with those electrons (i.e., the protonsthat will be detected in quasielastic kinematics in the opposite sector (sector 1)) will beeliminated along with the peninsula. Figure 45 shows this effect. The region θp = 50 − 70

in sector 1 is now flat while the peninsula can still be seen in the other sectors. In our final

84


Figure 45: Eliminating the peninsula.

sample of generating the proton fiducial cuts we included positive pions from e− π+ eventssince their acceptance should be same as protons [17] and including them in our samplesignificantly improved the statistical quality. We also required that the mass of the recoilingsystem have W > 1.4 GeV to reduce the the number of correlated quasielastic events. Anexample of the final event sample is shown in Figure 46. The effect of cuts on the trapezoidalfitting procedure is shown in Figure 47. The black points show the position of the edgesfound in the first generation fits without the cuts described above to produce a more uniformazimuthal distribution. Note the dramatic shift in the edge positions extracted from thesefirst generation fits in the region θp = 50 − 70. The red points show the positions of theedges found with the trapezoidal fitting method after the constraints described above wereincluded. For hadrons produces at θh < 45, the agreement between the two methods isexcellent. For θh > 45, the ‘peninsula’ has disappeared. The positions of the edges moreclosely follow the CLAS acceptance.

Once the edges have been found with the trapezoidal fit method, the θp dependenceof each side of the CLAS acceptance in each sector is fitted in a manner similar to the fitsdescribed in Appendix A (second generation electron fits). The functions used are shownin Equations 27-28. Last, the proton momentum dependence of the second generation fitsis itself fitted. The results for all sectors and running conditions are shown in Appendix D.An example of the final hadron acceptance for the 2.6-GeV, reversed torus polarity data setis shown in Figure 47.

85


Figure 46: Final hadron sample.

Figure 47: Comparison of hadron edges positions before and after eliminating correlatedevents.

86


Figure 48: Final hadron acceptance for e − p coincidences for the 2.6-GeV, reversed toruspolarity data set.

87


D Proton Fiducial Fits


2008-09-10 21:48:45

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93


E Acceptance Effects in 〈sinφpq〉±

To more clearly understand Equation 20 which relates 〈sin φpq〉± to A′

LT and the acceptancerecall again the expression for the differential cross section for d(~e, e′p)n.

d3σ

dνdΩedΩp

= σ± = c[ρLfL + ρT fT + ρLT fLT cos(φpq) + ρTT fTT cos(2φpq) + hρ′LT f ′LT sin(φpq)]

(29)

= σL + σT + σLT cos φpq + σTT cos 2φpq + hσ′LT sin φpq (30)

The sin φpq moment of the data at a given Q2 and θcmpq or pm is defined by the following

expression.

〈sin φpq〉± =

∫

2π

0σ± sin φpqdφ∫

2π

0σ±dφ

(31)

Now letσ± = κǫ(φpq)N

±(φpq) (32)

where N± is the number of counts for each helicity, ǫ is the CLAS acceptance and mayvary with φpq, and κ contains all the other helicity-independent, kinematic factors needed todetermine cross sections. In turn, N± is composed of different longitudinal and transversecomponents so

N±(φpq) = N±

L + N±

T + N±

LT cos φpq + N±

TT cos 2φpq + hN±

LT

′sin φpq . (33)

Hereafter, we will suppress the ± superscript for clarity and it will be assumed that all N ′sdepend on the helicity. Finally, the CLAS acceptance as a function of φpq at a given Q2 andθcm

pq or pm can be expressed as

ǫ(φpq) = A0 +

∞∑

m=1

(am sin mφpq + bm cos mφpq) (34)

where we have taken advantage of the completeness of the sines and cosines. We expect anyφpq dependence in the CLAS acceptance to vary slowly so we approximate it by taking thesum in Equation 43 up to m = 2 so

ǫ(φpq) = A0 + a1 sin φpq + b1 cos φpq + a2 sin 2φpq + b2 cos 2φpq . (35)

Substituting Equations 41, 42, and 44 into Equation 40 one obtains (after doing some algebraand some integrals) the following expression

〈sin φpq〉± =

(NL + NT −NTT

2)a1 + NLT a2

2±N ′

LT A0

2(NL + NT )A0 + NLT b1 + NTT b2 + N ′

LT a1

(36)

where we have used h = ±1. In the numerator, NTT and NLT are both much less thanNL + NT so we can neglect their contribution. We retain the N ′

LT term since since it willsurvive when we take the difference between the moments for the positive and negative

94


helicities (the NTT and NLT terms will cancel in the difference). In the denominator, we canapply the same reasoning and neglect the NLT and NTT terms. Here we can also neglect theN ′

LT term because it will have a small effect on the final difference. The result is

〈sin φpq〉± =

(NL + NT )a1 + N ′

LT A0

2(NL + NT )A0

(37)

=a1

2A0

+N ′

2(NL + NT )(38)

= α +σ′LT

2(σL + σT )(39)

which is the form of Equation 20. We have used Equation 41 to eliminate the N ’s andlabeled the first term α to be consistent with the text.

95


F Monte Carlo Simulation of Quasielastic Scattering

in Deuterium

To simulate the quasielastic production we treat the deuteron as composed of two, on-shell nucleons, one of which will act as a spectator in the interaction. We start with theexisting, elastic, nucleon form factors. The differential cross section for elastic electron-nucleon scattering can then be calculated in the laboratory frame as [27]

dσ

dΩ= σMott

[(

F 2

1 +κ2Q2

4M2F 2

2

)

+Q2

2M2(F1 + κF2)

2 tan2

(

θ

2

)]

(40)

where θ is the electron scattering angle and σMott is

σMott =α2E ′ cos2( θ

2)

4E3 sin4( θ2)

. (41)

It is preferable to define different electromagnetic form factors that are related to the chargeand magnetization density of the nucleon in the appropriate kinematics. These so-calledSachs form factors are defined as

GE = F1 −κQ2

4M2F2 GM = F1 + κF2 (42)

so Equation 2 can be written as

dσ

dΩ= σMott

(

G2

E +τ

ǫG2

M

)

(

1

1 + τ

)

(43)

where

τ =Q2

4M2and ǫ =

1

1 + 2(1 + τ) tan2( θ2)

. (44)

We used Equations 40-44 and made the following assumptions about the form factors

GpE ≈ GD =

1

(1 + Q2/∆)2Gp

M ≈ µpGD GnM ≈ µnGD Gn

E ≈ 0 (45)

where µn and µp are the neutron and proton magnetic moments and ∆ = 0.71 GeV2. Thenumber of quasielastic events in a particular Q2 bin is calculated from the elastic form factors.Next, the Fermi momentum ~pf for one of the nucleons is chosen at random (the spectatornucleon has momentum −~pf ) and we simulate the kinetics of the scattering. The nucleonmomentum ~pf inside the deuteron is chosen from the Hulthen distribution shown in Figure61 which depends only on the pf [28].

We also have to account for combined effect of the Fermi motion and the beam energydependence of the elastic cross section. A nucleon whose Fermi motion is directed towardsthe incoming electron will observe a higher energy beam in its rest frame and (because ofthe elastic cross section dependence on the beam energy) will have a lower cross section forinteracting. Conversely, a nucleon ‘running away’ from the beam will see a lower effective

96


p (GeV/c)0 0.1 0.2 0.3 0.4 0.5

-1dP

/dp

(GeV

/c)

0

2

4

6

8

10

12

Hulthen Distribution

Hulthen distribution

Figure 61: Hulthen distribution representing the nucleon Fermi momentum inside thedeuteron.

beam energy and have a higher cross section. For a given choice of Fermi momentum pf andnucleon polar angle cos θ there is an effective beam energy in the rest frame of the movingnucleon. The size of the cross section at this effective beam energy in the nucleon rest frameand the Hulthen distribution will determine the relative weight of this pf−cos θ combination.At each effective beam energy in the quasielastic case the Brash parameterization [29] of thenucleon cross section is used to obtain the cross section dependence on the electron scatteringangle. This angular dependence is then integrated over the CLAS angular acceptance toobtain the weighting for this effective beam energy (and pf − cos θ point). Multiplyingthis effective-beam-energy weight with the Hulthen distribution yields the weight functionfor electron-proton scattering shown in Figure 62. The Hulthen distribution produces along ridge in the range of the Fermi momentum pf ≈ 0.04 − 0.05 GeV/c and the crosssection dependence on the effective beam energy creates a downward slope along this ridgefrom forward to backward angles. The azimuthal angle φf of the nucleon is chosen froma uniform, random distribution in the range φf = 0 − 2π. Once the Fermi momentum ischosen, a relativistic boost is made to the rest frame of the nucleon for all particles andthe coordinate system is rotated so the incoming electron is along the z axis. A new beamenergy is calculated. A nucleon, rest-frame electron scattering angle is chosen from a randomdistribution weighted by the Brash parameterization. Last, the momenta of the electron andnucleon are transformed back to the laboratory frame. This method was implemented in theprogram QUEEG and used to simulate quasielastic events in here [13].

To summarize, we use the Brash parameterization of the elastic cross section to choosethe number of quasielastic events in a particular Q2. For the inelastic cross section weinterpolate between the measured inclusive cross section. The Fermi momentum for each ischosen with the combined weights of the Hulthen distribution the effective of the differentcross sections for different effective beam energies at each pf − cos θ point. Once the Fermimomentum is determined, the system is boosted to the nucleon rest frame. The final 4-

97


-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

θcos

(G

eV/c

)f

p

Figure 62: Plot of the weighting function for electron-proton (left-hand panel) and electron-neutron (right-hand panel) scattering

vectors are chosen from the Brash parameterization (quasielastic case) and the final statesare then transformed back to the laboratory frame.

98


G Systematic Uncertainties

2.6 GeV2.6 GeV



0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

-0.005

0.000

0.005

0.010

pm HGeVcL

DA

LT

’Effect of changing MM2 cut

Figure 63: Systematic Uncertainty due to the MM2 cut.

2.6 GeV



0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

-0.005

0.000

0.005

0.010

pm HGeVcL

DA

LT

’

Effect of changing Quasielastic cut on W

Figure 64: Systematic Uncertainty due to the quasielastic cut on W .

99


2.6 GeV Red - Normal torus polarity


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

-0.005

0.000

0.005

0.010

pm HGeVcL

DA

LT

’

EC track coordinate cut uncertainty

Figure 65: Systematic Uncertainty due to the electromagnetic calorimeter tracking coordi-nate cut.

2.6 GeV2.6 GeV Red - Normal torus polarity


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

-0.005

0.000

0.005

0.010

pm HGeVcL

DA

LT

’

EC sampling fraction cut uncertainty

Figure 66: Systematic Uncertainty due to the electromagnetic calorimeter sampling fractioncut.

100


2.6 GeV Red - Normal torus polarity


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

-0.005

0.000

0.005

0.010

pm HGeVcL

DA

LT

’

EC pion threshold cut uncertainty

Figure 67: Systematic Uncertainty due to the electromagnetic calorimeter pion thresholdcut.



0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

-0.005

0.000

0.005

0.010

pm HGeVcL

DA

LT

’

CC photoelectron cut uncertainty

Figure 68: Systematic Uncertainty due to the Cherenkov counter photoelectron cut.

101




0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

-0.005

0.000

0.005

0.010

pm HGeVcL

DA

LT

’

Systematic uncertainty due to DPe

Figure 69: Systematic Uncertainty due to the beam polarization.

102


H Radiative Corrections

To test our modifications to EXCLURAD we will compare them with the more traditionalapproaches. Below we describe how to relate the parameters of the Schwinger-style calcula-tion with the approach used in EXCLURAD. In the Schwinger method one calculates theradiative correction for the scattering of an electron in a Coulomb field. This correspondsto inclusive electron scattering. An essential step in the calculation is to integrate over theradiative tail of the energy of a scattered electron to arrive at a correction factor for the yieldlost to the emission of photons. The parameters of that integration are defined in Figure 15[30]. The parameter ∆E is the energy range over which the integral is performed (starting

E resradiative tail

Elo

Ehi

resE =

choose E > ∆ resE

one-halfintrinsicresolution

E∆

Region of integration from E to Elo hi

EE’

ω

E is the beam energy

E’ is the peak energy ofthe scattered electron

Figure 70: Energy spectrum of scattered electron showing definitions of quantities used inSchwinger radiative correction calculation.

at the unradiated energy of the electron) to estimate the yield lost to radiated photons.Afanasev, at al. follow an analogous procedure in their more sophisticated approach

[24]. They integrate over the radiative tail of the scattered electron, but they perform theintegration in terms of the covariant ‘inelasticity’ v defined as

v = Λ2 −m2

u (46)

where mu is the mass of the undetected hadron and Λ is the four-momentum of the missingor undetected particles. The quantity v describes the missing mass due to the emission of abremsstrahlung photon and can be rewritten as

v = W 2 + m2

h −m2

u − 2WEh (47)

where W is the mass of the system recoiling against the electron, mh is the mass of thedetected hadron, and Eh is the center-of-mass energy of the detected hadron. To determinethe relationship between ∆E and v consider the usual expression for W 2

W 2 = M2 + 2M(E − E ′)−Q2 (48)

103


where

Q2 ≈ 4EE ′ sin2θ

2(49)

M is the target mass, and θ is the electron scattering angle. However, for an event with aradiated photon, the measured energy of the scattered electron is not E ′, but some lowerenergy

Elo = E ′ −∆E (50)

so W for this event will not be ‘correct’. The new value of W is

W 2

rad = M2 + 2M(E −Elo)− 4EElo sin2θ

2(51)

Using Equations 33 and 34 in the expression for v in Equation 30 one obtains the followingfunction of ∆E.

v = M2 + 2M(E − E ′ + ∆E)− 4E(E ′ + ∆E) sin2θ

2

+ m2

h −m2

u − 2Eh

√

M2 + 2M(E −E ′ + ∆E)− 4E(E ′ + ∆E) sin2θ

2(52)

This expression can be re-arranged so

v = W 2

0 + m2

h −m2

u + 2∆E(M + 2E sin2θ

2)− 2Eh

√

W 20 + 2∆E(M + 2E sin2

θ

2) (53)

where

W 2

0 = M2 + 2M(E − E ′)− 4EE ′ sin2θ

2(54)

and the quantities E, E ′, and θ are determined by the electron kinematics. The hadronenergy Eh is determined by the choice of the angle of the outgoing hadron relative to ~q, thethree-vector of the momentum transfer. The masses M , mh, and mu are all known.

As an example of applying Equation 35 consider the following kinematics. The results of

E = 2.558 GeV E ′ = 2.345 GeV θ = 14.84

mh = 0.938 GeV mu = 0.940 GeV θcmh = 45

M = 1.876 GeV Q2 = 0.52 (GeV/c)2 W = 1.93 GeV

Table 9: Kinematics for calculating v(∆E).

the calculation are shown in Figure 6. The dependence of v on ∆E is almost linear implyingthe importance of that term in Equation 36 over the sum of all the other terms.

104


E (MeV)∆

0 50 100 150 200 250 300 350 400

E)

∆v(

0

200

400

600

800

1000

1200 E=2.558 GeV

E’=2.345 GeV

o = 14.8θ

Wed Dec 18 14:32:08 2002

E)∆v(

Figure 71: Dependence of v on ∆E for the kinematics listed in Table 1.

105

report on sabbatical leave for dr. gerard p gilfoyle gerard p gilfoyle university of richmond

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