Tanja Horn

Jefferson Lab

11

The Pion Form The Pion Form Factor Factor

Nuclear Physics Seminar, University of Virginia25 September, 2007

Present status and future outlook

• Quantum Chromo-Dynamics (QCD) is very successful describing strong interactions

• BUT, we are unable to construct a quantitative description of hadrons in terms of the underlying constituents, quarks and gluons.– We know that there is an asymptotic limit, but how do we get there

and what governs the transition?

22

• Form factors provide important information about the transition from collective degrees of freedom to quarks and gluons– i.e., from the non-perturbative to the perturbative regime

Short Distance

Asymptotic Freedom

Perturbative QCD

Long Distance

Binding

Collective DOF?

Hadronic Form FactorsHadronic Form Factors

• The study of Fπ is one of the most fundamental experimental studies for understanding hadronic structure

– Simple qq valence structure of π+

• In QFT, Fπ is the overlap integral,

– The pion wave function can be separated into φsoft with low momentum contributions (k<k0) and a hard tail, φhard

• Hard scattering part can be calculated in pQCD

The Pion Charge Form FactorThe Pion Charge Form Factor

q)(pπφ(p)*πφdp)

2(QFπ

QCD Hard Scattering Picture

•At large Q2, perturbative QCD (pQCD) can be used

at asymptotically high Q2,, only the hardest portion of the wave function remains

and Fπ reduces to the factorized form

G.P. Lepage, S.J. Brodsky, Phys.Lett. 87B(1979)359.

22 2

2 22 2

0

4 ( )( ) log 1 ( ),

n

F Sn s

n

C Q Q mF Q a O QQ Q

2

3( ) (1 )

Qc

fx x x

n

2

2 22

2

16 ( )( ) s

Q

Q fF Q

Q

where f 2

=93 MeV is the +→+ decay constant.

• At experimentally accessible Q2 both hard and soft components contribute– Transverse momentum effects

• The interplay of hard and soft components is not well understood – Non-perturbative hard

components of higher twist cancel soft components [V. Braun et al., PRD 61 (2000) 07300]

55

Intermediate QIntermediate Q2 2 regimeregime

Meson Form Factors and QCD

• The simple valence quark structure of mesons presents the ideal laboratory for testing our understanding of bound quark systems– All hadronic structure models use π+ as a test case

qq

• Excellent opportunity for studying the transition from effective degrees of freedom to quarks and gluons, i.e., from the soft to hard regime

•Situation for nucleon is even more complicated

• Many studies of Fπ, but the interplay of hard and soft contributions is not well understood– Constraints on theoretical models require high precision data– JLab is the only experimental facility capable of the necessary

measurements

• At low Q2, Fπ can be measured directly from π+e scattering up to Q2~0.3 GeV2 [S.R. Amendolia et al., NP B277 (1986)]

– Accurate measure of the π+ charge radius, rπ=0.657 ± 0.012 fm

• At larger Q2 values, one must use the “virtual pion cloud” of the proton to extend the Fπ measurement– t-channel diagram dominates σL at small –t

• In the Born term model:

77

πNNg

Measuring FMeasuring Fππ

),()()(

2222

2

tQFtgmt

tQ

dt

dNN

L

Pion electroproduction

• Extraction of Fπ relies on the pole dominance of σL

– For maximum contribution from the π+ pole to σL, need data at the smallest possible –t

– At fixed Q2, a higher value of W allows for smaller -tmin

88

• Extraction of Fπ requires knowledge of the -t dependence of σL

– Only three of Q2, W, t, and θπ are independent

– Must vary θπ to measure the -t dependence (off-parallel)

– In off-parallel kinematics, LT and TT must also be determined

Q2= |q|2 – ω2t=(q - pπ)2

W=√-Q2 + M2 + 2Mω

scattering plane

reaction plane

Pion Electroproduction Pion Electroproduction KinematicsKinematics

πcos2φdφdt

dσεπcosφdφdt

dσ1)(εε2dφdtσ2d TTLT

dφdtdσε

dφdtdσ LT

1)]2eθ

(2tan)2Q

2ω(12[1ε

99

Extraction of FExtraction of Fππ from p(e,e’from p(e,e’ππ++)n )n datadata

• + production data are obtained at –t>0 (away from the -t=mπ

2 pole)

• Early experiments used “Chew-Low” extrapolation technique– Need to know the –t

dependence through the unphysical region

– A reliable extrapolation is not possible

• More reliable technique is to use a model including the π+ reaction mechanism and extract Fπ from σL data– Fit data in the physical region

• Electroproduction starts from a virtual pion– Can this method yield the physical

form-factor?

• Test the method by comparing Fπ values extracted from p(e,e’π+)n data with those obtained from π+e elastic scattering at the same kinematics

• DESY electroproduction data at Q2 = 0.35 GeV2 consistent with extrapolation of elastic data

[Ackerman et al., NP B277 (1986) 168]

1010

• An improved check will be performed after the JLab Upgrade– Lower Q2 (Q2=0.30 GeV2)– Lower –t (-t=0.005 GeV2)

Electroproduction Method TestElectroproduction Method Test

1111

?

FFππ before 1997 before 1997

• Large Q2 data from Cornell– Use extrapolation of σT fit at

low Q2 to isolate σL

– Extract Fπ from unseparated cross sections

• Largest Q2 points also taken at large –t

– Carlson&Milana predict MpQCD/Mpole grows significantly for –tmin>0.2 GeV2 [PRL 65 (1990) 1717]

– Pole term may not dominate

• –tmin<0.2 GeV2 constraint limits Q2 reach of F measurements

• Measurement of σL for 0 could help constrain pQCD backgrounds– JLab PAC31 proposal

• In a GPD framework, + and 0 cross sections involve different combinations of same GPDs – but 0 has no pole contribution

1212

)~~

(~ dd

uup

HeHeA o

)~~

(~ dd

uup

EeEeB o

))(~~

(~ dudu

peeHHA

))(~~

(~ dudu

peeEEB

0+

VGG GPD-based calculation

pole

non-pole

FFππ Backgrounds Backgrounds

1313

• Two superconducting Linacs – Three experimental

Halls operating concurrently

• E<~ 5.7 GeV– Hadron-parton

transition region

• C.W. beam with currents of up to 100 uA– Luminosity ~1038

Fπ measurements

Jefferson LabJefferson Lab

Exp Q2

(GeV2)

W (GeV)

|t|

(Gev)2

Ee

(GeV)

Fpi1 0.6-1.61.6 1.95 0.03-0.1500.150 2.445-4.045

Fpi2 1.61.6,2.45 2.22 0.0930.093,0.189 3.779-5.246

1414

• Fpi2 extends the earlier Fpi1 data to the highest possible value of Q2 with 6 GeV beam at JLab– Fpi2 data at higher W,

smaller -t

– Repeat Q2=1.60 GeV2 closer to t=m2

π to study model uncertainties

• Full L/T/TT/LT separation in π+ production

• Measurement of separated π+/π- ratio to test the reaction mechanism

HMS: 6 GeV SOS: 1.7 GeV

The FThe Fππ Program at JLab Program at JLab

R. Ent, D. Gaskell, M.K. Jones, D. Mack, D. Meekins, J. Roche, G. Smith, W. Vulcan,

G. Warren, S. WoodJefferson Lab, Newport News, VA , USA

E. Brash,E. Brash, G.M. Huber, V. Kovaltchouk, G.J. Lolos, C. Xu

University of Regina, Regina, SK, Canada

H. Blok, V. TvaskisVrije Universiteit, Amsterdam, Netherlands

E. Beise, H. Breuer, C.C. Chang, T. Horn, P. King, J. Liu, P.G. Roos

University of Maryland, College Park, MD, USA

W. Boeglin, P. Markowitz, J. ReinholdFlorida International University, FL, USA

J. Arrington, R. Holt, D. Potterveld, P. Reimer, X. Zheng

Argonne National Laboratory, Argonne, IL, USA

H. Mkrtchyan, V. TadevosyanYerevan Physics Institute, Yerevan, Armenia

S. Jin, W. KimKyungook National University, Taegu, Korea

M.E. Christy, L.G. TangHampton University, Hampton, VA, USA

J. VolmerDESY, Hamburg, Germany

T. Miyoshi, Y. Okayasu, A. MatsumuraTohuku University, Sendai, Japan

B. Barrett, A. SartySaint Mary’s University, Halifax, NS Canada

K. Aniol, D. Margaziotis California State University, Los Angeles, CA, USA

L. Pentchev, C. PerdrisatCollege of William and Mary, Williamsburg, VA, USA

I. NiculescuJames Madison University, Harrisonburg, VA, USA

V. PunjabiNorfolk State University, Norfolk, VA, USA

E. GibsonCalifornia State University, Sacramento, CA, USA

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Jefferson Lab Fpi2 Jefferson Lab Fpi2 CollaborationCollaboration

1616

• Hall C spectrometers– Coincidence measurement – SOS detects e- – HMS detects π+

• Targets– Liquid 4-cm H/D cells– Al (dummy) target for background

measurement– 12C solid targets for optics calibration

HMS Aerogel– Improvement of p/π+/K+ PID at large

momenta, first use in 2003– Built by Yerevan group [Nucl. Instrum. Meth. A548(2005)364]

Experimental DetailsExperimental Details

• Coincidence measurement between charged pions in HMS and electrons in SOS– Coincidence time resolution

~200-230 ps– Cut: ± 1ns

• Protons in HMS rejected using coincidence time and aerogel Cerenkov– Electrons in SOS identified

by gas Cerenkov and Calorimeter

• Exclusive neutron final state selected with missing mass cut– 0.92 ‹ MM ‹ 0.98 GeV

1717

• After PID cuts almost no random coincidences

p(e,e’p(e,e’ππ+)n Event Selection+)n Event Selection

1818

• W/Q2 phase space covered at low and high ε is different

• For L/T separation use cuts to define common W/Q2 phase space

• Have full coverage in φ BUT acceptance not uniform

• Measure σTT and σLT by taking data at three angles: θπ=0, +4, -3 degrees

Θπ=0Θπ=+4 Θπ=-3

-t=0.1

-t=0.3Q2=1.60, High ε

Radial coordinate: -t, azimuthal coordinate: φ

Q2=1.60 GeV2

Q2=2.45 GeV2

Fpi2 Kinematic CoverageFpi2 Kinematic Coverage

Source Pt-Pt Scale t-correlated

Acceptance 1.0(0.6)% 1.0% 0.6%

Radiative Corrections

0.1% 2.0% 0.4%

Pion Absorption - 2.0% 0.1%

Pion Decay 0.03% 1.0% -

Model Dependence 0.2% - 1.1(1.3)%

Kinematics 0.2% - 1.0%

HMS Tracking 0.1% 1.0% 0.4%

Charge - 0.5% 0.3%

Target Thickness - 0.8% 0.2%

Detection Efficiency - 0.5% 0.3%

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• Uncertainties in spectrometer quantities parameterized using over-constrained 1H(e,e’p) reaction – Beam energy and momenta

to <0.1%– Spectrometer angles to

~0.5mrad• Spectrometer acceptance

verified by comparing e-p elastic scattering data to global parameterization– Agreement better than 2%

• Statistical uncertainty in ranges between 1 and 2%• Uncorrelated systematic uncertainty: 1.1(0.9)%• Total correlated uncertainty: 3.5%

Magnetic Spectrometer Magnetic Spectrometer CalibrationCalibration

2020

πcos2φdφdt

dσεπcosφdφdt

dσ1)(εε2dφdt

dσεdφdtσd TTLTT

2 dφdt

dσL

• σL is isolated using the Rosenbluth separation technique– Measure the cross section at two

beam energies and fixed W, Q2, -t– Simultaneous fit using the measured

azimuthal angle (φπ) allows for extracting L, T, LT, and TT

• Careful evaluation of the systematic uncertainties is important due to the 1/ε amplification in the σL extraction– Spectrometer acceptance,

kinematics, and efficiencies

Determination of Determination of σσLL

• MAID – unitary isobar model for pion photo- and electroproduction– Only useful for W < 2 GeV, Fπ-2 kinematics above this region– Too many free parameters

• Born term models– Do not describe t-dependence well away from pole

• VGL/Regge [Vanderhaeghen, Guidal, Laget, PRC 57 (1998) 1454]

– Appropriate at W > 2 GeV– Model parameters fixed from pion photoproduction data– Fπ is the only free parameter in the calculation of σL

• Constituent Quark Model (Obukhovsky et al., Phys. Lett. B634 (2005)

– Same kinematic range as VGL/Regge, two free parameters– Model still in development, not yet used in data analysis

Pion Electroproduction ModelsPion Electroproduction Models

2222

Λπ2=0.513 (0.491) GeV2, Λπ

2=1.7 GeV2 uses the VGL Regge model, which describes pion electroproduction in terms of the exchange of π and ρ like particles [Vanderhaeghen, Guidal, Laget, PRC 57 (1998), 1454]

– Model parameters fixed from pion photoproduction

– Free parameters: Fπ and Fρ

/Q11

πF 2

2πΛ

- The error bars denote statistical and systematic

uncertainties in quadrature (1.0 (0.6)%)

- Yellow band denotes the normalization and –t

correlated systematic uncertainty (3.5%, 1.8(9)%)

Fit to σL to model gives Fπ at each Q2

T. H

orn et al., Phys. R

ev. Lett. 97 (2006) 192001.

Extraction of FExtraction of Fππ from Fpi2 data from Fpi2 data

2323

• Extract Fπ for each t-bin separately– Fπ values are insensitive

(<2%) to the t-bin used

• This result gives confidence in the applicability of the VGL Regge model in the kinematic regime of Fpi2 data

Fpi2 model testFpi2 model test

FFππ t-dependence t-dependence

• Fπ precision data deviate from 0.657 fm charge radius at Q2=2.45 GeV2 by ~1σ

– The monopole reflects the soft (VMD) physics at low Q2

– The deviation suggests that the π+ “harder” at this Q2

2424

T. Horn et al., Phys. Rev. Lett. 97 (2006)192001.

V. Tadevosyan et al., nucl-ex/0607007.

JLab Experimental ResultsJLab Experimental Results

P. Brauel et al., Z. Phys. C3 (1979) 101

H. Ackermann et al., Nucl. Phys. B137 (1978) 294

S. R. Amendolia et al., Nucl. Phys. B277 (1986) 168

• Fπ is still far from the pQCD prediction– Including transverse

momentum effects has no significant impact

• New point from πCT (2004) in good agreement with Fpi experiments

T. Horn et al., arXiv:0707.1794 (2007).

Fpi Interpretation IssuesFpi Interpretation Issues

2525

• t dependence of Fpi1 σL is significantly steeper than VGL/Regge at the lowest Q2

– May be due to resonance contributions not included in Regge

– Linear fit to Λπ2 to tmin gives the best

estimate of Fπ at each Q2

• Check the model dependence of the mass pole extrapolation– Good agreement between Fpi1

(tmin=0.093 GeV2) and Fpi2 (tmin=0.150 GeV2) gives confidence in the reliability of the method

2626

A.P. Bakulev et al. Phys. Rev. D70 (2004).

Chernyak & Zhitnitsky(CZ) DA

Asymptotic DA

• Bakulev et al. use analytic perturbation theory at the parton amplitude level

– π DA is consistent to 1σ level

with CLEO πγ transition data

– Analytic perturbation theory at the parton amplitude level

• Fπ˚ results taken as evidence that

asymptotic π DA appropriate as low as Q2=1 GeV2, BUT …

pQCD LO+NLO Calculations (I)pQCD LO+NLO Calculations (I)

• For Fπ+ soft contributions from quark-hadron duality model need to be included to describe the data

2727

A.P. Bakulev et al. Phys. Rev. D70 (2004).

• Hard component is only slightly larger than the one calculated with asymptotic DA in all considered schemes– To describe the data must

include soft contribution – here, via local duality

pQCD LO+NLO Calculations (II)pQCD LO+NLO Calculations (II)

2828

T. Horn et al., Phys. Rev. Lett. 97 (2006) 192001.

FFππ in 2007 in 2007

• QCD Sum Rules [V.A. Nesterenko and A.V. Radyushkin,

Phys. Lett.B115 (1982)410]

– Use properties of Green functions – spectral function contains pion pole

• Bethe-Salpeter/Dyson-Schwinger [P.Maris and P. Tandy, Phys.Rev.C62

(2000)055204]

– Systematic expansion in terms of dressed particle Schwinger equations

• Anti de Sitter/Conformal Field Thry [S.J. Brosdky and G.F. de Teramond,

arXiv:0707.3859]

T. Horn et al., arXiv:0707.1794 (2007).

• [[A.P. Bakulev et al, Phys. Rev. D70 (2004)]Hard contribution to NLO with improved π DASoft contribution from local duality

FFππ time-like vs. space-like (2007) time-like vs. space-like (2007)

• Expect same asymptotic prediction for both space-like and time-like data– The way one gets there

may be different– pQCD under-predicts both

cases

• Calculations in time-like region complicated by explicit resonances

Timelike data from P.K. Zweber Ph.D. thesis (2006)

3030

• Hall C High Momentum Spectrometer and Short Orbit Spectrometer at present– Form Factors and simple

quark systems– Color Transparency– Nuclei with strange quarks

• Add a Super-High Momentum Spectrometer for studies of– Form Factors and simple

quark systems– Color Transparency– Semi-inclusive DIS

SHMSSHMS

HMS HMS (QQQD)(QQQD)

SOS SOS (QQD)(QQD)

Hall C at 12 GeVHall C at 12 GeV

• Significant progress on theoretical front expected in next 5 years– Lattice, GPDs etc.

3131

• The 11 GeV electron beam and the SHMS in Hall C with θ=5.5º allows for– Precision data up tp Q2=6 GeV2 to

study the transition to hard QCD– Test of the electroproduction

method at Q2=0.3 GeV2 with the upper limit of elastic scattering data

– Most stringent test of the model dependence in the Fπ extraction by comparing data at several values of W

FFππ after the JLab Upgrade after the JLab Upgrade

• Fπ is a good observable to study the transition from collective degrees of freedom to quarks and gluons

• Fπ measurements from JLab yield high quality data – in part due to– Continuous electron beam provided by JLab accelerator– Magnetic spectrometers and detectors with well-understood properties

• The highest Q2 JLab results indicate that Q2Fπ is still increasing, but ~1σ below the monopole parameterization of the charge radius– Still far from the QCD prediction

• Studies of Fπ at higher electron beam energies will allow to reach the kinematic range where hard contributions are expected to dominate– Planned measurement of Fπ at JLab after the upgrade to Q2=6 GeV2

• Further development of QCD techniques for the non-perturbative physics are anticipated

3232

SummarySummary

Measurement of KMeasurement of K++ Form Factor Form Factor

• Similar to + form factor, elastic K+ scattering from electrons used to measure charged kaon for factor at low Q2 [Amendolia et al, PLB 178, 435 (1986)]

• Can “kaon cloud” of the proton be used in the same way as the pion to extract kaon form factor via p(e,e’K+)L ?

• Kaon pole further from kinematically allowed region

• Can we demonstrate that the “pole” term dominates the reaction mechanism?

Kaon Form Factor at Large Kaon Form Factor at Large QQ22

• JLAB experiment E93-018 extracted –t dependence of K+ longitudinal cross section near Q2=1 GeV2

• A trial Kaon FF extraction was attempted using a simple Chew-Low extrapolation technique

• gKLN poorly known

– Assume form factor follows monopole form

– Used measurements at Q2=0.75 and 1 GeV2 to constrain gKLN and FK simultaneously

• Improved extraction possible using VGL model?

)()()(

2 22222

2

QFegkmt

tQKNK

KL

Test Extraction of Test Extraction of KK++ Form Factor Form Factor

-t dependence shows some “pole-like” behavior

“Chew-Low” type extraction

G. Niculescu, PhD. Thesis, Hampton U.

• Lattice QCD allows for calculations from first principles– This is different from QCD-inspired models where confinement

must be put in by hand

3636

• BUT LQCD requires a number of approximations– Lattice discretization errors – improved LQCD action helps– Chiral extrapolation of LQCD is used to obtain the pion mass – Quenching errors – need to include disconnected quark loops

• Advances in computational techniques have improved over the last two decades– Potential for precision predictions of hadronic properties

FFππ on the Lattice on the Lattice

• Unquenched (dynamical) domain-wall action calculation – Lattice Hadron Physics

Collaboration (Jefferson Lab, Regina,Yale)

– F. Bonnet et al., hep-lat/0411028

3737

• Lattice calculations are consistent with experimental data within large statistical and systematic errors, dominated by chiral extrapolation– Primary goal is to test proof-of-principle of different techniques

• For future calculations expect mπ sufficiently small to yield small chiral extrapolation errors– Require higher Q2 data to validate new LQCD methods

pQCD→

FFππ from a recent unquenched from a recent unquenched Lattice QCD calculationLattice QCD calculation

Fpi1

Fpi2

2sv

2sv

L

L

|AA||AA|

σ

σR

• Extraction of Fπ relies on dominance of t-channel (pole dominance)

– t-channel diagram is purely isovector

3838

• R consistent with the model predictions indicates t-channel dominance of the data

Competing Reaction Competing Reaction ChannelsChannels

• Pole dominance tested using π-/π+ from D(e,e’p) – G-parity: If pure pole then

necessary R=1

Constituent Quark ModelConstituent Quark Model

• Obukhovsky et al. use microscopic description on basis of CQM– Calculate σL using both t-

pole and s-, u-pole contributions

– Free parameters: Fπ and strong FπNN

• Calculation at Λπ2=0.54

– Shape similar for σL

– Significant difference in σT

I. Obukhovsky et al hep-ph/0506319M. Vanderhaeghen, M Guidal, J-M Laget Phys Rev C57 (1998)