Proton Form Factor Measurements with Polarization Method

L.Pentchev

The College of William and Mary

For the GEp-2 and GEp-III

collaborations

JLab , June 8-10, 2009

Outline

GEp-III (E04-108) and GEp-2(E04-019) experiments

Polarization transfer method, experimental set-up, kinematics

Elastic/background separation

Spin transport in HMS

GEp-2 experiment: precise (1%) measurement of two polarization quantities; test of the limits of Born approximation in polarization method

2 exchange theoretical calculations

Longitudinal transferred polarization (preliminary results), beam polarization measurements

-dependence of the form factor ratio (preliminary results)

Reconstruction of the real part of the ep elastic amplitudes

GEp-III: measurement of the proton form factor at high Q2

Preliminary results

Comparison with theoretical calculation, asymptotic behavior

Summary

Polarization Method

2tan)1(20

eMpEpt GGPI

A.I.Akhiezer and M.P.Rekalo, Sov.J.Part.Nucl. 3, 277 (1974)

R.Arnold, C.Carlson, and F.Gross, Phys. Rev. C 23, 363 (1981)

2tan)1()(

1 220

eMpebeam

pl GEEM

PI

220 MpEp GGI

22 4/ pMQ

2tan)1(21

1

2 e

In Born (one-photon exchange) approximation:

2tan

2

)( e

p

ebeam

l

t

Mp

Ep

M

EE

P

P

G

G

•Form Factor ratio can be obtained without knowing analyzing power, Ay, and beam helicity, h, (both cancel out in the ratio), and without measuring cross-section.

•Systematic uncertainty dominated by the spin transport from the polarimeter to the target.

elasticpepe

GEP-3 and GEP-2gamma experimental set-up in Hall C

1.87- 5.71 GeV beam

80-100 A beam current

80-85% pol.

20cm LH target

e

e’

pHigh Momentum Spectrometer

Double Focal Plane Polarimeter

Big E.M. Calorimeter

DetectorsChanges in standard HMS detector package:

•Focal Plane Polarimeter with Double Analyzer:

-> 70% increased efficiency (30% for FOM)

• Scintillator plane S0 in front of drift chambers

-> deteriorates angular resolution but needed for triggering

1744 channel E.M. Calorimeter (BigCal):

• from (due to radiation damage)

needed for triggering

• beter than 10 mm position resolution – most

important parameter for elastic separation

E

23%to

E

6.8%

Goal of The Experiments

Ee, GeV pp Ee’ p, deg e range <Q2

>

1.867 2.068 0.527 14.49 105 .130-.160 2.5

2.839 2.068 1.507 30.98 45.3 .611-.647 2.5

3.549 2.068 2.207 35.39 32.9 .765-.786 2.5

3.650 2.068 2.307 36.14 31.7 .772-.798 2.5

KEY IDEA OF THE METHOD: FIXED Q2

• same spin transport

• same analyzing power

precision limited only by statistics (~ 1%),

very small p.t.p systematics:

Ay , h cancel out in the Pt/Pl ratio

Q2 fixed, Pp fixed, spin precession fixed

Two polarization observables are measured: Pt/Pl and Pl separately

• GEp-2gamma: dependence of R at 2.5 GeV2

• GEp-3: high Q2 measurementsEe, GeV pp Ee’ p,

dege <Q2>

4.053 3.589 1.274 17.94 60.3 .377 5.2

5.714 4.464 2.090 19.10 44.2 .507 6.8

5.714 5.407 1.164 11.6 69.0 .236 8.5

•5.2 GeV2 point “overlapping” with GEp-II (4.0 and 5.6 GeV2)

• two higher Q2 points

Data analyses: elastic separation

All triggers Elastics after BigCal-HMS correlations Estimated background Range used in analyses

2.5 GeV2 =0.15 8.5 GeV2 =0.24

• (PCAL-PHMS)/P0 gives better resolution then (Pp-PHMS)/P0, because of worse HMS angular resolution

•Background estimated by interpolation, dominated by p -> 0 p

• Polarization of the background measured below the elastic peak looking at events with hits at the calorimeter outside expected position of the elastic electron ()

=0.11%

=0.10%

Background contribution: 13%Absolute correction to R: +0.10

Background contribution: 0.5%Correction to R: +0.35%

Spin transport in HMS

)1(Dispersive precession

QQQD type spectrometer: rotations are additive in the quads and total precession is

sum of dispersive (main) and non-dispersive precession:

Non-dispersive precession

)1(

•Non-dispersive precession – the dominant source of systematics, because it mixes the two polarization components in the reaction plane

•Requires very good knowledge of non-

dispersive bend angle

• uncertainty of used for the preliminary analyses of 1mrad

• using dedicated optical studies, we expect to reduce the uncertainty by factor of ~3

2.5 GeV2 =0.15

Allows to use simple geometrical model, giving results very similar to COSY calculations used for the results presented here

GEp/GMp Crisis: discrepancy in the data

“The discrepancy is a serious problem as it generates confusion and doubt about the whole methodology of lepton scattering experiments”

P.A.M. Guichon and

M.Vanderhaeghen

GEp-2: Beyond Born Approximation

Mo and Tsai, and others:• prescriptions for radiative corrections commonly used

• two-photon exchange: (e), (f) – only with one soft photon, neglecting proton structure

Generalized Form Factors (ep elastic amplitudes)

PG

d

G

GYl

M

red

M

M

( )( )(

~)

1 1 1 22

1

2

2

P.A.M. Guichon and M.Vanderhaeghen, Phys.Rev.Lett. 91, 142303 (2003)

M.P. Rekalo and E. Tomasi-Gustafsson, E.P.J. A 22, 331 (2004)

d GR G

GR

G

G

RYred M

M

M

E

M

/(

~) (

~)2

2

21 2 2 2 1

(~

) ( ) (~

( , ))G G Q G QM M M2 2

R G GE M /

(~

) ( ) (~

( , ))G G Q G QE E E2 2

YF Q

G M2

32

01 1

1

( )( ) (~

( , ))

Born Approximation Beyond Born Approximation

e+/e- x-section ratio

Rosenbluth non-linearity

this experiment

Two-Photon Exchange: theoretical predictions

Both theories describe Rosenbluth data but have opposite predictions for GE/GM

.

Hadronic calculations

•P.Blunden et al., Phys.Rev.C72: 034612 (2005) elastic (at the figure)

•S.Kondratyuk et al., Phys.Rev.Lett. 95: 172503 (2005) including Delta reduces the effect

• S.Kondratyuk et al., nucl-th/0701003 (2007) including 1/2 and 3/2 resonances – no effect

GPD

A.Afanasev et al., Phys.Rev.D72:013008 (2005) – GPD models: Gauss (figure),

smaller effect with Regge, or non-zero quark mass

Valid at high region (vertical line at figure)

LO pQCD

N. Kivel and M. Vanderhaeghen arXiv:0905.0282 [hep-ph] LO pQCD using two different distribution amplitude models: BLW (good agreement with lattice QCD!) and COZ

Valid in high region (vertical line at figure)

Longitudinal transferred polarization: stability of the measurements

•open circles: this experiment

(hAyPl)meas/(Plborn Ay(

• filled circles – Moller measurements of beam polarization (h)

• open boxes (connected with line): beam polarization predicted from quantum efficiency measurements (Dave Gaskell, private comm.)

• 1.873 GeV beam energy, =0.15

• 2.846 GeV e=0.64

• 3.549 GeV e=0.78

•3.680 GeV e=0.79

PRELIMINARY

Beam polarization: dominant source of systematic error for PL measurements

Longitudinal transferred polarization: stability of the measurements

•open circles: this experiment

(hAyPl)meas/(Plborn Ay(

• filled circles – Moller measurements of beam polarization (h)

• open boxes (connected with line): beam polazrization predicted from quantum efficiency measurements (Dave Gaskell, private comm.)

• 1.873 GeV beam energy, =0.15

• 2.846 GeV e=0.64

• 3.549 GeV e=0.78

•3.680 GeV e=0.79

PRELIMINARY

Preliminary results: longitudinal polarization

Beam polarization p.t.p. systematics 0.5%

Uncertainties in the overall normalization of the data due to uncertainties in Ay

NO RADIATIVE CORRECTIONS APPLIED,

Less than 1% (Afanasev et.al, Phys.Rev. D64 (2001) 113009)

PRELIMINARY

PRELIMINARY

Preliminary results: form factor ratio

PRELIMINARY

NO RADIATIVE CORRECTIONS APPLIED,

Less than 1% (Afanasev et.al, Phys.Rev. D64 (2001) 113009)

Theoretical predictions are with respect to the Born approximation

Narrow acc. matching all kinematics

Wide acc. matching =0.64 and =0.79

GEP3 preliminary results: FF ratio

•Results at 2.5 and 5.2 GeV2 agree (within one sigma) with previous Hall A results

•No zero crossing; slower decrease with Q2

GEP3 results

• No evidence for the Q2 F2/F1 scaling

• Modified (logarithmic) scaling still holds

CONCLUSIONS

GEp-2: POLARIZATION METHOD PASSED THE TEST : no evidence for effects beyond Born approximation at 2% level in the polarization data at Q2 of 2.5 GeV2

Slight deviations from Born approximation at two sigma level both of longitudinal polarization and of form factor ratio require further investigations: possible “standard” radiative corrections, not applied yet

The preliminary results do not exclude with high confidence any of existing 2-exchange theoretical models; yet high- data favor GPD and pQCD models. Expected reduction of systematic error and especially, knowledge of Born FF ratio (from e+/e- experiments) will greatly help in constraining theoretical predictions.

Measuring two polarization observables for a fixed Q2 in a wide kinematical range with 1% precision allows to constrain the real parts of both, ratio of the generalized electric to magnetic form factors, and the third non-Born amplitude contribution Y2, without model assumptions.

GEp-III: First high Q2 proton FF ratio measurements outside Hall A confirm previous results at one sigma level, though Hall C data possibly slightly higher

New FF ratio data up to 8.5 GeV2 exhibit slower decrease with Q2 (favoring existing VMD, GPD models) still consistent with modified (logarithmic) scaling of F2/F1; no zero crossing yet

Measurements above 8.5 GeV2 with 12 GeV machine are certainly very important

BACK-UP SLIDES

STARTING HERE

Elastic amplitude reconstruction

Three amplitudes (Re parts): R=Re(GE)/Re(GM), Y2, Re(GM) and Ay unknown

Plotted: Re(GM) (dPt/Pl,R), Y2g(Pt/Pl,R), Ay(Ay*Pl,R)

Three observables measured at

2.5 GeV2:

• Pt/Pl

• Ay*Pl

• d

Important note:

Elastic amplitude reconstruction is different from full Born / non-Born separation: need e+/e- data and triple polarization observables (M.P.Rekalo and E. Tomasi-Gustafsson Nucl.Phys.A740:271-286,2004)

Still here one can constrain the contribution from the third non-Born amplitude Y2.

PRELIMINARY

Background corrections

Two-Photon Exchange: theoretical predictions

Hadronic calculations

•P.Blunden et al., Phys.Rev.C72: 034612

(2005) elastic (Figure)

•S.Kondratyuk et al., Phys.Rev.Lett. 95:

172503 (2005) including Delta reduces the effect

• S.Kondratyuk et al., nucl-th/0701003 (2007) including 1/2 and 3/2 resonances – no effect

•Yu. Bystricky, E.A.Kuraev, E. Tomasi-Gustafsson

Phys. Rev. C75, 015207 (2007) structure function

method: 2effects small, higher orders change Rosenbluth slope (Figure)

•D.Borisuyk, A.Kobushkin arXiv:0804.4128: proton off-shell form factors are not needed to calculate TPE amplitudes

Two-Photon Exchange: theoretical predictions

•A.Afanasev et al., Phys.Rev.D72:013008 (2005) – GPD models: Gauss on Fig., smaller effect with Regge, or non-zero quark mass

Absolute correction to FF ratio Ge/Gm:

•slow Q2 variation, strong effects at low

• valid for high Q2 or high

GPD calculations

Analyzing Power

Polarization Method: Spin Transport

)1(Non-dispersive precessionDispersive precession )1(

to Reaction PlaneReaction Plane

2tan

2

)( e

p

ebeam

l

t

Mp

Ep

M

EE

P

P

G

G

TargetTarget

Longitudinal and transverse polarizations Pt and Pl are helicity dependent (transferred)

Normal polarization Pn is helicity independent; zero in Born approximation

GEp/GMp Crisis: asymptotic behavior

asymptoticpQCDconstF

FQ

GGF

GGF

EM

EM

.

)1(

1

1

22

2

1

Dirac and Pauli form factors:

Polarization Method: Systematics

P

P

P

S S S

S S S

S S S

P

P

P

nfp

tfp

lfp

nn n t n l

tn tt tl

lt ll

n

t

l

ln

S n t s in cos s in cos s in cos

S n l cos s in

S tt cos cos

S tl s in

dS

d t

e

mS

gB

gB

21

2

2||

dv

d t

e

mv B

B || 0

gf

21

( ) s in ( ) ( ) ( ) s ins s fd s fs

d fp0

Relate the evolution of the velocity (trajectory) to the evolution of the spin:

COSY

Geom. Approx.

Geometrical Approx.

( ) cos ( ) ( ) ( )( cos )s s fd s fs

d fp 0

1

High Q2 Measurements