1. 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

2. 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 Q 2 Preliminary results Comparison with theoretical calculation, asymptotic behavior Summary

3. Polarization Method 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) In Born (one-photon exchange) approximation : 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.

4. 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’ p High Momentum Spectrometer Double Focal Plane Polarimeter Big E.M. Calorimeter

5. Detectors Changes 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

6. Goal of The Experiments E e, GeVp Ee’Ee’  p, deg ee  range 1.8672.0680.52714.49105.130-.1602.5 2.8392.0681.50730.9845.3.611-.6472.5 3.5492.0682.20735.3932.9.765-.7862.5 3.6502.0682.30736.1431.7.772-.7982.5 KEY IDEA OF THE METHOD: FIXED Q 2 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 Q 2 fixed, Pp fixed, spin precession fixed Two polarization observables are measured: Pt/Pl and Pl separately GEp-2gamma:  dependence of R at 2.5 GeV 2 GEp-3: high Q 2 measurements E e, GeVp Ee’Ee’  p, deg ee  4.0533.5891.27417.9460.3.3775.2 5.7144.4642.09019.1044.2.5076.8 5.7145.4071.16411.669.0.2368.5 5.2 GeV 2 point “overlapping” with GEp-II (4.0 and 5.6 GeV 2 ) two higher Q 2 points

7. Data analyses: elastic separation All triggers Elastics after BigCal-HMS correlations Estimated background Range used in analyses 2.5 GeV 2  =0.15 8.5 GeV 2  =0.24 (P CAL -P HMS )/P 0 gives better resolution then (P  p -P HMS )/P 0, 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%

8. Spin transport in HMS 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 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 GeV 2  =0.15 Allows to use simple geometrical model, giving results very similar to COSY calculations used for the results presented here

9. 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

10. 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

11. Generalized Form Factors (ep elastic amplitudes) 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) Born ApproximationBeyond Born Approximation e + /e - x-section ratio Rosenbluth non-linearity this experiment

12. Two-Photon Exchange: theoretical predictions Both theories describe Rosenbluth data but have opposite predictions for  G E /G M. 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)

13. 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 P L measurements

14. 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

15. 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

16. 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

17. GEP3 preliminary results: FF ratio Results at 2.5 and 5.2 GeV 2 agree (within one sigma) with previous Hall A results No zero crossing; slower decrease with Q 2

18. GEP3 results No evidence for the Q2 F2/F1 scaling Modified (logarithmic) scaling still holds

19. CONCLUSIONS GEp-2  : POLARIZATION METHOD PASSED THE TEST : no evidence for effects beyond Born approximation at 2% level in the polarization data at Q 2 of 2.5 GeV 2 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 Q 2 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 Q 2 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 GeV 2 exhibit slower decrease with Q 2 (favoring existing VMD, GPD models) still consistent with modified (logarithmic) scaling of F2/F1; no zero crossing yet Measurements above 8.5 GeV 2 with 12 GeV machine are certainly very important

20. BACK-UP SLIDES STARTING HERE

21. Elastic amplitude reconstruction Three amplitudes (Re parts): R=  Re(G E )/Re(G M ), Y2 , Re(G M ) and Ay unknown Plotted: Re(G M ) (d  Pt/Pl,R), Y2g(Pt/Pl,R), Ay(Ay*Pl,R) Three observables measured at 2.5 GeV 2 : 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

22. Background corrections

23. 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 : 2  effects 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 amplitudesarXiv:0804.4128

24. 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 Q 2 variation, strong effects at low  valid for high Q 2 or high  GPD calculations

26. Analyzing Power

27. Polarization Method: Spin Transport Non-dispersive precession Dispersive precession to Reaction Plane Reaction Plane Target Longitudinal and transverse polarizations Pt and Pl are helicity dependent (transferred) Normal polarization Pn is helicity independent; zero in Born approximation

28. GEp/GMp Crisis: asymptotic behavior Dirac and Pauli form factors :

29. Polarization Method: Systematics Relate the evolution of the velocity (trajectory) to the evolution of the spin: COSY Geom. Approx. Geometrical Approx.

30. High Q2 Measurements