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Proton Form Factor Measurements with Polarization Method

Proton Form Factor Measurements with Polarization Method. L.Pentchev The College of William and Mary For the GEp-2 g and GEp-III collaborations. JLab , June 8-10, 2009. Outline. GEp-III (E04-108) and GEp-2 g (E04-019) experiments

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Proton Form Factor Measurements with Polarization Method

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  1. Proton Form Factor Measurements with Polarization Method L.Pentchev The College of William and Mary For the GEp-2g and GEp-III collaborations JLab , June 8-10,2009

  2. Outline • GEp-III (E04-108) and GEp-2g (E04-019) experiments • Polarization transfer method, experimental set-up, kinematics • Elastic/background separation • Spin transport in HMS • GEp-2g experiment: precise (1%) measurement of two polarization quantities; test of the limits of Born approximation in polarization method • 2g exchange theoretical calculations • Longitudinal transferred polarization (preliminary results), beam polarization measurements • e-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

  3. Polarization Method 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. 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)

  4. GEP-3 and GEP-2gamma experimental set-up in Hall C e e’ Big E.M. Calorimeter p High Momentum Spectrometer Double Focal Plane Polarimeter 1.87- 5.71 GeV beam 80-100 mA beam current 80-85% pol. 20cm LH target

  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 • GEp-2gamma: e dependence of R at 2.5 GeV2 • KEY IDEA OF THE METHOD: FIXED Q2 • same spin transport • same analyzing power Two polarization observables are measured: Pt/Pl and Pl separately 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 • GEp-3: high Q2 measurements • 5.2 GeV2 point “overlapping” with GEp-II (4.0 and 5.6 GeV2) • two higher Q2 points

  7. Data analyses: elastic separation All triggers Elastics after BigCal-HMS correlations Estimated background Range used in analyses 2.5 GeV2 e=0.15 8.5 GeV2e=0.24 s=0.10% s=0.11% Background contribution: 0.5% Correction to mR: +0.35% Background contribution: 13% Absolute correction to mR: +0.10 • (PCAL-PHMS)/P0 gives better resolution then (Pqp-PHMS)/P0, because of worse HMS angular resolution • Background estimated by interpolation, dominated by g p -> p0 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 (p0 -> gg)

  8. Spin transport in HMS QQQD type spectrometer: rotations are additive in the quads and total precession is sum of dispersive (main) and non-dispersive precession: Dispersive precession Non-dispersive precession Allows to use simple geometrical model, giving results very similar to COSY calculations used for the results presented here • 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 Df • uncertainty of Df used for the preliminary analyses of 1mrad • using dedicated optical studies, we expect to reduce the uncertainty by factor of ~3 2.5 GeV2 e=0.15

  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-2g: 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) this experiment e+/e- x-section ratio Rosenbluth non-linearity Born Approximation Beyond Born Approximation 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)

  12. Two-Photon Exchange: theoretical predictions • 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 e 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 e region (vertical line at figure) . Both theories describe Rosenbluth data but have opposite predictions for mGE/GM

  13. Longitudinal transferred polarization: stability of the measurements Beam polarization: dominant source of systematic error for PL measurements PRELIMINARY • open circles: this experiment • (hAyPl)meas/(Plborn Ay(q)) • 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, e=0.15 • 2.846 GeV e=0.64 • 3.549 GeV e=0.78 • 3.680 GeV e=0.79

  14. Longitudinal transferred polarization: stability of the measurements • open circles: this experiment • (hAyPl)meas/(Plborn Ay(q)) • 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, e=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 PRELIMINARY PRELIMINARY NO RADIATIVE CORRECTIONS APPLIED, Less than 1% (Afanasev et.al, Phys.Rev. D64 (2001) 113009) Uncertainties in the overall normalization of the data due to uncertainties in Ay Beam polarization p.t.p. systematics 0.5%

  16. Preliminary results: form factor ratio PRELIMINARY Narrow acc. matching all kinematics Wide acc. matching e=0.64 and e=0.79 Theoretical predictions are with respect to the Born approximation NO RADIATIVE CORRECTIONS APPLIED, Less than 1% (Afanasev et.al, Phys.Rev. D64 (2001) 113009)

  17. 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

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

  19. CONCLUSIONS • GEp-2g: 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 2g-exchange theoretical models; yet high-e 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 Y2g, 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

  20. BACK-UP SLIDES STARTING HERE

  21. Elastic amplitude reconstruction • Three observables measured at 2.5 GeV2: • Pt/Pl • Ay*Pl • ds PRELIMINARY 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 Y2g. Three amplitudes (Re parts): R=mRe(GE)/Re(GM), Y2g,Re(GM) and Ay unknown Plotted: Re(GM) (ds, Pt/Pl,R), Y2g(Pt/Pl,R), Ay(Ay*Pl,R)

  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: 2g effects small, higher orders change Rosenbluth slope (Figure) • D.Borisuyk, A.KobushkinarXiv:0804.4128: proton off-shell form factors are not needed to calculate TPE amplitudes

  24. Two-Photon Exchange: theoretical predictions GPD calculations • Absolute correction to FF ratio mGe/Gm: • slow Q2 variation, strong effects at low e • valid for high Q2 or high e • A.Afanasev et al., Phys.Rev.D72:013008 (2005) – GPD models: Gauss on Fig., smaller effect with Regge, or non-zero quark mass

  25. Analyzing Power

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

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

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

  29. High Q2 Measurements

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