Proton Form Factor Measurements Using Recoil Polarization: Beyond Born Approximation

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Proton Form Factor Measurements Using Recoil Polarization: Beyond Born Approximation. L.Pentchev The College of William and Mary. Trieste, May 12-16, 2008. Outline. Introduction GEp crisis: 8 years history Experimental Status Polarization transfer method vs Rosenbluth separation
Proton Form Factor Measurements Using Recoil Polarization: Beyond Born ApproximationL.PentchevThe College of William and MaryTrieste, May 12-16,2008Outline
  • Introduction
  • GEp crisis: 8 years history
  • Experimental Status
  • Polarization transfer method vs Rosenbluth separation
  • Beyond Born Approximation: theoretical predictions
  • GEP-2gamma experiment at JLab: precise (1%) measurement of two polarization quantities; test of the limits of the polarization method
  • Preliminary results
  • Reconstruction of the real part of the ep elastic amplitudes
  • Summary
  • Introduction Nucleon structure as revealed by elastic electron scattering, investigated experimentally and theoretically for over 50 yearsForm factor data of great interest as a testing ground for QCD: lattice QCD becomes increasingly accurate and realistic; testing asymptotic pQCD predictionsAs first GPD moments, form factors measured precisely, provide stringent constraints on the GPD parameterizations Sachs form factors, GE and GM , traditionally obtained by Rosenbluth separation: GM known up to 30 GeV2 but due to decreasing contribution to the cross-section, GE suffers from inconsistency in the dataSignificant theoretical and experimental efforts have been made over the past 8 years aiming to explain the discrepancy between the proton form factor ratio data obtained at JLab using the polarization method and the previous Rosenbluth measurementsGEp/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 andM.VanderhaeghenEvolution of Polarization MethodElectron Spectrometer (HRS)E.M. calorimeterebeampProton spectrometer (HRS)POLARIMETER Polarization MethodIn 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)Discrepancy at fixed Q2Q2 = 2.64 GeV 2Experimental Status
  • Polarization method
  • Experimental errors are well understood
  • Experimental errors are small and can’t explain the discrepancy between Rosenbluth and polarization measurements; it would require significant uncertainties in the trajectory bending angles, totally inconsistent with the optical studies
  • Consistency of different measurements:
  • two experiments in HallA (GEP-1 and GEP-2) overlapping at 3.5 GeV2
  • ongoing GEP-3/GEP-2Gamma experiments using different (HallC) detectors; overlapping measurements at 2.5, 2.7 and 5.2 GeV2
  • Rosenbluth method
  • JLab experiment (Super Rosenbluth) confirmed previous SLAC results: registering proton instead of electron; different radiative corrections
  • Recent JLab experiment collected data over large Q2 and e range
  • The method has reduced sensitivity for Q2 > ~3 GeV2
  • NO EXPERIMENTAL EXPLANATION OF THE DISCREPANCY FOUNDBeyond Born ApproximationMo 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)this experimente+/e- x-section ratioRosenbluth non-linearityBorn ApproximationBeyond Born ApproximationP.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)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
  • Two-Photon Exchange: theoretical predictionsGPD 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
  • Two-Photon Exchange: theoretical predictionshadronic (elastic): dominated by correction to GMGPD (includes inelastic): dominated by Y2g and correction to GEBoth theories describe Rosenbluth data but have opposite predictions for mGE/GM. Goal of This Experiment: e dependence of R at 2.5 GeV2
  • same spin transport
  • same analyzing power
  • Two polarization observables are measured: Pt/Pl and Pl separatelyee’Big E.M. Calorimeter80 uA beam current85% pol.20cm LH targetpHigh Momentum SpectrometerDouble Focal Plane Polarimeterprecision limited only by statistics(~ 1%), unlike Rosenbluth,very small p.t.p systematics:Ay , h cancel out in the Pt/Pl ratioQ2 fixed, Pp fixed, spin precession fixedDetectorsFocal Plane Polarimeter with double Analyzer1744 channel E.M. CalorimeterData analyses: elastic separationAll triggersInelasticsElastics after ep kinematical correlationEstimated backgroundCircles –longitudinal asymmetry at target Boxes – transverse asymmetry at targetBackground contribution max of 0.5% for e=0.15 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 results: longitudinal polarizationPRELIMINARYUncertainties in the overall normalization of the data due to uncertainties in AyNO RADIATIVE CORRECTIONS APPLIED, Less than 1% (Afanasev, Phys.Rev. D64 (2001) 113009)Beam polarization p.t.p. systematics 0.5%Preliminary results: form factor ratioPRELIMINARYTheoretical predictions are with respect to the Born approximationNO RADIATIVE CORRECTIONS APPLIED, Less than 1% (Afanasev, Phys.Rev. D64 (2001) 113009)Elastic amplitude reconstructionPRELIMINARY
  • Three observables measured at 2.5 GeV2:
  • Pt/Pl
  • Ay*Pl
  • ds
  • Three amplitudes (Re parts): R=mRe(GE)/Re(GM), Y2g,Re(GM) and Ay unknownPlotted: Re(GM) (ds, Pt/Pl,R), Y2g(Pt/Pl,R), Ay(Ay*Pl,R)Elastic Amplitude ReconstructionPRELIMINARYImportant 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. Y2g vs R=mRe(GE)/Re(GM) reconstructed from this experiment (1s area) GEP resultsGEP preliminary results at 2.5 and 5.2 GeV2CONCLUSIONS
  • POLARIZATION METHOD PASSED THE TEST : no evidence for effects beyond Born approximation at 1% level in the polarization data at Q2 of 2.5 GeV2
  • Slight deviation from Born approximation at a two sigma level for longitudinal polarization requires attention
  • Discrepancy between Rosenbluth and polarization method
  • No experimental explanation was found
  • Radiative corrections (two-photon exchange and/or higher order corrections) are the most likely candidate but it requires further experimental and theoretical investigation
  • 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. Including precise cross-section data will constrain also the real part of the magnetic form factor.
  • Preliminary resultsNo radiative corrections applied (<1%)BACK-UP SLIDESSTARTING HEREGEP-2G goals: e dependence of pt, pl at Q2=2.5 GeV2
  • p.t.p. sytematic uncertainties:
  • 1% beam polarization
  • 0% analyzing power :
  • Q2 fixed, pp fixed, Ay fixed
  • 0.75% absolute systematic error: (0.45% non-dispersive bend angle, 0% dispersive (1080 prec. angle), 0.3% FPP chambers misalignment)
  • Analyzing Power Polarization Method: Spin Transport Non-dispersive precessionDispersive precessionTargetTargetto Reaction PlaneReaction PlaneLongitudinal and transverse polarizations Pt and Pl are helicity dependent (transferred) Normal polarization Pn is helicity independent; zero in Born approximationGEp/GMp Crisis: asymptotic behavior Dirac and Pauli form factors: Polarization Method: Systematics Relate the evolution of the velocity (trajectory) to the evolution of the spin:COSYGeom. Approx.Geometrical Approx. Rosenbluth methodQ2=2.64Q2=3.2Q2=4.1The real FPPHigh Q2 MeasurementsE.M. calorimetereebeamppMagnetPOLARIMETERProton spectrometer (HRS)HCALPOLARIMETERGeP-15 (E12-07-109) Large Acceptance Proton Form Factor Measurements at 13 and 15 GeV2 Using Recoil Polarization Method, C.Perdrisat, L.Pentchev, E.Cisbani, V.Punjabi, B.WojtsekhowskiHigh Q2 Measurements
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