Jaminion, S.

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Virtual Compton Scattering at Jefferson Lab :preliminary results at Q2 = 1. and 1.9 GeV2S. JaminionTo cite this version:S. Jaminion. Virtual Compton Scattering at Jefferson Lab : preliminary results at Q2 = 1.and 1.9 GeV2. Electromagnetic Interactions with Nucleons and Nuclei, Oct 2001, Santorini,Greece. pp.1-22, 2001. <in2p3-00010661>HAL Id: in2p3-00010661http://hal.in2p3.fr/in2p3-00010661Submitted on 5 Dec 2001HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.1Virtual Compton Scattering at JLab : Preliminary results Q2 = 1. and 1.9 GeV2Stephanie JaminionLPC, Universite Blaise PascalIN2P3-CNRSE93050 collaborationfor the hall A Collaboration of Jefferson Lab.SANTORINI 2001Electromagnetic Interactions with Nucleonsand Nuclei2-7 october 2001Santorini2001 jaminion@clermont.in2p3.fr2Virtual Compton Scattering below π0 thresholdhadronic system( ) 22   and   ' qQkkq −=−=pp γγ →∗Real Compton Scattering ( )02 =  , QβαVirtual Compton Scattering : ( )02 ≠  , Qβα + new observablesγ∗(q )p(p ) p’(p’)e(k ) e’(k’)γ (q’)Generalized Polarizabilitiesof the nucleon(γ p     γ p)goal : to constrain models of nucleon structure at low energy3Generalized PolarizabilitiesPhoton electroproduction is the coherent sum of 2 processesVCS : is emitted bynucleon : Born term entirely calculable(proton electromagnetic form factors :                      )excited state : Non Born term : UNKNOWNNBBBHep TTTT ++=γcalculable unknown (GPs)γPMPE GG andphoton electroproduction amplitude :=γ(q’)p’(p’)p(p)e(k) e’(k’)+ +*γ (q) *γ (q)*γ (q)Bethe-Heitler VCSSantorini2001 jaminion@clermont.in2p3.fr4P Guichon : develop amplitude in polynomial of q’cmLow Energy Theorem[ ] ( )2BBH55 '' cmcmBBHep qqdd OMM 00 +−Φ+= ++σσ γ(P. Guichon and M. Vanderhaegen, Prog.Part. Nucl. Phys.  41 (1998) 125)(F.E. Low, Phys. Rev. 96 (1954) 1428)(q’cm= outgoing photon momentum in            center mass)( )p*γphase space factor( )BBH+− 00 MM is the lowest order term containing an effect ofGeneralized Polarizabilities (know combination)6 GPs are needed to describe Tepγ(D.Drechsel et al, Phys. Rev. C55 (1997) 424)5 GPs in unpolarized case, and we extract two structure2given at   and1QPPP LTTTLL ε−Santorini2001 jaminion@clermont.in2p3.frfunctions5Photon electroproduction cross sectionSantorini2001 jaminion@clermont.in2p3.fr: Bosted parametrisation(P.E. Bosted, Phys. Rev. C51 (1995) 409)pMGpEG : ratio measured at Jefferson Lab :)()(22QGQGPMPEPµ10-310-210-1110-150 -100 -50 0 50 100 150D. Drechsel,M. Gorchtein,A. Metz,B. Pasquini,M. VanderhaegenDispersion Relation formalismBH+B cross section(M.K. Jones, et al, Phys. Rev. Lett. 84 (2000) 1398)[ ]°+°−∈ 100,260cmγγθ6VCS experiments1st experiment at Mami (1995-1997)(J. Roche, et al, Phys. Rev. Lett. 85 (2000) 708)2nd experiment at Jefferson Lab(march-april 1998)Generalized Polarizabilities atQ2 = 1 and 1.9 GeV2VCS in resonance region3rd experiment at BatesatQ2 = 0.05 GeV2(2000)4th experiment at Batesin resonance region (2001)Generalized Polarizabilities atQ2 = 0.33 GeV2Santorini2001 jaminion@clermont.in2p3.fr7Jefferson Lab : Hall A(4 GeV/c)beam targetHRS_eHRS_h(3 GeV/c)(1-2 GeV/c)Spectrometer resolution attarget(FWHM) :mrad 2:tgθmrad 6.0:tgφmm 5.1:tgy-410 1.: δdispersive angle (vertical)transverse angle(horizontal)transverse coordinaterelative momentumhttp:hallaweb.jlab.org/equipement/high_resol.htmlSantorini2001 jaminion@clermont.in2p3.fr8Missing mass for events in coincidenceelectron  and proton are  detected in coincidence γisa missing particleSantorini2001 jaminion@clermont.in2p3.frnn9VCS below π0threshold : momentum of outgoing photon MeV/c126'≤cmqKinematicconventions3 binsin q’ cm[][][] MeV/c120,90' MeV/c90,60' MeV/c60,30'∈∈∈cmcmcmqqq18 binsin in-plane angle θ γγcm02004006008001000120014000100200300γ∗(q     )cmin plane virtual photon50o30o10o02004006008001000120014001600-150-100-500501001503bin in out-of-plane angleSantorini2001 jaminion@clermont.in2p3.fr[0°:50°][50°:80°][80°:90°]and we have data aboveπ0threshold atQ2 =1 and 1.9 GeV210Santorini2001 jaminion@clermont.in2p3.frCross sectionandratio atQ2 =1. GeV2BH+Born (GPs=0)experimentalθγ∗γ cm   (deg)(d5σe-d5σBHB)/d5σBHBq , =45 MeV/cgreen: lepton +- 30o it1θγ∗γ cm   (deg)(d5σe-d5σBHB)/d5σBHBq , =75 MeV/cθγ∗γ cm   (deg)(d5σe-d5σBHB)/d5σBHBq , =105 MeV/c024 -250-200-150-100-50050100024 -250-200-150-100-50050100024 -250-200-150-100-50050100BBHBBHep ddd++− σσσγ 555θγ∗γ cm   (deg)d5σ (pb/MeV/sr2)q , =45 MeV/cQ2=1.0 GeV2      φ=0o   lepton +- 30o it2θγ∗γ cm   (deg)d5σ (pb/MeV/sr2)q , =75 MeV/cθγ∗γ cm   (deg)d5σ (pb/MeV/sr2)q , =105 MeV/c10-210-11 -250-200-150-100-5005010010-210-11 -250-200-150-100-5005010010-210-11 -250-200-150-100-5005010011Cross sectionandratio atQ2 =1.9 GeV2BH+Born (GP s=0)Q2=1.9 Gev2.  d5 σ(EP→EPγ)/dk, dΩe,lab dΩγγ,cm10-310-210-1-250-200-150-100-5005010010-310-210-1-250-200-150-100-5005010010-310-210-1-250-200-150-100-50050100Q2=1.9 GeV2. (Exp-BHB)/BHB  (BHB=BetheHeitler+Born)-1-0.500.51-250-200-150-100-50050100-1-0.500.51-250-200-150-100-50050100-1-0.500.51-250-200-150-100-50050100BBHBBHep ddd++− σσσγ 555experimentalSantorini2001 jaminion@clermont.in2p3.fr12θγ∗γ cm   (deg)d5σ (pb/MeV/sr2)q , =45 MeV/cQ2=1.0 GeV2      φ=0o   lepton it1θγ∗γ cm   (deg)d5σ (pb/MeV/sr2)q , =75 MeV/cθγ∗γ cm   (deg)d5σ (pb/MeV/sr2)q , =105 MeV/c10-210-11 -250-200-150-100-5005010010-210-11 -250-200-150-100-5005010010-210-11 -250-200-150-100-50050100Dispersion Relation FormalismBH+Born (GPs=0)Cross section atQ2 =1. GeV2andQ2 =1.9 GeV2 Santorini2001 jaminion@clermont.in2p3.fr13Virtual Comton Scattering in resonance regionSantorini2001 jaminion@clermont.in2p3.frfor the Hall A collaboration1411.522.533.544.550.80.850.90.9511.051.11.151.2all off-plane angles()()2exp525exp5121σσσχdddNBBHN i∆−=+=∑Santorini2001 jaminion@clermont.in2p3.frGlobal normalization factor atQ2 =1.9 GeV215Santorini2001 jaminion@clermont.in2p3.fr[]()2BBH55''cmcmBBHepqqddOMM00+−Φ+=++σσγ()()()cmLTLTcmTTcmLLLLBBHqPvqPqPvMM+   −=−+ε100kinematiccoefficientsM0-M0BH+B: containsthe Generalized Polarizabilities0M ∆Generalized PolarizabilitiesPhoton electroproductioncross section five fold differential: 16Extrapolation at q’cm=0 MeV/c  atQ2 =1.9 GeV2belowπ0threshold:ordinate: abscissa: q’ cmcmBBHqddM'5exp5Φ−=∆+σσextrapolation by a constantSantorini2001 jaminion@clermont.in2p3.fr17atQ2 =1.0 GeV2atQ2 =1.9 GeV2Generalized Polarizabilities extractionSantorini2001 jaminion@clermont.in2p3.fr                        18Santorini2001 jaminion@clermont.in2p3.frPreliminaryvalues of Generalized Polarizabilities                        1.9Q  (GeV )22Q  (GeV )221.911=0.95ε=0.88ε=0.62ε=0.9ε[+0.2, +0.8] +/-  0.08 (stat)[-0.3, +0.1] +/-  0.05 (stat)[-2, -1] +/-  0.3 (stat)[+4, +7] +/-  0.7 (stat)JLab E93-050Gm proton: fromBosted param. Ge proton: fromJlabmuGe/Gm19Conclusionwehave todetermine the systematic errorsother approach using data below andabove π0thresholdtogetherwithdispersion relation formalismfirstextraction of Generalized Polarizabilities229.11at    and1GeVandQPPPLTTTLL=−εSantorini2001 jaminion@clermont.in2p3.fr20Santorini2001 jaminion@clermont.in2p3.fr∆M below and above π πππ0threshold21θγ∗γ cm   (deg)(d5σe-d5σBHB)/d5σBHBq , =45 MeV/cgreen: lepton +- 30o it1θγ∗γ cm   (deg)(d5σe-d5σBHB)/d5σBHBq , =75 MeV/cθγ∗γ cm   (deg)(d5σe-d5σBHB)/d5σBHBq , =105 MeV/c024 -250-200-150-100-50050100024 -250-200-150-100-50050100024 -250-200-150-100-50050100Ratio atQ2 =1.0 GeV2BBHBBHep ddd++− σσσγ 555experimentalDispersion Relation FormalismSantorini2001 jaminion@clermont.in2p3.fr22beamproton from VCSproton from (ep) elasticphoton from VCSphoton from(ep) elastic* γe’collimator

Virtual Compton Scattering at Jefferson Lab : preliminary results at Q $^2$ = 1. and 1.9 GeV $^2$

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Virtual Compton Scattering at Jefferson Lab : preliminary results at Q $^2$ = 1. and 1.9 GeV $^2$