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H adron form factor measurements at large momentum transfer

H adron form factor measurements at large momentum transfer. Egle Tomasi-Gustafsson IRFU, SPhN- Saclay , and IN2P3- IPN Orsay France. PLAN. Introduction What is new? Space - like region : new data at JLab Rosenbluth separation ( unpolarized scattering )

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H adron form factor measurements at large momentum transfer

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  1. Hadron form factor measurements at large momentum transfer EgleTomasi-Gustafsson IRFU, SPhN-Saclay, and IN2P3- IPN Orsay France Egle Tomasi-Gustafsson

  2. PLAN • Introduction • Whatis new? • Space-likeregion : new data atJLab • Rosenbluthseparation (unpolarizedscattering) • Recoil proton polarization • (A.I. Akhiezer and M.P. Rekalo in 1968) • Time-likeregion • Plans at PANDA • Global description in a widekinematicalregion • Asymptotics • Countingrules • Two photon exchange Egle Tomasi-Gustafsson

  3. Hadron Electromagnetic Form factors Characterize the internal structure of a particle ( point-like) Elastic form factors contain information on the hadron ground state. In a P- and T-invariant theory, the EM structure of a particle of spin S is defined by 2S+1 form factors. Neutron and proton form factors are different. Deuteron: 2 structure functions, but 3 form factors. Playground for theory and experiment at low q2 probe the size of the nucleus, at high q2 test QCD scaling Egle Tomasi-Gustafsson

  4. e- e- q2<0 p p Electromagnetic Interaction The electron vertex isknown,gm The interaction iscarried by a virtual photon of mass q2 The proton vertex isparametrized in terms of FFs: Pauli and Dirac F1,F2 What about high order radiative corrections? or in terms of Sachs FFs: GE=F1-t F2, GM=F1+F2, t=-q2/4M2 Egle Tomasi-Gustafsson

  5. Crossing Symmetry Scattering and annihilation channels: - Described by the same amplitude : - function of two kinematical variables, sandt - which scan different kinematical regions k2→ – k2 p2→ – p2 Egle Tomasi-Gustafsson

  6. e- e- e+ p q2>0 q2<0 p e- p p Analyticity Space-like Asymptotics - QCD - analyticity Time-like GE(0)=1 GM(0)=mp p+p ↔ e++e-+p Unphysical region _ FFs are real FFs are complex _ q2=4mp2 q2 e+p  e+p p+p ↔ e++e- GE=GM Egle Tomasi-Gustafsson

  7. Proton Form Factors ...before Dipole approximation: GD=(1+Q2/0.71 GeV2)-2 Rosenbluth separation/ Polarization observables Egle Tomasi-Gustafsson

  8. Dipole Approximation • Classical approach • Nucleon FF (in the Breit system) are Fourier transform of the charge or magnetic distribution. Dipole approximation: GD=(1+Q2/0.71 GeV2)-2 • The dipole approximation corresponds to an exponential density distribution. • ρ = ρ0exp(-r/r0), • r02= (0.24 fm)2, <r2> ~(0.81 fm) 2  m2D=0.71 GeV2 Egle Tomasi-Gustafsson

  9. Dipole Approximation and pQCD Dimensional scaling • Fn(Q2)= Cn [1/( 1+Q2/mn) n-1], • mn=n2 , <quark momentum squared> • n is the number of constituent quarks • Setting 2 =(0.471±.010) GeV2(fitting pion data) • pion: F(Q2)= C[1/ (1+Q2/0.471 GeV2)1], • nucleon: FN(Q2)= CN [1/( 1+Q2/0.71GeV2)2], • deuteron: Fd(Q2)= Cd [1/( 1+Q2/1.41GeV2)5] V. A. Matveev, R. M. Muradian, and A. N. Tavkhelidze (1973), Brodsky and Farrar (1973), Politzer(1974), Chernyak & Zhitnisky (1984), Efremov & Radyuskin (1980)… Egle Tomasi-Gustafsson

  10. The Rosenbluth separation Q2fixed Linearity of the reduced cross section e • tan2qe dependence • Holds for 1g exchange only PRL 94, 142301 (2005) Egle Tomasi-Gustafsson

  11. Rosenbluth separation Contribution of the electric term =0.5 =0.8 …to becompared to the absolute value of the error on s and to the size and e dependenceof RC =0.2 Egle Tomasi-Gustafsson

  12. The polarization method (1967) The polarization induces a term in the cross section proportional to GE GM Polarized beam and target or polarized beam and recoil proton polarization Egle Tomasi-Gustafsson

  13. The polarization method (exp) The simultaneous measurement of Pt and Pl reduces the systematic errors C. Perdrisat et al, JLab-GEp collaboration Egle Tomasi-Gustafsson

  14. Polarization experiments - Jlab GEp collaboration • "standard" dipole function for the nucleon magnetic FFs GMp and GMn 2) linear deviation from the dipole function for the electric proton FF Gep 3) QCD scaling not reached 3) Zero crossing of Gep? 4) contradiction between polarized and unpolarized measurements A.I. Akhiezer and M.P. Rekalo, 1967 A.J.R. Puckett et al, PRL (2010) Egle Tomasi-Gustafsson

  15. Issues • Some models (IJL 73, Di-quark, soliton..) predicted such behavior before the data appeared BUT • Simultaneous description of the four nucleon form factors... • ...in the space-like and in the time-like regions • Consequences for the light ions description • When pQCD starts to apply? • Source of the discrepancy Egle Tomasi-Gustafsson Kolomna, 11-VI-2010

  16. Neutron/proton form factors ratio GEn (Hall A) Egle Tomasi-Gustafsson

  17. The IA deuteron structure:S=1, T=0 • The nucleon • form factors: 2) The S (u) and D (w) deuteron wave function Egle Tomasi-Gustafsson

  18. GEn from the deuteron • GEn > GEp starting from 2-3 GeV2 ! E. T-G. and M. P. Rekalo, Europhys. Lett. 55, 188 (2001) Egle Tomasi-Gustafsson

  19. Iachello, Jakson and Landé (1973) ,ρ, * Isoscalar and isovector FFs Egle Tomasi-Gustafsson

  20. The nucleon form factors E. T.-G., F. Lacroix, Ch. Duterte, G.I. Gakh,EPJA (2005) Electric Magnetic VDM : IJL F. Iachello..PLB 43, 191 (1973) proton Hohler NPB 114, 505 (1976) Extended VDM (G.-K. 92): E.L.Lomon PRC 66, 045501 2002) Bosted PRC 51, 409 (1995) neutron Egle Tomasi-Gustafsson

  21. Time-like observables: | GE| 2 and | GM| 2 . A. Zichichi, S. M. Berman, N. Cabibbo, R. Gatto, Il NuovoCimento XXIV, 170 (1962) B. Bilenkii, C. Giunti, V. Wataghin, Z. Phys. C 59, 475 (1993). G. Gakh, E.T-G., Nucl. Phys. A761,120 (2005). As in SL region: - Dependence on q2 contained in FFs - Even dependence on cos2q (1g exchange) - No dependence on sign of FFs - Enhancement of magnetic term but TL form factors are complex! Egle Tomasi-Gustafsson

  22. Models in T.L. region proton VDM : IJL F. Iachello..PLB43 191 (1973) Extended VDM (G.-K. 92): E.L.Lomon PRC66 045501(2002) neutron ‘QCD inspired’ E. T-G., F. Lacroix, C. Duterte, G.I. Gakh EPJA 2005 Egle Tomasi-Gustafsson

  23. Spin Observables Analyzing power, A Double spin observables Egle Tomasi-Gustafsson

  24. Angular Distributions The form of the differential cross section: is equivalent to: Cross section at 900 Angular asymmetry E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001) Egle Tomasi-Gustafsson

  25. Models in T.L. Region (polarization) Ayy Ay Axx VDM : IJL Ext. VDM ‘QCD inspired’ Axz Azz Angular Asymmetry E. T-G., F. Lacroix, C. Duterte, G.I. Gakh, EPJA 2005 Egle Tomasi-Gustafsson

  26. Proton-Antiproton Annihilation SIS PANDA HESR • needof • highestrates • goodresolution • GoodParticleIdentification • Parameters of HESR • Injectionof p at 3.7 GeV • Slow synchrotron (1.5-14.5 GeV/c) • Storage ring forinternaltargetoperation • Luminosityupto L~ 2x1032 cm-2s-1 • Beam cooling (stochastic & electron) http://www-panda.gsi.de/ Egle Tomasi-Gustafsson

  27. Physical Background M. Sudol et al, arXiv:0907.4478 [nucl-ex] • 3 body reactions • kinematical constraints • PID • 2 body reactions (hadrons) • π+π-, K+K- High statistics GEANT4 simulations • < few 0/00misidentified events / cosCMbin • < 1% on the total cross section up to 16 GeV2 It is possible to discriminatee+e-fromπ+ π- 27 Egle Tomasi-Gustafsson

  28. ExpectedResults L = 2  10 32cm-2 s-1 M. Sudol et al, EPJA 2010, arXiv:0907.4478 [nucl-ex] 100 jours R=GE/GM BaBAR Individual determination of GE and GM up to large Q2 PS170 PANDA sim Egle Tomasi-Gustafsson

  29. Phragmèn-Lindelöf theorem Asymptotic properties for analytical functions If f(z) a as z along a straight line, and f(z) b as z along another straight line, and f(z) is regular and bounded in the angle between, then a=b and f(z) a uniformly in the angle. D=0.05, 0.1 E. T-G. and G. Gakh, Eur. Phys. J. A 26, 265 (2005) Egle Tomasi-Gustafsson

  30. Phragmèn-Lindelöf theorem Connection with QCD asymptotics? Applies to NN and NN Interaction (Pomeranchuk theorem) t=0 : not a QCD regime! E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001) E. T-G. e-Print: arXiv:0907.4442 [nucl-th] Egle Tomasi-Gustafsson

  31. Radiative Corrections (ep) Andivahiset al., PRD50, 5491 (1994) Q2=1.75 GeV2 May change the slope of sR (and even the sign!!!) Q2=5 GeV2 Q2=3.75 GeV2 • RC to the cross section: • - large (mayreach 40%) • e and Q2dependent • -calculatedat first order E. T.-G., G. Gakh, PRC 72, 015209 (2005) Egle Tomasi-Gustafsson

  32. Scattered electron energy final state emission Initial state emission Quasi-elastic scattering 3% Not so small! Y0 Shift to LOWER Q2 All orders of PT needed  beyond Mo & Tsai approximation! Egle Tomasi-Gustafsson

  33. Short history (I) Schwinger: corrections to cross section for electron scattering in external field • s=s0(1+d) (1) • Yennie, Frauchi, Suura: cross section of any pure process (without real photon emission) is zero. • Kessler, Ericsson, Baier, Fadin, Khoze, Y. Tsai : quasi real electron method. Emission of hard photon is described in terms of a convolution of a radiative function with Born cross section. •  (1) Not adequate Egle Tomasi-Gustafsson

  34. The Structure Function Method E. A. K. and V.S. FADIN, Sov. J. of Nucl. Phys. 41, 466 (1985) Distinguish: -leading contributions of higher order -non leading ones • The SF methodisbased on: • Renormalization group evolutionequation • Drell-Yan parton picture of the cross section in QCD Electron SF: probability to ‘find’ electron in the initial electron, with energy fractionx and virtuality up to Q2 Egle Tomasi-Gustafsson

  35. LSF: ‰ precision E. A. K. and V.S. FADIN, Sov. J. of Nucl. Phys. 41, 466 (1985) LLA (Leading Logarithm Approximation) Precision of LLA Including K-factor Even when corrections in first order PT ared~100%, the accuracy of higher order RC (LSF) isa/p d1% ! Egle Tomasi-Gustafsson

  36. The LSF cross section (for ep ) • If the electronisdetected in a calorimeter: the cross section isintegrated over the scatteredelectronenergy fraction: • The K-factor includes all non leading contributions: Egle Tomasi-Gustafsson

  37. QED Radiative Corrections and DVCS Q2=2.3 GeV2 Helicity asymmetry xBj=0.36 Charge asymmetry RC Born V.V. Bytev, E.A. Kuraev, E.T.G., Phys.Rev.C77:055205,2008. Egle Tomasi-Gustafsson

  38. Unpolarized cross section • Induces four new terms • Odd function of q: • Does not contribute at q =90° Two Photon Exchange: M.P. Rekalo and E. T.-G., EPJA 22, 331 (2004) G.I. Gakh and E. T.-G., NPA761, 120 (2005) Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  39. Symmetry relations • Properties of the TPE amplitudes with respect to the transformation: cos  = - cos  i.e.,    -  (equivalent to non-linearity in Rosenbluth fit) • Based on these properties one can remove or single out TPE contribution E. T.-G., G. Gakh, NPA (2007) Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  40. Symmetry relations (annihilation) • Differential cross section at complementary angles: The SUM cancels the 2g contribution: The DIFFERENCE enhances the 2g contribution: Egle Tomasi-Gustafsson

  41. Simulations q2=5.4,8.2,13.8 GeV2 Main effect: oddcosq-distribution • Approximations: • Neglect contributions to GE,GM • Consideronly real part Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  42. Fitting the angulardistributions... The form of the differential cross section: is equivalent to: Cross section at 900 Angular asymmetry E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001) Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  43. Fitting the angulardistributions... 1 g exchange: Linear Fit incos2q 2 g exchange Quadratic Fit inx=cosq E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001) Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  44. Fitting the angular distributions... q2=5.4 GeV2 2g 0 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  45. Fitting the angular distributions... q2=5.4 GeV2 2g 0.02 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  46. Fitting the angular distributions... q2=5.4 GeV2 2g 0.05 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  47. Fitting the angulardistributions… q2=5.4 GeV2 2g 0.20 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  48. 1g 2g 0.05 0.20 0.02 q2=5.4 GeV2 q2= 8.2 GeV2 q2=13.8 GeV2 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  49. N=a0+a2cosq sinq+a1 cos2q, a2~2g Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  50. Gep III results (2010) BystritskiySF No radiative corrections applied to the data No evidence of two photon effects Egle Tomasi-Gustafsson

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