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Proton Form Factors

Proton Form Factors. Q 2 ≤ 1 GeV 2. F1. F2. Over a period of time lasting at least 2000 years, Man has puzzled over and sought an understanding of the composition of matter…. Electromagnetic Hadron Form Factors in Space and Time-like regions. Egle Tomasi-Gustafsson Saclay, France.

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Proton Form Factors

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  1. Proton Form Factors Q2≤1 GeV2 F1 F2 Over a period of time lasting at least 2000 years, Man has puzzled over and sought an understanding of the composition of matter… Egle TOMASI-GUSTAFSSON

  2. Electromagnetic Hadron Form Factors in Space and Time-like regions Egle Tomasi-GustafssonSaclay, France JLab, May 2, 2008 Egle TOMASI-GUSTAFSSON

  3. PLAN Experimental view: • space-like (ep-scattering) • time-like (e+e- or pp annihilation) Model Independent Statements • Symmetry properties of fundamental interactions • Kinematical constraints Models and ‘exact’ calculations Radiative corrections Egle TOMASI-GUSTAFSSON

  4. 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 protonform factors are different. • Deuteron: 2 structure functions, but 3 form factors. • Playground for theory and experiment. Egle TOMASI-GUSTAFSSON

  5. Space-like and time-like regions • FFs are analytical functions. • In framework of one photon exchange, FFs are functions of the momentum transfer squared of the virtual photon, t = q2 = -Q2. t<0 t>0 Scattering Annihilation _ _ e- + h => e- + h e+ + e- => h+ h Form factors are real in the space-like region complex in the time-like region. Egle TOMASI-GUSTAFSSON

  6. 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

  7. Proton Form Factors Egle TOMASI-GUSTAFSSON

  8. Proton Form Factors Ratio SLAC Rosenbluth L. Andivahis PRD50,5491 (1994) Jlab Super Rosenbluth I.A. Qattan et al.PRL 94 142301 (2005) POLARIZATION Exp Jlab E93-027 , E99-007 Spokepersons:Ch. Perdrisat, V. Punjabi, M. Jones, E. Brash M. Jones et al., Phys. Rev. Lett. 84,1398 (2000) O. Gayou et al., Phys. Rev. Lett. 88,092301 (2002) V. Punjabi et al., Phys. Rev. C 71, 055202 (2005) Linear deviation from dipole: mGEpGMp Jlab E04-108/019 , NOW running ! Egle TOMASI-GUSTAFSSON

  9. The Rosenbluth separation (1950) • Elasticepcross section (1g exchange) • point-like particle:  Mott Linearity of the reduced cross section! Egle TOMASI-GUSTAFSSON

  10. The Rosenbluth separation The dynamics is contained in FFs t, Q2 The kinematics : energies, angles The reaction mechanism? Holds for 1gexchange only Egle TOMASI-GUSTAFSSON

  11. Rosenbluth separation Contribution of the electric term =0.5 =0.8 …to be compared to the absolute value of the error on s and to the size and e dependence of RC =0.2 • E.T-G, Phys. Part. Nucl. Lett. 4, 281 (2007) 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. Neutron Form Factors Egle TOMASI-GUSTAFSSON

  14. Neutron Form Factors Egle TOMASI-GUSTAFSSON

  15. The reaction d(e,e’n)p - Ax g* + d n + p FSI Select quasi-elastic kinematics Pol electron beam, pol target or neutron polarimeter Large dependence of asymmetry on GEn! GEn DWF GEp G.I. Gakh, A. P. Rekalo, E. T.-G. Annals of Physics 319, 150 (2005) Egle TOMASI-GUSTAFSSON

  16. The reaction d(e,e’n)p - Ax • The KHARKOV model: • - Impulse Approximation • - Deuteron structure • - Kinematics: proton spectator • - Polarization observables G.I. Gakh, A. P. Rekalo, E. T.-G. Annals of Physics 319, 150 (2005) Egle TOMASI-GUSTAFSSON

  17. The reaction d(e,e’n)p – Ax/Az GEn g* + d n + p Asymmetry ratio DWF Does not depend on beam helicity FSI A(0,1):T –LT SFs(W,Q2,q*) Generalization of the polarization method E.T-G., G.I. Gakh, A. P. Rekalo, M. P. Rekalo, PRC70,025202 (2004) Egle TOMASI-GUSTAFSSON

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

  19. The nucleon form factors E. T.-G., F. Lacroix, Ch. Duterte, G.I. Gakh, EPJA 24, 419 (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

  20. STATUS on EM Form factors Space-like region • "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) contradiction between polarized and unpolarized measurements 4) non vanishing electric neutron FF, GEn. Egle TOMASI-GUSTAFSSON

  21. Nucleon models... • Skyrme Models (Soliton) • Vector Dominance Models (G-K, IJL…) • Perturbative QCD • (Relativistic) Constituent Quark Model • Di-quark models • GPD • …….. Egle TOMASI-GUSTAFSSON

  22. The nucleon form factors E. T.-G., F. Lacroix, Ch. Duterte, G.I. Gakh, EPJA 24, 419 (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

  23. Time-like region Egle TOMASI-GUSTAFSSON

  24. Time-like observables: | GE| 2 and | GM| 2 . A. Zichichi, S. M. Berman, N. Cabibbo, R. Gatto, Il Nuovo Cimento 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

  25. Time-Like 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 24, 419 (2005) Egle TOMASI-GUSTAFSSON

  26. STATUS on EM Form factors Time-like region • No individual determination of GE and GM • Assume GE=GM (valid only at threshold) VMD or pQCD inspired parametrizations (for p and n): 3) TL nucleon FFs are twice larger than SL FFs 4) Recent data fromBabar (radiative return) : • interesting structures in the Q2 dependence of GM(=GE) • GM≠GE. A(p)= 56.3 GeV4 A(n)= 77.15 GeV4 L=0.3 GeV is the QCD scale parameter Egle TOMASI-GUSTAFSSON

  27. Spin Observables Analyzing power, A Double spin observables Egle TOMASI-GUSTAFSSON

  28. Models in T.L. Region (polarization) Ayy Ay Axx VDM : IJL Ext. VDM ‘QCD inspired’ Axz Azz R E. T-G., F. Lacroix, C. Duterte, G.I. Gakh, EPJA 24, 419(2005) Egle TOMASI-GUSTAFSSON

  29. Time-Like Region: GE versus GM | GM| 2 Cross section at 900 GE=0 Asym GE=GM GE=GD E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001) Egle TOMASI-GUSTAFSSON

  30. Perspectives in Time-Like region Frascati • GE = GM ? Panda Egle TOMASI-GUSTAFSSON

  31. Facilty for Antiproton and Ion Research (GSI, Darmstadt, Germany) • Proton linac (injector) • 2 synchrotons (30 GeV p) • A number of storage rings •  Parallel beams operation Physics Polarization Staging Signals Timeline

  32. Towards a unified description of Hadron Form factorsto clarify: - zero of GEp - asymptotic properties - reaction mechanism Egle TOMASI-GUSTAFSSON

  33. ComparisonBABAR-LEAR Analytical Expression for R(q2) Dispersion Relations (S. Pacetti) q2 (GeV2) Space-like Time-like Egle TOMASI-GUSTAFSSON

  34. 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

  35. Phragmèn-Lindelöf theorem Connection with QCD asymptotics? GM (TL) Applies to NN and NN Interaction (Pomeranchuk theorem ): t=0 : not a QCD regime! GM (SL) GE (SL) E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001) Egle TOMASI-GUSTAFSSON

  36. Reaction mechanism1g-2g interference Egle TOMASI-GUSTAFSSON

  37. Two-photon exchange Different results with different experimental methods !! - Both methods based on the same formalism - Experiments repeated New mechanism? • 1g-2g ~ a=e2/4p=1/137 • 1970’s: Gunion, Lev… Egle TOMASI-GUSTAFSSON

  38. e± + p→ e±+ p • 4 spin ½ fermions →16 amplitudes in the general case. • T-invariance of EM interaction, • identity of initial and final states, • helicity conservation, • unitarity • Two EM form factors • Real (in SL region) • Functions of one variable (t) • Describe e+ and e- scattering • Three structure functions • Complexe • Functions of TWO variables (s,t) • Different for e+ and e- scattering 1g exchange 2g exchange Egle TOMASI-GUSTAFSSON

  39. Model independent considerations for e± N scattering Determination of EM form factors, in presence of 2g exchange: • electron and positron beams • - longitudinally polarized , • - in identical kinematical conditions, M. P. Rekalo, E. T.-G. , EPJA (2004), Nucl. Phys. A (2003) Egle TOMASI-GUSTAFSSON

  40. Model independent considerations for e± N scattering If no positron beam… Either three T-odd polarization observables…. • Ay: unpolarized leptons, transversally polarized target (or Py: outgoing nucleon polarization with unpolarized leptons, unpolarized target ) • Depolarization tensor (Dab): dependence of the b-componentof the final nucleon polarization on thea-component of the nucleon target with longitudinally polarized leptons ..or five T-even polarization observables…. among ds/dW, Px(le), Pz(le), Dxx, Dyy, Dzz, Dxz M. P. Rekalo, E. T.-G. , EPJA (2004), Nucl. Phys. A (2003) Egle TOMASI-GUSTAFSSON

  41. 1g-2g interference M. P. Rekalo, E. T.-G. and D. Prout, Phys. Rev. C60, 042202 (1999) 1g 2g { { 1{g Egle TOMASI-GUSTAFSSON

  42. The 1g-2g interference destroys the linearity of the Rosenbluth plot! Egle TOMASI-GUSTAFSSON

  43. 1g-2g interference (e-d) D/A C/A M. P. Rekalo, E. T-G and D. Prout, Phys. Rev. C60, 042202 (1999) Egle TOMASI-GUSTAFSSON

  44. Egle TOMASI-GUSTAFSSON

  45. Parametrization of 2g-contribution for e+p From the data: deviation from linearity << 1%! E. T.-G., G. Gakh, Phys. Rev. C 72, 015209 (2005) Egle TOMASI-GUSTAFSSON

  46. Two-Photon exchange • The 2g amplitude is expected to be mostly imaginary. • In this case, the 1g-2g interference is more important in time-like region, as the Born amplitude is complex. Egle TOMASI-GUSTAFSSON

  47. TL unpolarized cross section • Induces four new terms • Odd function of q: • Does not contribute at q =90° e+ +e- p + p 2g-contribution: E. T.-G., G. Gakh, NPA (2007) Egle TOMASI-GUSTAFSSON

  48. 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

  49. Symmetry relations • Differential cross section at complementary angles: The SUM cancels the 2g contribution: The DIFFERENCE enhances the 2g contribution: Egle TOMASI-GUSTAFSSON

  50. Radiative Return (ISR) e+ +e- p + p +  Egle TOMASI-GUSTAFSSON

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