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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 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
Electromagnetic Hadron Form Factors in Space and Time-like regions Egle Tomasi-GustafssonSaclay, France JLab, May 2, 2008 Egle TOMASI-GUSTAFSSON
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
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
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
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
Proton Form Factors Egle TOMASI-GUSTAFSSON
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: mGEpGMp Jlab E04-108/019 , NOW running ! Egle TOMASI-GUSTAFSSON
The Rosenbluth separation (1950) • Elasticepcross section (1g exchange) • point-like particle: Mott Linearity of the reduced cross section! Egle TOMASI-GUSTAFSSON
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
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
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
Neutron Form Factors Egle TOMASI-GUSTAFSSON
Neutron Form Factors Egle TOMASI-GUSTAFSSON
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
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
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
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
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
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
Nucleon models... • Skyrme Models (Soliton) • Vector Dominance Models (G-K, IJL…) • Perturbative QCD • (Relativistic) Constituent Quark Model • Di-quark models • GPD • …….. Egle TOMASI-GUSTAFSSON
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
Time-like region Egle TOMASI-GUSTAFSSON
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
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
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
Spin Observables Analyzing power, A Double spin observables Egle TOMASI-GUSTAFSSON
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
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
Perspectives in Time-Like region Frascati • GE = GM ? Panda Egle TOMASI-GUSTAFSSON
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
Towards a unified description of Hadron Form factorsto clarify: - zero of GEp - asymptotic properties - reaction mechanism Egle TOMASI-GUSTAFSSON
ComparisonBABAR-LEAR Analytical Expression for R(q2) Dispersion Relations (S. Pacetti) q2 (GeV2) Space-like Time-like Egle TOMASI-GUSTAFSSON
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
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
Reaction mechanism1g-2g interference Egle TOMASI-GUSTAFSSON
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
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
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
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
1g-2g interference M. P. Rekalo, E. T.-G. and D. Prout, Phys. Rev. C60, 042202 (1999) 1g 2g { { 1{g Egle TOMASI-GUSTAFSSON
The 1g-2g interference destroys the linearity of the Rosenbluth plot! Egle TOMASI-GUSTAFSSON
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
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
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
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
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
Symmetry relations • Differential cross section at complementary angles: The SUM cancels the 2g contribution: The DIFFERENCE enhances the 2g contribution: Egle TOMASI-GUSTAFSSON
Radiative Return (ISR) e+ +e- p + p + Egle TOMASI-GUSTAFSSON