Proton Form Factors Over a period of time lasting at least 2000 years, 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… JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Electromagnetic Hadron Form Factors in Space and Time-like regions Egle Tomasi-Gustafsson Saclay, France JLab, May 2, 2008 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 JLab, May 2,2008 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 proton form factors are different. Deuteron: 2 structure functions, but 3 form factors. Playground for theory and experiment. JLab, May 2,2008 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. JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Crossing Symmetry Scattering and annihilation channels: p2 → – p2 - Described by the same amplitude : - function of two kinematical variables, s and t - which scan different kinematical regions k2 → – k2 p2 → – p2 JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Proton Form Factors JLab, May 2,2008 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: mGEpGMp Jlab E04-108/019 , NOW running ! JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

The Rosenbluth separation (1950) Elastic ep cross section (1g exchange) point-like particle:  Mott Linearity of the reduced cross section! JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

The Rosenbluth separation The dynamics is contained in FFs  t, Q2 The kinematics : energies, angles The reaction mechanism?  Holds for 1g exchange only JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Rosenbluth separation Contribution of the electric term =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 =0.5 E.T-G, Phys. Part. Nucl. Lett. 4, 281 (2007) JLab, May 2,2008 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 JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Neutron Form Factors JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Neutron Form Factors JLab, May 2,2008 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) JLab, May 2,2008 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) JLab, May 2,2008 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) JLab, May 2,2008 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) JLab, May 2,2008 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 JLab, May 2,2008 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. JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Nucleon models... Skyrme Models (Soliton) Vector Dominance Models (G-K, IJL…) Perturbative QCD (Relativistic) Constituent Quark Model Di-quark models GPD …….. JLab, May 2,2008 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 JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Time-like region JLab, May 2,2008 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! JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Time-Like Region proton neutron VDM : IJL Extended VDM (G.-K. 92): 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) JLab, May 2,2008 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 from Babar (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 JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Spin Observables Double spin observables Analyzing power, A JLab, May 2,2008 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) JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Time-Like Region: GE versus GM Cross section at 900 GE=0 Asym GE=GM GE=GD E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001) JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Perspectives in Time-Like region Frascati GE = GM ? Panda JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Physics Polarization Staging Signals Timeline 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 factors to clarify: Towards a unified description of Hadron Form factors to clarify: - zero of GEp - asymptotic properties - reaction mechanism JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Comparison BABAR-LEAR Analytical Expression for R(q2) Dispersion Relations (S. Pacetti) q2 (GeV2) Space-like Time-like JLab, May 2,2008 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) JLab, May 2,2008 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) JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Reaction mechanism 1g-2g interference JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Two-photon exchange New mechanism? 1g-2g ~ a=e2/4p=1/137 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… JLab, May 2,2008 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 JLab, May 2,2008 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) JLab, May 2,2008 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-component of the final nucleon polarization on the a-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) JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

{ { 1g-2g interference 1g 2g 1{g M. P. Rekalo, E. T.-G. and D. Prout, Phys. Rev. C60, 042202 (1999) 1g 2g 1{g { { JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

The 1g-2g interference destroys the linearity of the Rosenbluth plot! JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

1g-2g interference (e-d) C/A D/A M. P. Rekalo, E. T-G and D. Prout, Phys. Rev. C60, 042202 (1999) JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

JLab, May 2,2008 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) JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

The 2g amplitude is expected to be mostly imaginary. 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. JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

TL unpolarized cross section e+ +e-  p + p 2g-contribution: Induces four new terms Odd function of q: Does not contribute at q =90° E. T.-G., G. Gakh, NPA (2007) JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

(equivalent to non-linearity in Rosenbluth fit) 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) JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Symmetry relations Differential cross section at complementary angles: The SUM cancels the 2g contribution: The DIFFERENCE enhances the 2g contribution: JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Radiative Return (ISR) e+ +e-  p + p +  JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Angular distribution Mpp=1.877-1.9 Mpp=2.4-3 JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Mpp=1.877-1.9 A=0.01±0.02 Mpp=2.4-3 E. T.-G., E.A. Kuraev, S. Bakmaev, S. Pacetti, Phys. Lett. B (2008) JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Radiative Corrections to the data - RC can reach 40% on s - Declared error ~1% Same correction for GE and GM - Have a large e-dependence - Affect the slope sel=smeas · RC slope Slope negative if : The slope is negative starting from 2-3 GeV2 JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Reduced cross section and RC Data from L. Andivahis et al., Phys. Rev. D50, 5491 (1994) Q2=1.75 GeV2 Q2=2.5 GeV2 Q2=3.25 GeV2 Q2=4 GeV2 Q2=5 GeV2 Q2=6 GeV2 Slope from P. M. Radiative Corrected data Q2=7 GeV2 Raw data without RC E. T.-G., G. Gakh, PRC 72, 015209 (2005) JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

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! JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Radiative Corrections (SF method) SLAC data JLab data Polarization data Yu. Bystricky, E.A.Kuraev, E. T.-G, Phys. Rev. C75, 015207 (2007) JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Instead of Conclusions… Fundamental measurement: the electric and the magnetic distributions of the proton are different in SL region. What about TL ? Separation of GE and GM via angular dependence of differential cross section Unified description in TL and SL region : zero of GEp? Asymptotic properties : QCD and analyticity Clarify reaction mechanism: 2g - exchange by model independent symmetry requirements Model independent properties Lessons from QED JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

The work presented here was initiated in a collaboration with Prof. M. P. REKALO JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Experimental correlation E.T-G, Phys. Part. Nucl. Lett. 4, 281 (2007) sel=smeas · RC RC(e) only published values!! Q2 > 2 GeV2 Q2 < 2 GeV2 JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Experimental correlation E.T-G, Phys. Part. Nucl. Lett. 4, 281 (2007) Correlation (<RC•e>) Q2 < 2 GeV2 JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

The Pauli and Dirac Form Factors The electromagnetic current in terms of the Pauli and Dirac FFs: Normalization F1p(0)=1, F2p(0)= κp Related to the Sachs FFs : GEp(0)=1, GMp(0)=μp=2.79 JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

electron-muon scattering constitutes an upper limit! Two Photon Exchange No exact calculation for ep scattering ( inelastic intermediate states..) but electron-muon scattering constitutes an upper limit! JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Interference of 1 2 exchange Explicit calculation for structureless proton The contribution is small, for unpolarized and polarized ep scattering Does not contain the enhancement factor L The relevant contribution to K is ~ 1 E.A.Kuraev, V. Bytev, Yu. Bystricky, E.T-G, Phys. Rev. D74, 013003 (1076) JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

proton electron QED versus QCD Imaginary part of the 2g amplitude JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

QED versus QCD Q2=0.05 GeV2 Q2=1.2 GeV2 Q2=2 GeV2 JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Structure Function method E. A. Kuraev and V.S. Fadin, Sov. J. of Nucl. Phys. 41, 466 (1985) SF method applied to QED processes: calculation of radiative corrections with precision of 0.1%. Takes into account the dynamics of the process Formulated in terms of parton densities (leptons, antileptons, photons) Many applications to different processes Lipatov equations (1975) Electron SF: probability to ‘find’ electron in the initial electron, with energy fraction x and virtuality up to Q2 JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Unpolarized Cross section Q2=1 GeV2 Q2=3 GeV2 Born +dipole FFs (=unpolarized experiment+Mo&Tsai) SF (with dipole FFs) SF+2 exchange Q2=5 GeV2 SF: change the slope! 2 exchange very small! JLab, May 2,2008 Egle TOMASI-GUSTAFSSON

Polarization ratio 2 exchange very small! 2 destroys linearity! Yu. Bystricky, E.A.Kuraev, E. T.-G, Phys. Rev. C 75, 015207 (2007) q =80° Born SF SF+2 exchange q =60° q =20° 2 exchange very small! 2 destroys linearity! JLab, May 2,2008 Egle TOMASI-GUSTAFSSON