CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Polarization Observables and Hadron Structure (1) Egle Tomasi-Gustafsson Saclay, France

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, MOTIVATIONS In the traditional view, the atom’s nucleus appears as a cluster of nucleons - protons and neutrons. A deeper view reveals quarks and gluons inside the nucleons. CEBAF’s continuous, energetic beams of probing electrons let physicists examine how the two view fit together. Ultimately, the process of bridging the views will yield a complete understanding of nuclear matter …. Istitutional plan 2002….

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, GENERAL PLAN Lecture 1 –Introduction-Motivations –How to measure proton form factors? –Recent Results Lecture 2 –Consequences Space and time-like regions Asymptotics Two photon exchange Radiative corrections Model Independent Statements

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, PLAN Introduction-Motivations How to measure form factors? Unpolarized method (Rosenbluth separation) Recoil polarization Experiment (Polarimetry) Results

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Proton Form Factors Over a period of time lasting at least 2000 years, Man has puzzled over and sought an understanding of the composition of matter… F2 F1 Q 2 =1 GeV 2

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 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.

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 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. Scattering e - + h => e - + he + + e - => h + h _ Annihilation Annihilation _ Form factors are real in the space-like region and complex in the time-like region. t<0t>0

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, How to measure?

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Electromagnetic interaction One photon-exchange The electromagnetic vertex is known (what about radiative corrections ?). The strong vertex contains the hadron structure. Validity of one-photon exchange at large t? Observables: differential cross section, polarization observables

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Proton Form Factors...before Rosenbluth separation/ Polarization observables Dipole approximation: G D =(1+Q 2 /0.71 GeV 2 ) -2

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Dipole Approximation Classical approach –Nucleon FF (in the Breit system) are Fourier transform of the charge or magnetic distribution. The dipole approximation corresponds to an exponential density distribution. –ρ = ρ 0 exp(-r/r 0 ), –r 0 2 = (0.24 fm) 2, ~(0.81 fm) 2  m 2 D =0.71 GeV 2 Dipole approximation: G D =(1+Q 2 /0.71 GeV 2 ) -2

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Dipole Approximation and pQCD Politzer (1974), Chernyak & Zhitnisky (1984), Efremov & Radyuskin (1980) Matveev (1985), Brodsky & Lepage (1989) Dimensional scaling –F n (Q 2 )= C n [1/( 1+Q 2 /m n ) n-1 ], m n = n  2, n is the number of constituent quarks –Setting  2 =(0.471±.010) GeV 2 (fitting pion data) pion: F  (Q 2 )= C  [1/ (1+Q 2 /0.471 GeV 2 ) 1 ], nucleon: F N (Q 2 )= C N [1/( 1+Q 2 /0.71 GeV 2 ) 2 ], deuteron: F d (Q 2 )= C d [1/( 1+Q 2 /1.41 GeV 2 ) 5 ]

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Polarized/Unpolarized methods

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Rosenbluth separation (1950) Elastic ep cross section (1-γ exchange) point-like particle:  Mott Linearity of the reduced cross section!

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Rosenbluth separation  =0.5  =0.2  =0.8 Contribution of the electric term …to be compared to the absolute value of the error on  and to the size and  dependence of RC

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, The Rosenbluth data (SLAC) L. Andivahis et al. Phys. Rev. D 50, 5491 (1994)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, The polarization induces a term in the cross section proportional to G E G M Polarized beam and target or polarized beam and recoil proton polarization The polarization method (1967)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, The simultaneous measurement of P t and P l reduces the systematic errors The polarization method (exp)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, HADRON POLARIMETRY

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Hadron Polarimetry Polarized beams Polarized targets Polarimeters

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Hadron Polarimetry Working principle: measurement of the azymuthal asymmetry in a secondary scattering Large cross section (statistical errors) Large analyzing power (systematic errors) Vector polarization: inclusive scattering on light targets: p+C → one charged particle +X Tensor polarization: exclusive scattering: d+p → d+p (elastic scattering) d+p → p+p+n (charge exchange reaction)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Charge exchange reaction Idea from I. Pomeranchuk (1938) d +p → (pp) + n The deuteron is a bound np system in T=0, S=1 state ( l=0 or 2). Selecting a pair of protons in relative s- state, requires a spin-flip due to Pauli principle, anti-symmetric total wave function Large tensor analyzing power!

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Vector Polarimeter Inclusive reaction: p(d)+C1 Charged particle+X

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Proton polarimeter Inclusive reaction: p+C 1 Charged particle+X Calibration: analyzing powers Calibration: analyzing powers Measurement: polarization Measurement: polarization

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, HADRON POLARIMETRY The Efficiency The Figure of merit: The Error on the Polarization Measurement

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Polarimetry at 4-5 GeV Pomme polarimeter......JINR -LHE synchrophasotron

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Figure of merit HYPOM Analyzing powers

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, The experimental set-up Trigger on proton: background, target walls and pion electroproduction The solid angle is defined by the proton

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, JLab - HALL A

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, The HALL A-calorimeter Assembled a 1.35 x 2.55 m 2 calorimeter 17 rows and 9 columns of 15x15 lead-glass blocks Electron detection

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Proton momentum and scattering angle

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Identify coincidence events Good separation peak/background

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Identify elastic events In-plane and out-of- plane angular correlation Angles measured in the calorimeter and in the spectrometer

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Identify elastic events After angular selection

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Focal plane polarimeter P t fpp and P n fpp are the physical asymmetries at the FPP

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Azymuthal distribution Q 2 =5.6 GeV/c 2

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Discussion of the results

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, THE RESULTS Jlab E93-027, E Spokepersons: Ch. Perdrisat, V. Punjabi, M. Jones, E. Brash M. Jones et ql. Phys. Rev. Lett. 84,1398 (2000) O. Gayou et al. Phys. Rev. Lett. 88: (2002) Linear deviation from dipole  G Ep  G Mp

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Nucleon models... Skyrme Models (Soliton) Vector Dominance Models (G-K, IJL…) Perturbative QCD (Relativistic) Constituent Quark Model Di-quark models GPD ……..

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Comparison with theory

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Issues 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

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, The nucleon form factors VDM : IJL F. Iachello..PLB 43, 191 (1973) Extended VDM (G.-K. 92): E.L.Lomon PRC 66, ) Hohler NPB 114, 505 (1976) Bosted PRC 51, 409 (1995) ElectricMagnetic neutron proton E. T.-G., F. Lacroix, Ch. Duterte, G.I. Gakh, EPJA (2005)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, The neutron Form Factor

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Electric NEUTRON Form Factor –Smaller than for proton, but not so small –New results, also based on polarization method

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, The reaction d(e,e’n)p - A x -The KHARKOV model: - Impulse Approximation - Deuteron structure - Kinematics: proton spectator - Polarization observables G.I. Gakh, A. P. Rekalo, E. T.-G. Annals of Physics (2005)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, The reaction d(e,e’n)p - A x Select the quasi-elastic Kinematics Large dependence of the asymmetry on GEn! Polarized electron beam, polarized target or neutron polarimeter G.I. Gakh, A. P. Rekalo, E. T.-G. Annals of Physics (2005)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Neutron electric form factor Longitudinally polarized electrons, polarized target: a method similar to the polarization method, which takes into account the deuteron structure. Phys. Rev. C 70, (2004) Real Amplitudes, functions of , W, Q 2

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, The IA deuteron structure: S=1, T=0 1)The nucleon form factors: 2) The S (u) and D (w) deuteron wave function

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, G En from e-deuteron elastic scattering G En > G Ep starting from 2 GeV 2 ! E. T-G. and M. P. Rekalo, Europhys. Lett. 55, 188 (2001)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, The IA deuteron structure E. T-G. and M. P. Rekalo, Europhys. Lett. 55, 188 (2001)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Polarization Observables and Hadron Structure (2) Egle Tomasi-Gustafsson Saclay, France

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, GENERAL PLAN Lecture 1 –Introduction-Motivations –How to measure proton form factors? –Recent Results –Space and time-like regions Lecture 2 –Consequences Space and time-like regions Asymptotics Two photon exchange Radiative corrections

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Time-like region

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Crossing Symmetry Scattering and annihilation channels: - Described by the same amplitude : - function of two kinematical variables, s and t p 2 → – p 1 k 2 → – k 2 - which scan different kinematical regions

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, The matrix element:

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, The matrix element: Conservation of hadronic and leptonic current:

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, G E =G M at threshold Leptonic current: Hadronic current: At threshold: L=0,   1: L=0L=2 G E =G M  (M. P. Rekalo)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Time-like observables: | G E | 2 and | G M | 2. As in SL region: - Dependence on q 2 contained in FFs - Even dependence on cos 2  exchange  - No dependence on the sign of FFs - Enhancement of the magnetic term but TL form factors are complex! 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, and E.T-G., Nucl. Phys. A761,120 (2005).

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Time-like observables: | G E | 2 and | G M | 2. - The Total Cross Section Cross section at The angular asymmetry, R Due to limited statistics, no experimental determination of individual FFs in TL region, yet: G E =G M or G E =0

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Time-Like region G E =0 G E =G M G E =G D E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001) | G M | 2 Angular Asymmetry

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Models in T.L. region E. T-G., F. Lacroix, C. Duterte, G.I. Gakh EPJA 2005 VDM : IJL F. Iachello..PLB (1973) Extended VDM (G.-K. 92): E.L.Lomon PRC (2002) ‘QCD inspired’ proton neutron

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Spin Observables Analyzing power, A Double spin observables

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Models in T.L. Region (polarization) VDM : IJL Ext. VDM ‘QCD inspired’ R AyAxx Ayy Axz Azz E. T-G., F. Lacroix, C. Duterte, G.I. Gakh

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Asymptotics

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, pQCD predictions Scaling laws probability to keep the hadron intact, the momentum transfer is equally shared among the constituents test: form factors Helicity conservation: vector interaction between gluons and massless quarks test: polarization bservables Reduced nuclear amplitudes introduce non perturbative corrections,by removing the complex structure of the nucleon test: reduced cross section

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Scaling? pQCD: F 1  1/Q 4, F 2  1/Q 6 F 1 / F 2  Q 2 Corrections logarithmiques?

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, The deuteron (S=1)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, The deuteron Cross section A(Q 2 ) B(Q 2 ) A(Q 2 )

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, The Deuteron Polarization Observables Jlab E Spokepersons: B. Beise, S. Kox D. Abbott et ql. Phys. Rev. Lett. 84,5053 (2000)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Reduced deuteron form factors L.Alexa et al., PRL 82, 1374 (1999), HallA, JLab

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Reduced deuteron form factors L.Alexa et al., PRL 82, 1374 (1999), HallA, JLab S. Platchkov et al., NPA 510, 740 (1990), ALS, Saclay R.G. Arnold et al., PRL 57, 174 (1986), Slac

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, ed-elastic cross section A(Q 2 ) f D (Q 2 )= F D (Q 2 ) /(F N (Q 2 /4) G Ep (Q 2 /4)) f D (Q 2 )= F D (Q 2 ) /G 2 Ep (Q 2 /4) f D (Q 2 )= F D (Q 2 ) / F 2 N (Q 2 /4)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, From ed-elastic cross section f D (Q 2 )= F D (Q 2 )/ F 1 2 (Q 2 /4) f D (Q 2 )= F D (Q 2 )/(F 1 (Q 2 /4)F 2 (Q 2 /4)) f D (Q 2 )= F D (Q 2 )/ F 2 2 (Q 2 /4)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Fitting f D Large instability for Λ!

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 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. E. T-G. and G. Gakh, Eur. Phys. J. A 26, 265 (2005) 

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Phragmèn-Lindelöf theorem E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001) Applies to NN and NN Interaction (Pomeranchuk theorem ): t=0 : not a QCD regime! Connection with QCD asymptotics? G M (TL) G M (SL) G E (SL)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Two photon exchange

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Two-photon exchange? Electric proton FF Different results with different experimental methods !! New mechanism?

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Two-Photon exchange 1  -2  interference is of the order of  =e 2 /4  =1/137 (in usual calculations of radiative corrections, one photon is ‘hard’ and one is ‘soft’) In the 70’s it was shown [J. Gunion and L. Stodolsky, V. Franco, F.M. Lev, V.N. Boitsov, L. Kondratyuk and V.B. Kopeliovich, R. Blankenbecker and J. Gunion] that, at large momentum transfer, due to the sharp decrease of the FFs, if the momentum is shared between the two photons, the 2  contribution can become very large  The 2  amplitude is expected to be mostly imaginary. In this case, the 1  -2  interference is more important in time-like region, as the Born amplitude is complex.

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Qualitative estimation of 2  exchange From quark counting rules: F d ~ t -5 and F N ~t -2 For t = 4 GeV 2, For d, 3 He, 4 He, 2  effect should appear at ~1 GeV 2, for protons ~ 10 GeV 2 q/2 For ed elastic scattering:

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Two-Photon exchange In 1999 M.P. Rekalo, E. T.-G. and D. Prout found a model-independent parametrization of the 2  contribution and applied to ed-elastic scattering data. → Discrepancy between the results from Hall A [L.C. Alexa et al. Phys. Rev. Lett. 82, 1374 (1999)] and Hall C [D. Abbott et al. Phys. Rev. Lett. 82, 1379 (1999)]. M. P. Rekalo, E. T-G and D. Prout, Phys. Rev. C60, (1999)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, {g1{g 1  -2  interference { 22 11 { M. P. Rekalo, E. T.-G. and D. Prout Phys. Rev. C (1999)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Crossing Symmetry Scattering and annihilation channels: - Described by the same amplitude : - function of two kinematical variables, s and t p 2 → – p 1 k 2 → – k 2 - which scan different kinematical regions

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31,  -2  interference M. P. Rekalo, E. T-G and D. Prout, Phys. Rev. C60, (1999) C/A D/A

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, e ± + p→ e ± + p 1  exchange Two EM form factors Real (in SL region) Functions of one variable (t) Describe e + and e - scattering 2  exchange Three structure functions Complexe Functions of TWO variables (s,t) Different for e + and e - scattering → 4 spin ½ fermions → 16 amplitudes in the general case.  T-invariance of EM interaction,  identity of initial and final states,  helicity conservation,  unitarity

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Model independent considerations Determination of EM form factors, in presence of 2  exchange - electron and positron beams, - longitudinally polarized, - in identical kinematical conditions, Where? VEPP3 (Novosibirsk) ( cf. S. Serednyakov), HERA.. Generalization of the polarization method (A. Akhiezer and M.P. Rekalo)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 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

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, If no positron beam… Either three T-odd polarization observables…...or five T-even polarization observables…. among d  /d , Px( e), Pz( e), Dxx, Dyy, Dzz, Dxz very difficult experiments only model independent ways (without positron beams) M. P. Rekalo and E. T-G Nucl. Phys. A740 (2004) 271, M. P. Rekalo and E. T-G Nucl. Phys. A742 (2004) 322

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, e ± Model independent considerations for e ± N scattering Determination of EM form factors, in presence of 2  exchange - electron and positron beams, - longitudinally polarized, - in identical kinematical conditions, 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 d  /d , Px( e), Pz( e), Dxx, Dyy, Dzz, Dxz M. P. Rekalo, E. T.-G., EPJA (2004), Nucl. Phys. A (2003)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31,

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Parametrization of 2  for ep elastic scattering With the correct symmetry properties: or: Q 2 -dependence: Simple parametrization:

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, From the data: deviation from linearity << 1%! Parametrization of 2  -contribution for e+p E. T.-G., G. Gakh, Phys. Rev. C (2005)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, The proton magnetic form factor The difference is not at the level of the measured observables, but on the slope (derivative)! E. Brash et al. Phys. Rev. C65, (2002) Polarization results induce 1.5-3% global effect

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Radiative Corrections to the data Slope negative if : - RC can reach 40% on  - Declared error ~1% - Same correction for G E and G M - Have a large  -dependence - Affect the slope The slope is negative starting from 2-3 GeV 2  el =  meas · RC slope

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Reduced cross section and RC Data from L. Andivahis et al., Phys. Rev. D50, 5491 (1994) Q 2 =1.75 GeV 2 Q 2 =5 GeV 2 Q 2 =3.25 GeV 2 Q 2 =4 GeV 2 Q 2 =2.5 GeV 2 Q 2 =7 GeV 2 Q 2 =6 GeV 2 With RC Without RC Slope from P. M. E. T.-G., G. Gakh, Phys. Rev. C (2005)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Experimental correlation Two parameters linear fit Correlation G Ep 2 – G Mp 2 100% Depends on  and on the size of RC:  el =  meas · RC

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Structure Function method 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 E. A. Kuraev and V.S. Fadin, Sov. J. of Nucl. Phys. 41, 466 (1985) Electron SF: probability to ‘find’ electron in the initial electron, with energy fraction x and virtuality up to Q 2 Lipatov equations (1975)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Structure Function method (Applications) - e+e-  hadrons( J/  width) E. A. KURAEV and V.S. FADIN, Sov. J. of Nucl. Phys. 41, 466 (1985) - ep  e’X (elastic and inelastic scattering) E. A. KURAEV ;N.P. MERENKOV and V.S. FADIN, Sov. J. of Nucl. Phys. 47,1009 (1988) –Decay width of mesons (FSI) E. A. KURAEV, JETP Lett.65, 127 (1997) –ep  e’p(  ) polarized and unpolarized cases (in progress) Y. Bystricky, E.A.Kuraev., E. T.-G, Phys Rev. C 75, (2007) –Compton and double Compton scattering A.N.Ilyichev, E.A. Kuraev, V.Bytev and Y. P. Peresun'ko, J. Exp. Theor. Phys (2005) –Radiative corrections for LEP beam (small angle BHABHA scattering) A.B.Arbuzov, E.A.Kuraev et al, Phys. Lett.B 399, 312 (1997)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Short history (I) Schwinger: corrections to cross section for electron scattering in external field  s=s 0 (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

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Short history (II) 1977: Altarelli Parisi Gribov Lipatov, Dokshitzer: (DGLAP) Asymptotic freedom, evolution equation, Collins Factorization theorem. Drell-Yan picture of hard processed in QED : application of QCD ideas to QED: radiative corrections in form of structure functions and Drell-Yan picture Leading terms: and non leading terms explicitely taken into account in DGLAP evolution equations. In QED known as Lipatov equations (1975).

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Scattered electron energy All orders of PT needed  beyond Mo & Tsai approximation! Initial state emission final state emission Quasi-elastic scattering 3% Y0Y0 Not so small! Shift to LOWER Q 2

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, The structure function method Electron detected in a calorimeter:  The cross section is integrated on the scattered electron energy fraction: The cross section: The K-factor includes all non leading contributions:

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Structure function method

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Unpolarized Cross section Born +dipole FFs (=unpolarized experiment+Mo&Tsai) SF (with dipole FFs) SF+2  exchange Q 2 =3 GeV 2 Q 2 =5 GeV 2 SF: change the slope! Q 2 =1 GeV 2 2  exchange very small!

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 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. D (2006)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Polarization ratio Born SF SF+2  exchange  =60° 2  destroys linearity! 2  exchange very small!  =80°  =20°

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Correction (SF method) Polarization data JLab data SLAC data Yu. Bystricky, E.A.Kuraev, E. T.-G, Phys. Rev. C 75, (2007)

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Conclusions and Perspectives Fundamental measurement: the electric and the magnetic distributions of the proton are different! Extension at larger q 2 –In SL region: observe a zero of G Ep ?

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, When G E p =0? 0 Jlab E –approved 07/2001,07/2004 –scheduled 2007 –Spokepersons: Ch. Perdrisat, V. Punjabi, M. Jones, E. Brash –20 Laboratories, 80 people Hall A => Hall C New polarimeter New calorimeter G e p IV : up to 12 GeV 2, after the upgrade of Cebaf

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Conclusions and Perspectives Fundamental measurement: the electric and the magnetic distributions of the proton are different! Extension at larger q 2 –In SL region: observe a zero of G Ep ? –In TL region: Separation of G E and G M Access their relative phase (polarization) through the angular dependence of differential cross section and polarization observables

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, FF measurement: projected accuracy (Frascati) Integrated luminosity  pb -1 KLOE in last 12 months: 1800 pb -1 at  mass prototne protonneutron

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Perspectives in Time-Like region Frascati Panda

CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, Conclusions Fundamental measurement: the electric and the magnetic distributions of the proton are different! Extension at larger q 2 –In SL region: observe a zero of G Ep ? –In TL region: Separation of G E and G M Access their relative phase (polarization) Novosibirsk-VEPP3 through the angular dependence of differential cross section and polarization observables Coherent description in SL and TL regions Revise radiative corrections! IHEP