1. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 1 Polarization Observables and Hadron Structure (1) Egle Tomasi-Gustafsson Saclay, France

2. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 2 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….

3. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 3 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

4. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 4 PLAN Introduction-Motivations How to measure form factors? Unpolarized method (Rosenbluth separation) Recoil polarization Experiment (Polarimetry) Results

5. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 5 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

6. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 6 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.

7. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 7 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

8. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 8 How to measure?

9. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 9 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

10. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 10 Proton Form Factors...before Rosenbluth separation/ Polarization observables Dipole approximation: G D =(1+Q 2 /0.71 GeV 2 ) -2

11. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 11 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

12. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 12 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 ]

13. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 13 Polarized/Unpolarized methods

14. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 14 Rosenbluth separation (1950) Elastic ep cross section (1-γ exchange) point-like particle:  Mott Linearity of the reduced cross section!

15. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 15 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

16. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 16 The Rosenbluth data (SLAC) L. Andivahis et al. Phys. Rev. D 50, 5491 (1994)

17. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 17 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)

18. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 18 The simultaneous measurement of P t and P l reduces the systematic errors The polarization method (exp)

19. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 19 HADRON POLARIMETRY

20. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 20 Hadron Polarimetry Polarized beams Polarized targets Polarimeters

21. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 21 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)

22. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 22 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!

23. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 23 Vector Polarimeter Inclusive reaction: p(d)+C1 Charged particle+X

24. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 24 Proton polarimeter Inclusive reaction: p+C 1 Charged particle+X Calibration: analyzing powers Calibration: analyzing powers Measurement: polarization Measurement: polarization

25. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 25 HADRON POLARIMETRY The Efficiency The Figure of merit: The Error on the Polarization Measurement

26. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 26 Polarimetry at 4-5 GeV Pomme polarimeter......JINR -LHE synchrophasotron

27. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 27 Figure of merit HYPOM Analyzing powers

28. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 28 The experimental set-up Trigger on proton: background, target walls and pion electroproduction The solid angle is defined by the proton

29. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 29 JLab - HALL A

30. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 30 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

31. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 31 Proton momentum and scattering angle

32. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 32 Identify coincidence events Good separation peak/background

33. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 33 Identify elastic events In-plane and out-of- plane angular correlation Angles measured in the calorimeter and in the spectrometer

34. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 34 Identify elastic events After angular selection

35. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 35 Focal plane polarimeter P t fpp and P n fpp are the physical asymmetries at the FPP

36. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 36 Azymuthal distribution Q 2 =5.6 GeV/c 2

37. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 37 Discussion of the results

38. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 38 THE RESULTS Jlab E93-027, E99-007 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. 88:092301 (2002) Linear deviation from dipole  G Ep  G Mp

39. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 39 Nucleon models... Skyrme Models (Soliton) Vector Dominance Models (G-K, IJL…) Perturbative QCD (Relativistic) Constituent Quark Model Di-quark models GPD ……..

40. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 40 Comparison with theory

41. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 41 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

42. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 42 The nucleon form factors VDM : IJL F. Iachello..PLB 43, 191 (1973) Extended VDM (G.-K. 92): E.L.Lomon PRC 66, 045501 2002) 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)

43. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 43 The neutron Form Factor

44. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 44 Electric NEUTRON Form Factor –Smaller than for proton, but not so small –New results, also based on polarization method

45. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 45 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)

46. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 46 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)

47. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 47 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, 025202 (2004) Real Amplitudes, functions of , W, Q 2

48. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 48 The IA deuteron structure: S=1, T=0 1)The nucleon form factors: 2) The S (u) and D (w) deuteron wave function

49. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 49 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)

50. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 50 The IA deuteron structure E. T-G. and M. P. Rekalo, Europhys. Lett. 55, 188 (2001)

51. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 51 Polarization Observables and Hadron Structure (2) Egle Tomasi-Gustafsson Saclay, France

52. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 52 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

53. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 53 Time-like region

54. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 54 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

55. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 55 The matrix element:

56. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 56 The matrix element: Conservation of hadronic and leptonic current:

57. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 57 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)

58. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 58 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).

59. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 59 Time-like observables: | G E | 2 and | G M | 2. - The Total Cross Section Cross section at 90 0 - 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

60. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 60 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

61. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 61 Models in T.L. region E. T-G., F. Lacroix, C. Duterte, G.I. Gakh EPJA 2005 VDM : IJL F. Iachello..PLB43 191 (1973) Extended VDM (G.-K. 92): E.L.Lomon PRC66 045501(2002) ‘QCD inspired’ proton neutron

62. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 62 Spin Observables Analyzing power, A Double spin observables

63. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 63 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

64. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 64 Asymptotics

65. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 65 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

66. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 66 Scaling? pQCD: F 1  1/Q 4, F 2  1/Q 6 F 1 / F 2  Q 2 Corrections logarithmiques?

67. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 67 The deuteron (S=1)

68. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 68 The deuteron Cross section A(Q 2 ) B(Q 2 ) A(Q 2 )

69. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 69 The Deuteron Polarization Observables Jlab E94-018 Spokepersons: B. Beise, S. Kox D. Abbott et ql. Phys. Rev. Lett. 84,5053 (2000)

70. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 70 Reduced deuteron form factors L.Alexa et al., PRL 82, 1374 (1999), HallA, JLab

71. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 71 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

72. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 72 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)

73. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 73 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)

74. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 74 Fitting f D Large instability for Λ!

75. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 75 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) 

76. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 76 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)

77. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 77 Two photon exchange

78. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 78 Two-photon exchange? Electric proton FF Different results with different experimental methods !! New mechanism?

79. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 79 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.

80. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 80 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:

81. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 81 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, 042202 (1999)

82. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 82 1{g1{g 1  -2  interference { 22 11 { M. P. Rekalo, E. T.-G. and D. Prout Phys. Rev. C (1999)

83. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 83 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

84. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 84 1  -2  interference M. P. Rekalo, E. T-G and D. Prout, Phys. Rev. C60, 042202 (1999) C/A D/A

85. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 85 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

86. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 86 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)

87. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 87 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

88. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 88 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

89. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 89 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)

90. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 90

91. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 91 Parametrization of 2  for ep elastic scattering With the correct symmetry properties: or: Q 2 -dependence: Simple parametrization:

92. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 92 From the data: deviation from linearity << 1%! Parametrization of 2  -contribution for e+p E. T.-G., G. Gakh, Phys. Rev. C (2005)

93. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 93 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, 051001 (2002) Polarization results induce 1.5-3% global effect

94. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 94 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

95. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 95 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)

96. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 96 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

97. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 97 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)

98. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 98 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, 015207 (2007) –Compton and double Compton scattering A.N.Ilyichev, E.A. Kuraev, V.Bytev and Y. P. Peresun'ko, J. Exp. Theor. Phys.100 31 (2005) –Radiative corrections for LEP beam (small angle BHABHA scattering) A.B.Arbuzov, E.A.Kuraev et al, Phys. Lett.B 399, 312 (1997)

99. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 99 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

100. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 100 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).

101. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 101 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

102. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 102 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:

103. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 103 Structure function method

104. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 104 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!

105. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 105 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 (2006)

106. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 106 Polarization ratio Born SF SF+2  exchange  =60° 2  destroys linearity! 2  exchange very small!  =80°  =20°

107. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 107 Correction (SF method) Polarization data JLab data SLAC data Yu. Bystricky, E.A.Kuraev, E. T.-G, Phys. Rev. C 75, 015207 (2007)

108. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 108 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 ?

109. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 109 When G E p =0? 0 Jlab E01-109 –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

110. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 110 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

111. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 111 FF measurement: projected accuracy (Frascati) Integrated luminosity  700-1000 pb -1 KLOE in last 12 months: 1800 pb -1 at  mass prototne protonneutron

112. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 112 Perspectives in Time-Like region Frascati Panda

113. CEA DSM Dapnia Egle Tomasi-Gustafsson Gomel, July 31, 2007 113 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