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Space-Like and Time-Like Form Factors Compared analysis

Space-Like and Time-Like Form Factors Compared analysis. Egle Tomasi-Gustafsson SPhN-Saclay and IPN-Orsay. Varenna, June 16, 2009. e +. p. q 2 >0. p. e -. PLAN. Introduction: Form factors in one photon exchange approximation. Experimental Situation Space-Like Time-like

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Space-Like and Time-Like Form Factors Compared analysis

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  1. Space-Like and Time-LikeForm Factors Compared analysis Egle Tomasi-GustafssonSPhN-Saclay and IPN-Orsay Varenna, June 16, 2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  2. e+ p q2>0 p e- PLAN • Introduction: Form factors in one photon exchange approximation • Experimental Situation • Space-Like • Time-like • Future Panda/FAIR and JLab 12 GeV: • Determination of proton form factors • Transition to QCD: Asymptotics • Reaction mechanism (1 or 2 g exchange) • Conclusions ….Model Independent Statements Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  3. Hadron Electromagnetic Form factors • Characterize the internal structure of a particle ( point-like) • In a P- and T-invariant theory, the EM structure of a particle of spin S is defined by 2S+1 form factors. • Elastic form factors bring information on the nucleon ground state • Neutron and protonform factors are different • Playground for theory and experiment • at low q2 probe the size of the nucleus, • at high q2 test QCD scaling Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  4. e- e- q2<0 p p Electromagnetic Interaction The electron vertex is known, gm The interaction is carried by a virtual photon of mass q2 The proton vertex is parametrized in terms of FFs: Pauli and Dirac F1,F2 or in terms of Sachs FFs: GE=F1-t F2, GM=F1+F2, t=-q2/4M2 What about high order radiative corrections? Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  5. e- e- e+ p q2>0 q2<0 p e- p p Analyticity Space-like Asymptotics - QCD - analyticity Time-like GE(0)=1 GM(0)=mp p+p ↔ e++e- +p Unphysical region _ FFs are real FFs are complex _ q2=4mp2 q2 e+p  e+p p+p ↔ e++e- GE=GM Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  6. The Rosenbluth separation Q2 fixed Linearity of the reduced cross section e • tan2qe dependence • Holds for 1g exchange only PRL 94, 142301 (2005) Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  7. 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 CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  8. 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 CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  9. e- e- q2<0 p p Experimental Status(space-like) Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  10. 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 To update…new data! 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 CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  11. Polarization Method (exp) A.I. Akhiezer, M.P. Rekalo The simultaneous measurement of Pt and Pl reduces the systematic errors ! Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  12. Statistics and Preliminary Results from GEp(III) C. Perdrisat, V. Punjabi New equipment worked beautifully:BigCal and FPP 8.54 GeV2point: 1.63 billion triggers collected Analyzing power at 5.4 GeV/c close to Dubna value 6.8 GeV2point: 160 million triggers 5.2 GeV2point: a test of the spin transport at 180o μpGEp/GMp=1.056-0.1427Q2 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  13. 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 CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  14. 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 CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  15. e+ p q2>0 p e- Experimental Status(time-like) Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  16. 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 CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  17. A(p)= 56.3 GeV4 A(n)= 77.15 GeV4 LQCD=0.3 GeV STATUS on EM Form factors Time-like region • No individual determination of |GE| and |GM| • Assume GE=GM (valid only at threshold) • TL nucleon FFs are twice larger than SL FF VMD or pQCD inspired parametrizations (for p and n): Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  18. 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 CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  19. Space-like andTime-like • E.T-G, Phys. Part. Nucl. Lett. 4, 281 (2007) FM=sM/stot FE=eG2E/sred 5 GeV2 e=0.8 ----- 8 GeV2 e=0.5 e=0.2 FE=sE/stot Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  20. Space-like andTime-like • E.T-G, Phys. Part. Nucl. Lett. 4, 281 (2007) FE=eG2E/sred 10% e=0.8 10% e=0.5 e=0.2 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  21. Radiative Return (ISR) e+ +e- p + p +  B. Aubert ( BABAR Collaboration) Phys Rev. D73, 012005 (2006) Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  22. Results (ISR) • GE = GM ? B. Aubert [Babar Collaboration, PRD 73, 012005 (2006) Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  23. Form Factors with p+p e++ e- • 1) Knowledge of proton form factors up to large q2 • 2) Transition to QCD: Asymptotics • 3) Reaction mechanism (1 or 2 photon exchange) Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  24. Physical Background • 3 body reactions: “easy” to eliminate • kinematical constraints • PID • 2 charged body reactions (π+π-, μ+μ-, K+K-) Most important background isπ+ π-: Are we able to discriminate e+e-fromπ+ π- ? High statistics GEANT4 simulations  YES ! Worse case : few 0/00 pollution / cosCM bin (0.1)  < 1% on the total cross section up to 16 GeV2 24 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO D. Marchand, IPN Orsay

  25. Expected Results(I) L = 2x1032 cm-2.s-1, 107 s (~100 days) R=GE/GM BaBAR Individual determination of GE and GM up to large Q2 PS170 PANDA sim Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  26. Proton: F2 /F1 and pQCD C. Perdrisat Brodsky and Farrar (75): Belitsky, Ji and Yuan (03): Q2F2/F1 constant → Q2F2/F1→ ln2(Q2/2) Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  27. Expected Results (II) • Asymptotic region • Test of analytical properties Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  28. 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 CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  29. Phragmèn-Lindelöf theorem Connection with QCD asymptotics? Applies to NN and NN Interaction (Pomeranchuk theorem) t=0 : not a QCD regime! E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001) Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  30. Conclusions • Hadron form factors: a bridge between perturbative and non perturbative QCD • Progress in experiment and theory • Next future (> 2014) • 12 GeV beams at JLab:increase Q2 to 15 GeV2. Two experiment in preparation - Fair@GSI, antiprotons up to 15 GeV/c Precise determination of |GE| and |GM| Cross section measurement up to q2 to ~20 GeV2. Towards a unified description of form factors, for a better comprehension of the hadron structure Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  31. GEp/GMp with 12 GeV at JLab Two new experiments approved to run after the 12 GeV upgrade (to be completed end of 2013). Whether they should run depends again on Dubna calibration to 7.5 GeV/c (12.5 GeV2). 31 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  32. Two-Photon exchange • 1g-2g interference is of the order of a=e2/4p=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…] that, at large momentum transfer, due to the sharp decrease of the FFs, if the momentum is shared between the two photons, the 2g- contribution can become very large. • The 2g amplitude is expected to be mostly imaginary. • The 1g-2g interference is more important in time-like region, as the Born amplitude is complex Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  33. Two Photon exchange Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  34. Fitting the angular distributions.. The form of the differential cross section: is equivalent to: Cross section at 900 Angular asymmetry E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001) Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  35. 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) Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  36. Simulations q2=5.4,8.2,13.8 GeV2 Main effect: odd cosq - distribution • Approximations: • Neglect contributions to GE,GM • Consider only real part Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  37. N=a0+a2cosq sin2q+a1 cos2q, a2~2g 1g 2g 0.02 q2=5.4 GeV2 2g 0.2 2g 0.05 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  38. Two photon exchange • The calculation of the box amplitude requires the description of intermediate nucleon excitation and of their FFs at any Q2 • Different calculations give quantitatively different results Theory not enough constrained! Model independent statements Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  39. 1g-2g interference M. P. Rekalo, E. T.-G. and D. Prout, Phys. Rev. C60, 042202 (1999) 1g 2g { 1{g { Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  40. Unpolarized cross section • Induces four new terms • Odd function of q: • Does not contribute at q =90° Two Photon Exchange: Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  41. 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 CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  42. Symmetry relations • Differential cross section at complementary angles: The SUM cancels the 2g contribution: The DIFFERENCE enhances the 2g contribution: Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  43. Is there any experimental evidence of two photon exchange? NO (real part) Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  44. Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  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 CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  46. Linear fit to e+4He scattering Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  47. 2γ-Gamma Models and Data C. Perdrisat,L. Pentchev Expt. Jlab 04-019 measured Ratio PL/PT for Q2=2.49 GeV2 at 3 values of ε PRELIMINARY NO ε-dependence at 0.01 level NO evidence of 2g contribution The inclusion of hard 2γ exchange: Chen et al (2003) with GPDs, Blunden et al (2003) in hadronic model Bystriskyi et al., LSF PR C75, 015207 (2007) 8/21/2014 47 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

  48. Asymptotics Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO

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