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Model independent properties of two photon exchange

Model independent properties of two photon exchange. Egle Tomasi-Gustafsson Saclay, France. Collaboration with M.P. Rekalo Presently with G.I. Gakh and E.A. Kuraev. Frascati, January 20, 2006. PLAN. Introduction Generalities on form factors Electric proton FF (space-like)

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Model independent properties of two photon exchange

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  1. Model independent properties of two photon exchange Egle Tomasi-GustafssonSaclay, France Collaboration with M.P. Rekalo Presently with G.I. Gakh and E.A. Kuraev Frascati, January 20, 2006 Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  2. PLAN • Introduction • Generalities on form factors • Electric proton FF (space-like) • Two-photon exchange • History • Model independent properties • Observables in time-like region • Signatures of two-photon exchange • Search for evidence in the data • Alternative explanation for the discrepancy of FFs ratio • Perspectives Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  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. • Neutron and protonform factors are different. • Elastic form factors contain information on the hadron ground state. • Playground for theory and experiment. Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  4. 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 and complex in the time-like region. Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  5. 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→ – p1 Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  6. The Rosenbluth separation (1950) • Elasticepcross section (1-γ exchange) • point-like particle:  Mott Linearity of the reduced cross section! Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  7. 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 Frascati, 20 Gennaio 2006

  8. THE RESULTS (>2000) Linear deviation from dipole mGEpGMp Jlab E93-027 , E99-007Spokepersons: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) Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  9. Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  10. Electric proton FF Different results with different experimental methods !! New mechanism: two-photon exchange? Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  11. 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 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 2g- contribution can become very large. • 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 Frascati, 20 Gennaio 2006

  12. Qualitative estimation of 2g exchange Foredelastic scattering: q/2 q/2 From quark counting rules: Fd ~ t-5 and FN~t-2 For t = 4 GeV2, For d, 3He, 4He, 2geffect should appear at ~1 GeV2, for protons ~ 10 GeV2 Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  13. Two-Photon exchange In 1999 M.P. Rekalo, E. T.-G. and D. Prout found a model-independent parametrizationof the2g- 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) Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  14. 1g-2g interference M. P. Rekalo, E. T.-G. and D. Prout Phys. Rev. C (1999) 1g 2g { { 1{g Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  15. 1g-2g interference D/A C/A M. P. Rekalo, E. T-G and D. Prout, Phys. Rev. C60, 042202 (1999) Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  16. The 1g-2g interference destroys the linearity of the Rosenbluth plot! Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  17. Model independent propertiesof two photon exchange Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  18. Model independent considerations for • 4 spin ½ fermions →16 amplitudes in the general case. • P- and T-invariance of EM interaction, • helicity conservation, 1g exchange: 1g exchange: Two (complex) EM FFs Functions of one variable (t) Three (complex) amplitudes Functions of two variables (s,t) Crossing symmetry, C-invariance, T-reversal connect: e± + N e± + N, N+Ne+ + e-, ande+ + e-  N+N Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  19. The Matrix Element for M. L. Goldberger, Y. Nambu and R. Oehme, Ann. Phys 2, 226 (1957) M.P. Rekalo and E. Tomasi-Gustafsson, EPJA 22, 331 (2004) Assuming P-invariance, and lepton helicity conservation,the matrix elementfor 1g+2g exchange is: vector axial For 1g -exchange: Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  20. Generalized Form Factors By analogy with Sachs and Fermi-Dirac FFs: complex functions of 2 variables Both F1Nand F2Ncontain 1g+2g! Decomposition of the amplitudes: 2g-terms Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  21. Unpolarized cross section 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). 2g-exchange induces three new terms, of the order of a Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  22. Symmetry relations • Odd properties of the 2g amplitudes with respect to the transformation: cos  = - cos  i.e.,    -  • One can remove or single out the 2g contribution by doing the sum or the difference of the differential cross section at the angles connected by this transformation Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  23. Remove the 2g contribution • Sum of the differential cross sections: • Total cross section: Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  24. Single out the 2g contribution • Angular asymmetry with • In terms of amplitudes - only interference terms! Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  25. 2g contribution • The sum: • is free from 2g contributions! Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  26. Electron and positron scattering e±N Model independent considerations for e± N scattering 2 real functions 3 complex functions 8 real functions determine the 6 complexe amplitudes fore± N→e±N • Relations among the functions! M. P. Rekalo and E. T-G Eur. Phys. Jour. A Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  27. Electron and positron scattering e±N In the same kinematical conditionsSum and Difference of e± N scattering e+ e- Model independent considerations which hold at O(a2) M. P. Rekalo and E. T-G Eur. Phys. Jour. A Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  28. Single spin observables • T-odd observable • TPE contribution: • Small, of the order of a • Relative role increases when q2 increases • Does not vanish, in the general case, for 1g exchange • At 90° expected small(vanishes for 1g exchange): • At threshold (vanishes for 1g exchange due to GE=GM): Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  29. Form Factor determination • C-odd properties of nucleon polarization with • is the phase difference of the form factors GE and GM Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  30. Form Factor ratioR=|GE| / |GM| • The sum: • is free from 2g contributions! • The Ratio R can be determined by: Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  31. Is there any evidence of presence of a 2g-contributionin the existing ep data? NON Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  32. Parametrization of 2g-contribution for e+p From the data: deviation from linearity << 1%! E. T.-G., G. Gakh Phys. Rev. C (2005) Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  33. Possible explanation for the FFs discrepancy: Radiative Corrections Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  34. Radiative corrections Mo and Tsai (1969) Schwinger (1949) • Effects of the order of - few percent on polarization observables, - up to 40% on cross section! • Complete calculations in progress Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  35. Structure function method Q2=1 GeV2 Q2=3 GeV2 Assumes dipole FFs Change the slope ! Q2=5 GeV2 SF Born Polarization RC Born E.A Kuraev, V.S. Fadin Sov. J. Nucl. Phys. 41, 466 (1985) Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

  36. Conclusions • We have derived model independent formulas for all experimental observables in presence of 2g exchange, as functions of three complex amplitudes for e+ + e- N+N • Using symmetry properties one can remove or single out 2g contributions • Crossing symmetry, C-invariance, T-reversal connect: e± + N e± + N, N+Ne+ + e-, ande+ + e- N+N Novosibirsk-VEPP3 • New data welcome in next future! • Revise Radiative Corrections! Egle Tomasi-Gustafsson Frascati, 20 Gennaio 2006

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