Two-photon exchange in p-p collisions

1. Two-photon exchange in p-p collisions Gennadiy I. Gakh (NSC-KFTI Kharkov) In collaboration with Egle Tomasi-Gustafsson Gennadiy GAKH

2. Gennadiy GAKH

3. 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. Gennadiy GAKH

4. Two-Photon exchange • The 2g amplitude may be mostly imaginary. • In this case, the 1g-2g interference is more important in time-like region, as the Born amplitude is complex. Gennadiy GAKH

5. Model independent considerations for • 4 spin ½ fermions →16 amplitudes in the general case. • P- and T-invariance of EM interaction, • helicity conservation, • For one-photon exchange: • Two (complex) EM form factors • Functions of one variable (t) • Fortwo-photon exchange: • Three (complex) amplitudes • Functions of two variables (s,t) Gennadiy GAKH

6. Decomposition of the amplitudes: Model independent considerations for M. L. Goldberger, Y. Nambu and R. Oehme, Ann. Phys 2, 226 (1957) P. Guichon and M. Vanderhaeghen, P. R.L. 91, 142303 (2003) M.P. Rekalo and E. Tomasi-Gustafsson, EPJA 22, 331 (2004) The hadronic current: For 1g -exchange: Gennadiy GAKH

7. Unpolarized hadronic tensor Hadronic tensor 2g-term Gennadiy GAKH

8. Unpolarized cross section • Induces four new terms • Odd function of q: • Does not contribute at q =90° 2g-term Destroys the linearity of the Rosenbluth fit in SL region! Gennadiy GAKH

9. Symmetry relations • Properties of the TPE amplitudes with respect to the transformation: cos  = - cos  i.e.,    -  • Based on these properties one can remove or single out TPE contribution • Introducing the sum or the difference of the differential cross section at the angles connected by this transformation one has: Gennadiy GAKH

10. Nucleon form factor ratio • The ratio of the FFs moduli is given by the following expression: Gennadiy GAKH

11. Single spin asymmetry • 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° (vanishes for 1g exchange): • At threshold (vanishes for 1g exchange due to GE=GM): Gennadiy GAKH

12. Symmetry for single spin asymmetry • This method can be applied to the polarization observables as, for example, the single spin asymmetry. Let us introduce: • This difference can be written as: •  is the phase difference of the form factors GM and GE Gennadiy GAKH

13. Double spin observables Gennadiy GAKH

14. Conclusions • We have derived • Model independent • Explicit formulas for all experimental observables in in presence of two photon exchange • Method applied also to the inverse reaction (of special interest in Frascati, Novosibirsk, and IHEP (Bejing)) • Using symmetry properties one can remove or single out TPE contributions • New data welcome in next future! Thank you for attention Gennadiy GAKH

15. Single spin polarization observables Symmetric hadronic tensor (also for 1g exchange) Gennadiy GAKH

16. Qualitative estimation of Two-Photon exchange ( for ed) q/2 q/2 Form factors → quark counting rules: Fd ~ t-5 and FN~t-2 For t = 4 GeV2, For d, 3He, 4He, 2g effect should appear at ~1 GeV2, for protons ~ 10 GeV2 Gennadiy GAKH

17. Double spin observables Gennadiy GAKH

18. Radiative corrections • Complete calculations in progress • Effects of the order of - few percent on polarization observables, - up to 30% on cross section! • Claimed error <1% Gennadiy GAKH