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)
For two-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, (2003)
M.P. Rekalo and E. Tomasi-Gustafsson, EPJA 22, 331 (2004)
The hadronic current:
Decomposition of the amplitudes:
For 1g -exchange:
Gennadiy GAKH

7. Unpolarized hadronic tensor
2g-term
Gennadiy GAKH

8. Unpolarized cross section
2g-term
Induces four new terms
Odd function of q:
Does not contribute at q =90°
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. Thank you for attention
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)
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