Gennadiy GAKHCEA DSM Dapnia 1

Two-photon exchange in p-p collisions

Gennadiy I. Gakh (NSC-KFTI Kharkov)

In collaboration with Egle Tomasi-Gustafsson

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Two-Photon exchange

•1-2 interference is of the order of =e2/4=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

2contribution can become very large

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Two-Photon exchange

•The 2 amplitude may be mostly imaginary.

•In this case, the 1-2 interference is more important in

time-like region, as the Born amplitude is complex.

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•For one-photon exchange: •Two (complex) EM form factors•Functions of one variable (t)

4 spin ½ fermions →→ 16 amplitudes in the general case.P- and T-invariance of EM interaction, helicity conservation,

Model independent considerations for

•For two-photon exchange: •Three (complex) amplitudes•Functions of two variables (s,t)

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Model independent considerations for

The hadronic current:

For 1 -exchange:

Decomposition of the amplitudes:

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)

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Unpolarized hadronic tensor

2term

Hadronic tensor

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Unpolarized cross section

•Induces four new terms•Odd function of •Does not contribute at =90°

2term

Destroys the linearity of the Rosenbluth fit in SL region!

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•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:

Symmetry relations

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Nucleon form factor ratio

•The ratio of the FFs moduli is given by the following expression:

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Single spin asymmetry•T-odd observable

•At 90° (vanishes for 1exchange) :

•At threshold (vanishes for 1exchange due to GE=GM) :

•TPE contribution:•Small, of the order of •Relative role increases when q2 increases

•Does not vanish, in the general case, for 1 exchange

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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

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Double spin observables

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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

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Single spin polarization observables

Symmetric hadronic tensor (also for 1 exchange)

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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, 2effect should appear at ~1 GeV2,for protons ~ 10 GeV2

q/2 q/2

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Double spin observables

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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%