Structure function method applied to polarized and unpolarized electron-proton scattering: A solution of theGE(p)/GM(p

Abstract

The cross section for polarized and unpolarized electron-proton scattering is calculated taking into account radiative corrections in leading and next-to leading logarithmic approximation. The expression of the cross section is formally similar to the cross section of the Drell-Yan process, where the structure functions of the electron play the role of Drell-Yan probability distributions. The interference of the Born amplitude with the two photon exchange amplitude (box-type diagrams) is expressed as a contribution to K-factor and it is larger when the momentum is equally shared between the two photons, assuming that proton form factors decrease rapidly with the momentum transfer squared. The calculation of the box amplitude is done when the intermediate state is a proton or the ∆-resonance. The results of numerical estimations show that the present calculation of radiative corrections can bring into agreement the conflicting experimental results on proton electromagnetic form factors an that the two photon contribution is very small. PACS numbers:

The form factors of the nucleons

“…The effect of the exchange of two photons of similar momenta is to correct the Rosenbluth ratio downwards. After this paper many others have been published (for example [22,23,25]), the reason for this plurality being the difficulty in evaluating such diagrams, as the proton in the intermediate state is off-shell, and can be exited to a number of isobaric states. Recently, at Jlab, a measurement of the G Ep /G Mp ratio was done, at a constant Q 2 of 2.5 GeV 2 but for 3 values of ǫ [11], to verify the prediction that only the Rosenbluth results would be significantly affected by two-photon exchange, not double polarization results, which are ratios of ratios (see Eqs.…”

“…Figure 5: Plotted in ordinate is the quantity −µ p (τ (1 + ǫ)/2ǫ) which, in Born approximation, is equal to G Ep /G E M ; error bars include systematics uncertainties. Curves: "hadronic" [22], "GPD" [23], "COZ BLW" [24] and "SF" [25]. Figure 6: Longitudinal proton polarization, P ℓ , divided by the Born value P ℓ Born calculated from G Ep /G E M in Fig.…”

The OLYMPUS experiment

“…This discrepancy might arise from a significant contribution to the elastic electron-proton cross section from hard two-photon exchange [21][22][23][24][25][26], a process that is neglected in the standard radiative corrections procedures. Since there is no theoretical consensus on the size of this contribution [21][22][23][24][25][26][27][28][29][30][31], definitive measurements are needed to determine if two-photon exchange resolves the form factor discrepancy.…”

Probing two-photon exchange with OLYMPUS

“…in hadronic [7,8], or partonic frameworks of generalized parton distributions and perturbative QCD [9,10]. Also the importance of higher-order radiative effects, not necessarily through two or more photons, has been emphasized [12].…”