Phenomenological extraction of two-photon exchange amplitudes from elastic electron-proton scattering cross section data

Background: The inconsistency in the results obtained from the Rosenbluth separation method and the high-Q2 recoil polarization results on the ratio μpGEp/GMp implies a systematic difference between the two techniques. Several studies suggest that missing higher-order radiative corrections to elastic electron-proton scattering cross section σR(Q2) and in particular hard two-photon-exchange (TPE) contributions could account for the discrepancy. Purpose: In this work, I improve on and extend to low and high Q2 values the extractions of the dependence of the real parts of the TPE amplitudes relative to the magnetic form factor, as well as the ratio Pl/PlBorn(Q2) by using world data on σR(Q2) with an emphasis on precise new data covering the low-momentum region which is sensitive to the large-scale structure of the nucleon. Method: I combine cross section and polarization measurements of elastic electron-proton scattering to extract the TPE amplitudes. Because the recoil polarization data were confirmed "experimentally" to be essentially independent of I constrain the ratio Pt/Pl(Q2) to its -independent term (Born value) by setting the TPE contributions to zero. This allows for the amplitude YM(Q2) and σR(Q2) to be expressed in terms of the remaining two amplitudes YE(Q2) and Y3(Q2) which in turn are parametrized as second-order polynomials in and Q2 to reserve as possible the linearity of σR(Q2) as well as to account for possible nonlinearities in the TPE amplitudes. Furthermore, I impose the Regge limit which ensures the vanishing of the TPE contributions to σR(Q2) and the TPE amplitudes in the limit →1. Results: I provide simple parametrizations of the TPE amplitudes, along with an estimate of the fit uncertainties. The extracted TPE amplitudes are compared with previous phenomenological extractions and TPE calculations. The Pl/PlBorn ratio is extracted by using the new parametrizations of the TPE amplitudes and compared to previous extractions, TPE calculations, and direct measurements at Q2=2.50(GeV/c)2. Conclusions: The extracted TPE amplitudes are on the few-percentage-points level and behave roughly linearly with increasing Q2 where they become nonlinear at high Q2. Contrary to YM, which is influenced mainly by elastic contributions, I find YE to be influenced by inelastic contributions at large Q2 values. While YE and Y3 differ in magnitude, they have opposite sign and tend to partially cancel each other. This suggests that the TPE correction to σR(Q2) is driven mainly by YM and to a lesser extent by Y3 in agreement with previous phenomenological extractions and hadronic TPE calculations.