Two-photon exchange correction in elastic unpolarized electron-proton scattering at small momentum transfer

Abstract

We evaluate the two-photon exchange (TPE) correction to the unpolarized elastic electron-proton scattering at small momentum transfer Q 2 . We account for the inelastic intermediate states approximating the double virtual Compton scattering by the unpolarized forward virtual Compton scattering. The unpolarized proton structure functions are used as input for the numerical evaluation of the inelastic contribution. Our calculation reproduces the leading terms in the Q 2 expansion of the TPE correction and goes beyond this approximation by keeping the full Q 2 dependence of the proton structure functions. In the range of small momentum transfer our result is in good agreement with the empirical TPE fit to existing data. Contents

Two-photon exchange correction to muon–proton elastic scattering at low momentum transfer

“…This is unlike the elastic electron-proton scattering case, where in the limit m 2 Q 2 M 2 , M E a non-analytic behavior of the type Q 2 ln Q 2 is present at low Q 2 [10,12].…”

“…11 that the integrand for the elastic e − p scattering displays a narrow peak corresponding with the quasi-real photon singularity (for both photons), see Ref. [10], which is absent for the μ − p case.…”

“…(5) for the process γ * (q 1 =q + q/2) + p(P − q/2) → γ * (q 2 =q − q/2) + p(P + q/2) in the low momentum transfer limit q → 0, i.e. q 1 ≈ q 2 , by [10]:…”

“…It is compared with the Feshbach term for pointlike particles, see Eq. (2), corrected by the recoil factor (1 + m/M), the elastic contribution based on the box graph evaluation with dipole form factors [9] and the e − p total TPE correction [10] 3.1 GeV < W < 4 GeV to δ…”

“…all possible intermediate states in the TPE box graphs beyond the proton state. As our aim is an estimate of such corrections for the MUSE experiment, which corresponds with very low momentum transfers, we will estimate the inelastic TPE corrections through the near forward doubly virtual Compton scattering process [10]. The essential hadronic information is contained in the unpolarized proton structure functions and in one subtraction function.…”