Abstract
We evaluate the two-photon exchange (TPE) correction to the muon-proton elastic scattering at small momentum transfer. Besides the elastic (nucleon) intermediate state contribution, which is calculated exactly, we account for the inelastic intermediate states by expressing the TPE process approximately through the forward doubly virtual Compton scattering. The input in our evaluation is given by the unpolarized proton structure functions and by one subtraction function. For the latter, we provide an explicit evaluation based on a Regge fit of high-energy proton structure function data. It is found that, for the kinematics of the forthcoming muon-proton elastic scattering data of the MUSE experiment, the elastic TPE contribution dominates, and the size of the inelastic TPE contributions is within the anticipated error of the forthcoming data.
Highlights
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 two-photon exchange (TPE) corrections through the near forward doubly virtual Compton scattering process [10]
We clarify the TPE correction coming from the subtraction function, and we provide an empirical determination of the subtraction function based on the high-energy behavior of the forward Compton amplitude T1
The TPE contribution, δ2γ, for the muon–proton scattering process is in general given by the interference of the one-photon exchange amplitude (T OPE) and the two-photon exchange amplitude (T TPE) as spin T TPE T OPE ∗
Summary
In this work we study the TPE correction at low momentum transfer to unpolarized elastic scattering of a charged lepton with mass m and initial (final) momentum k (k ) on a proton with mass M and initial (final) momentum p ( p ); see Fig. 1 for the notations of kinematics and helicities. The first TPE estimate is due to Feshbach and McKinley [11], who calculated the TPE contribution, corresponding with Coulomb photon couplings to the static proton (i.e. two γ 0 vertices). This so-called Feshbach term contribution to δ2γ in Eq (1) is denoted by δF and can be expressed through the scattering angle in the laboratory frame θ and the lepton velocity v as δF. In the low Q2 kinematics of the MUSE experiment, the inclusion of the FFs provides a reduction of the TPE by around 40 % at Q2 ≈ 0.025 GeV2, one should use the
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
