Lepton-proton two-photon exchange in chiral perturbation theory

Abstract

We use heavy baryon chiral perturbation theory to evaluate the two-photon exchange corrections to the low-energy elastic lepton-proton scattering at next-to-leading order accuracy, i.e., O(α, M −1 ), including a non-zero lepton mass. We consider the elastic proton intermediate state in the two-photon exchange invoking soft photon approximation. The infrared singular contributions are projected out using dimensional regularization. The resulting infrared singularity-free two-photon exchange contribution is in good numerical agreement with existing predictions based on standard diagrammatic soft photon approximation evaluations.

Radiative Correction to Lepton Proton Scatterings in Manifestly Lorentz-Invariant Chiral Perturbation Theory

“…4, comparing with conventional Feshbach's result [56] and recent papers, e.g., Refs. [22,23,32], the contributions are close to the results of hadron model [22,23] without using SPA. There are significant differences comparing with the estimation of HBχPT [32] when using SPA, whatever in ep or µp scatterings.…”

“…[22,23,32], the contributions are close to the results of hadron model [22,23] without using SPA. There are significant differences comparing with the estimation of HBχPT [32] when using SPA, whatever in ep or µp scatterings. At the same time, it can be seen that the so-called model independent results obtained from SPA in Ref.…”

“…The former cancels the IR divergence derived from the TPE corrections, and the latter cancels the IR divergence of the vertex corrections. [56](labeled as "Feshbach"), hadron model calculation [22](labeled as "Had"), modelindependent calculation based on SPA [16](labeled as "SPA") and recent HBχPT calculation also based on SPA [32](labeled as "HBχPT") are displayed.…”

“…In order to esitimate the QED radiative corrections in low energies (q 2 ∼ m 2 π ), effective field theory (EFT) provides a systematic formalism to study these processes. Recently, heavy baryon chiral perturbation theory (HBχPT) has been used to estimate TPE [32] and complete radiative corrections [33]. However, HBχPT has its own shortcomings [34,35].…”

“…Figure 4: Comparison of TPE finite contribution to e − p and µ − p elastic scatterings. The contributions of the Feshbach result[56](labeled as "Feshbach"), hadron model calculation[22](labeled as "Had"), modelindependent calculation based on SPA[16](labeled as "SPA") and recent HBχPT calculation also based on SPA[32](labeled as "HBχPT") are displayed.…”