Studies of low energy $l+p\to l+p+\gamma$ process in covariant chiral perturbation theory

TL;DR

This paper calculates the low-energy $l+p\to l+p+\gamma$ scattering amplitude using covariant chiral perturbation theory, highlighting the impact of lepton mass and discussing implications for nucleon polarizabilities.

Contribution

It provides a tree-level theoretical prediction for the process within chiral perturbation theory, including the effects of nonzero lepton mass and analyzing the validity domain.

Findings

Explicit lepton mass significantly affects low-energy differential cross sections.

Current experimental data are outside the validity domain of the theory.

Results can help determine nucleon generalized polarizabilities.

Abstract

This study presents a tree-level calculation of the scattering amplitude for the $lp\to lp\gamma$ (with a hard photon) process within the framework of Chiral Perturbation Theory. Our calculations, based on the $O(p^2)$ and $O(p^3)$ nucleon-pion Lagrangians, aim to provide a theoretical prediction for the differential cross-section. The result shows that explicit inclusion of the nonzero lepton mass significantly influences the low energy differential cross section for $\mu p\to \mu p \gamma$ process. The kinematic region of the present experimental data is beyond the validity domain of the $\chi$PT and is therefore not suitable for determining the low-energy constants (LECs). By comparing our results with future experimental data, we expect to determine the values of the LECs as a further test of $\chi$PT as an effective low-energy theory of QCD. The process is of significant interest as it can help to determine the generalized polarizabilities of the nucleon.