Relativistic elastic scattering of an electron by a muon in the field of a circularly polarized electromagnetic wave

TL;DR

This paper theoretically investigates relativistic electron-muon elastic scattering in a circularly polarized laser field using quantum electrodynamics, deriving analytical expressions for the amplitude and cross section, and analyzing the effects of laser dressing.

Contribution

It provides a detailed analytical study of electron-muon scattering in a laser field, including the effects of relativistic dressing of both particles, which was not fully explored before.

Findings

Laser field significantly reduces the differential cross section.

Muon dressing effects become noticeable at field strengths ≥ 10^9 V/cm.

Laser parameters influence the multiphoton scattering process.

Abstract

Within the framework of quantum electrodynamics, the scattering of an electron by a muon in the presence of a circularly polarized monochromatic laser field is investigated theoretically in the first Born approximation. The expressions for the amplitude and the differential cross section are derived analytically by adopting the Furry picture approach in which the calculations are carried out using exact relativistic Dirac-Volkov functions. We begin by studying the process taking into account the relativistic dressing of only the electron without muon. Then, in order to reveal the effect of the muon dressing, we fully consider the relativistic dressing of the electron and muon together in the initial and final states. As a result, the differential cross section is significantly reduced by the laser field. We find that the effect of laser-dressing of muon becomes noticeable at laser field strengths greater than or equal to $10^{9}~\text{V cm}^{-1}$ and therefore must be taken into account. The influence of the laser field strength and frequency on the differential cross section and multiphoton process is revealed. An insightful comparison with the laser-free results is also included.17