Probing Lorentz violation effects via a laser beam interacting with a high-energy charged lepton beam

In this work, the conversion of linear polarization of a laser beam to circular one through its forward scattering by a TeV order charged lepton beam in the presence of Lorentz violation correction is explored. We calculate the ratio of circular polarization to linear one (Faraday Conversion phase \(\Delta\phi\)) of laser photons interacting with either electron or muon beam in the framework of the quantum Boltzmann equation. We discuss how the interaction of laser beam and charged lepton beams can provide a suitable situation to constrain Lorentz violation coefficients, especially for \(c^{\mu \nu}\) coefficients. It is shown that \(\Delta\phi\) depends on the direction of both interacting beams and the location of the lab which can help to determine \(c^{\mu \nu}\) components individually. It should be mentioned that the laser and charged lepton beams considered here to reach an experimentally measurable \(\Delta\phi\), are currently available. This study provides a valuable supplementary to other theoretical and experimental frameworks for measuring and constraining Lorentz violation coefficients.