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 ÎÏFC ) of the laser beam interacting with either electron or the muon beam in the framework of the quantum Boltzmann equation. Regarding the experimentally available sensitivity to the Faraday conversion ÎÏFCâ10â3â10â2 , we show that the scattering of a linearly polarized laser beam with energy k0â¼0.1 eV and an electron/muon beam with flux ÏµÂ¯e,Î¼â¼1010/1012 TeV cm â2 s â1 places an upper bound on the combination of lepton sector Lorentz violation coefficients cÎ¼Î½ components (cTT+1.4 c(TZ)+0.25(cXX+cYY+2 cZZ) . The obtained bound on the combination for the electron beam is at the 4.35Ã10â15 level and for the muon beam at the 3.9Ã10â13 level. It should be mentioned that the laser and charged lepton beams considered here to reach the experimentally measurable ÎÏFC are currently available or will be accessible in the near future. This study provides a valuable supplementary to other theoretical and experimental frameworks for measuring and constraining Lorentz violation coefficients.
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