Muon precession from the aspect of Dirac equations

Abstract

In this paper, we propose a method to compute the muon anomalous precession frequency through solving the wave functions of the Dirac equations straightforwardly. The Lorentz violation terms are also considered. Our method is different from the traditional two-step algorithm in the literature, with the first step to extract the anomalous magnetic momentum factors through the Fouldy-Wouthuysen transformation or Born approximation comparison methods regarding the muon particle as a “quantum” object, and the second step to utilize the Thomas-Bargmann-Michel-Telegdi formula regarding the muon particle as a “classical” point-like object. Compared with the literature, the method we developed is more consistent and the Lorentz violation terms are taken into account in a unified and straightforward frameset, and expand perturbatively up to the lowest non-trivial order and find out that only b3, c11, c22, H12′ and d30 affect the precession up to this order.