Muon anomalous magnetic moment in the standard model extension

TL;DR

This paper investigates how Lorentz-violating parameters in the standard model extension affect the muon's anomalous magnetic moment, revealing energy dependence and setting experimental bounds on these parameters.

Contribution

It introduces a novel analysis of the energy dependence of the muon magnetic form factor within the SME framework and establishes the first experimental bounds on specific Lorentz-violating parameters.

Findings

Energy dependence of the magnetic form factor at one-loop level.

Enhancement of the muon anomalous magnetic moment at high energy.

New terrestrial bounds on SME Lorentz-violating parameters.

Abstract

We consider the standard model extension to explore the anomalous magnetic dipole moment of the muon. In the QED part of the theory for the CP and CPT-even Lorentz parameter $c_{\mu\nu}$, all independent electromagnetic form factors depend on a new scalar as $p'.c.p$. Therefore, the form factors, even in zero momentum transfer, can be energy dependent. We examine the magnetic form factor to find such an energy dependent up to the one loop level at the leading order of $c_{\mu\nu}$. We show that at the high energy limit (but low enough to satisfy $p^2/m^2\ll1$) there is an enhancement on the muon anomalous magnetic moment. For the first time, we find a bound on the $c_{\mu\nu}$ components for the muon as $[c_{TT}+0.35(c_{XX}+c_{YY})+0.28c_{ZZ}]$, which is about $10^{-11}$ in a terrestrial experiment