Access to improve the muon mass and magnetic moment anomaly via the bound-muon $g$ factor

TL;DR

This paper presents a theoretical framework for calculating the bound-muon g factor, incorporating quantum corrections and nuclear effects, and proposes a measurement method to improve the precision of the muon mass and magnetic moment anomaly.

Contribution

It introduces a comprehensive calculation of the bound-muon g factor with quantum and nuclear effects and proposes a measurement scheme to enhance muon property precision.

Findings

Calculated one-loop self-energy and multi-loop vacuum polarization corrections.

Evaluated nuclear effects on the bound-muon g factor.

Proposed measurement method can increase muon mass accuracy by over tenfold.

Abstract

A theoretical description of the $g$ factor of a muon bound in a nuclear potential is presented. One-loop self-energy and multi-loop vacuum polarization corrections are calculated, taking into account the interaction with the binding potential exactly. Nuclear effects on the bound-muon $g$ factor are also evaluated. We put forward the measurement of the bound-muon $g$ factor via the continuous Stern-Gerlach effect as an independent means to determine the free muons magnetic moment anomaly and mass. The scheme presented enables to increase the accuracy of the mass by more than an order of magnitude.