Improving the accuracy of the muon mass and magnetic moment anomaly via the bound-muon g factor

A theoretical description of the g factor of a muon bound in a nuclear potential is presented. One-loop self-energy and multiloop 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 muon's magnetic moment anomaly and mass. The scheme presented enables the increase of the accuracy of the mass by more than an order of magnitude.