Test of Rest Mass Dynamics Through Bound Muon Decay-in-Orbit Spectra

<title>Abstract</title> <p>The upcoming COMET and Mu2e experiments aim to search for charged-lepton flavor violation with unprecedented sensitivity, requiring an exact characterization of the muon decay-in-orbit (DIO) spectrum near its kinematic endpoint. Here, we present a testable prediction derived from rest mass dynamics and special relativistic energy conservation. In contrast to standard Quantum Electrodynamics —where the bound muon retains its invariant rest mass— our approach predicts that atomic binding intrinsically rescales the bound particle's internal dynamics. For muonic aluminum (Z=13), this yields two correlated, parameter-free signatures at the DIO endpoint: i) a downward endpoint displacement of approximately 0.95 MeV, and ii) a 0.9% horizontal compression of the spectrum corresponding to an equivalent retardation of the integrated decay rate. The simultaneous observation of these signatures would provide direct empirical evidence for the proposition that atomic binding modifies a bound particle's intrinsic rest mass.</p>