Reexamination of vacuum-polarization corrections to the self-energy in muonic bound systems

In muonic bound systems, the dominant radiative correction is due to vacuum polarization.Yet, for the interpretation of precision experiments, self-energy effects are also important.In turn, additional vacuum-polarization loops perturb the self-energy.Here, we show that combined selfenergy vacuum-polarization effects can perturb the bound-state self-energy at the percent level in one-muon bound systems with nuclear charges Z = 1-6.We also update previous treatments of the corrections for muonic hydrogen, muonic deuterium, and muonic helium bound systems.CONTENTS I. Introduction 1 II.Rederivation 2 A. NRQED Adapted to Muonic Systems 2 B. Low-Energy Part 3 C. High-Energy Part 5 D. End Result 7 III.Numerical Results 9 A. Numerical Methods 9 B. Leading Logarithm 9 C. Lamb Shift 10 IV. Conclusions 10