Wave function correction to the decay of pionium and heavy fermionium

Abstract

Abstract The decay rates of heavy atomic systems consisting of a particle and its own antiparticle are influenced by the probability density (“charge density”, square of the wave function) at the origin. In heavy systems, the one-loop electronic vacuum polarization induces a correction to the charge density (at the origin) of relative order α π . The correction is analyzed in this Letter, and results are provided for dimuonium ( μ + μ − atom), pionium ( π + π − atom), and the hypothetical heavy tauonium ( τ + τ − atom). We investigate the correction in the limit of strong binding and discuss the applicability of the effective charge approach to derive leading logarithmic asymptotics.