Limits on aπ-μatom anomaly

The decay rate of $K_L^0$ into $\pi \mu$ atoms provides a test for the existence of a possible short-range anomalous interaction between the pion and muon. For an elastic interaction, the effect would show up in the $\pi \mu$ wave function of the Coulomb bound state, and we examine mechanisms that could alter the wave function at the origin. An inelastic interaction that could lead to depletion of $\pi \mu$ atoms through the Konopinski-Mahmoud-allowed transition ${\pi }^{+}{\mu }^{-}\to {\pi }^{-}{e}^{+}$ is also considered. Limits on these interactions are computed from precise atomic measurements of energy levels in muonic atoms and from the measured muon $g-2\mathrm{}$ value and capture rates. These limits are then related to recent observations on the formation of $\pi \mu$ atoms in $K_L^0$ decay.