Muon Decay Asymmetries from $K^0_L \to \pi^0 \mu^+ \mu^-$ Decays

TL;DR

This paper investigates the decay $K^0_L o \pi^0 \mu^+ \mu^-$, showing that certain asymmetries and muon polarization measurements can reveal different CP violation sources within the Standard Model.

Contribution

It demonstrates how combined measurements of asymmetries and muon polarization can distinguish between direct and indirect CP violation in this decay.

Findings

Muon longitudinal polarization is proportional to direct CP violation.

Energy and out-of-plane polarization depend on both direct and indirect CP violation.

Asymmetries could be large (~1) despite small branching ratio.

Abstract

We have examined the decay $K^0_L \to \pi^0 \mu^+ \mu^-$ in which the branching ratio, the muon energy asymmetry and the muon decay asymmetry could be measured. In particular, we find that within the Standard Model the longitudinal polarization ($P_L$) of the muon is proportional to the direct CP violating amplitude. On the other hand the energy asymmetry and the out-of-plane polarization ($P_N$) depend on both indirect and direct CP violating amplitudes. Although the branching ratio is small and difficult to measure because of background, the asymmetries could be large $\cal{O}$(1) in the Standard Model. A combined analysis of the energy asymmetry, $P_L$ and $P_N$ could be used to separate indirect CPV, direct CPV, and CP conserving contributions to the decay.