Longitudinal Polarization in $K_L \to \mu^+ \mu^-$ in MSSM with large $tan\beta$

TL;DR

This paper explores how in the MSSM with large tanβ and light Higgs masses, the longitudinal polarization in the decay $K_L o \mu^+ \\mu^-$ can be significantly enhanced, providing a potential test for new physics beyond the Standard Model.

Contribution

It demonstrates that MSSM with large tanβ and light Higgs masses can increase lepton polarization in $K_L$ decays, offering a new observable for CP violation tests.

Findings

Lepton polarization can reach about 10^{-2} in MSSM with specified parameters.

Standard Model predicts polarization of order 10^{-3}.

Enhanced polarization could serve as a signal of new physics.

Abstract

A complete experiment on decay $K_L \to l^+ l^-$ will not only consist of measurement of the decay rates but also lepton polarization etc. These additional observations will yield tests of CP invariance in these decays. In $K_L$ and $K_S$ decays, the e mode is slower than the $\mu$ mode by roughly $(m_e/m_\mu)^2$ \cite{sehgal1}. As well discussed in literature \cite{herczeg} the Standard Model contribution to the lepton polarization is of order $2 \times \sim 10^{-3}$. We show that in MSSM with large \tanbeta and light higgs masses ($\sim 2 M_W$), the longitudinal lepton polarization in $K_L \to \mu^+ \mu^-$ can be enhanced to a higher value, of about $10^{-2}$.