LAB observables for the muon polarization in K^+ --> \pi^+ \mu^+ \mu^-

TL;DR

This paper investigates the muon polarization asymmetry in kaon decays, analyzing how it varies with reference frame and energy, and its sensitivity to flavor-mixing parameters within the Standard Model.

Contribution

It provides a detailed analysis of muon polarization asymmetry in kaon decays in the lab frame, highlighting frame dependence and energy effects on the asymmetry.

Findings

Asymmetry depends on the reference frame and is diluted at higher energies.

The analysis shows sensitivity of the asymmetry to flavor-mixing parameters.

The study extends to both K+ and K_L decays, providing comprehensive insights.

Abstract

We analyse the muon longitudinal polarization asymmetry \Delta_long in the decay K^+ --> \pi^+ \mu^+ mu^-. It is stressed that, since the muon helicities are not Lorentz-invariant quantities, the magnitude of \Delta_long depends in general on the reference frame. We consider the muon helicities in the LAB system, and study the sensitivity of the longitudinal polarization asymmetry to the flavour-mixing parameters in the Standard Model for stopped and in-flight decaying K^+. A similar analysis is carried out for the decay K_L --> \mu^+ \mu^-. We find that in both cases the asymmetry is diluted when increasing the energy of the decaying kaons.