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

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.