Measurement of muon polarization in $K^+\toπ^0μ^+ν_μ$ at a $ϕ$ factory

Abstract

The potentiality of an experiment measuring the muon polarization in $K^+\rightarrowπ^0μ^+ν_μ$ at a $ϕ$ factory is discussed, with particular attention to the possibility of revealing unexpected violation of Time reversal invariancethrough the transverse polarization component. An experimental method is proposed which is based on the reconstruction of the $K^+\rightarrowπ^0μ^+ν_μ$ decay products after stopping the charged kaons in a target placed around the beam pipe. The muon polarization is measured by observing the asymmetry in the angular distribution of positrons from the $μ^+ \rightarrow e^+ ν\barν$ decay of muons stopped in a polarization analyser. It is shown that an error $σ_P\simeq 5\cdot 10^{-4}$ on each muon polarization component can be obtained, which represents a factor ten improvement with respect to current limits on T invariance violation in the $K^+\rightarrowπ^0μ^+ν_μ$ decay and a precise measurement of the $Reξ$ parameter at the level of $2\cdot 10^{-3}$.