Search for T-violating transverse muon polarization in the K{sup +}{yields}{pi}{sup 0}{mu}{sup +}{nu} decay

At the 12-GeV proton synchrotron of KEK, an experiment (KEK-PS-E246) was performed to measure the transverse muon polarization (${P}_{T}$) in ${K}^{+}\\ensuremath{\\rightarrow}{\\ensuremath{\\pi}}^{0}{\\ensuremath{\\mu}}^{+}\\ensuremath{\\nu}$ decays as a direct search of violation of time reversal invariance ($T$-violation). ${P}_{T}$ is a very sensitive probe of $CP$ violation beyond the standard model. A stopped positive kaon beam was used. An elaborate high-acceptance detector, in conjunction with a 12-sector superconducting toroidal spectrometer, was utilized. The stopped kaon method provided several advantages in performing a high-precision experiment. The decay was identified by detecting a ${\\ensuremath{\\mu}}^{+}$ with the spectrometer and a ${\\ensuremath{\\pi}}^{0}$ with a CsI(Tl) calorimeter surrounding the target as two photons as well as one photon with high energy. For the ${P}_{T}$ measurement, ${\\ensuremath{\\pi}}^{0}$ events in the forward (fwd) and backward (bwd) regions in the calorimeter were relevant. Systematic errors were greatly suppressed by exploiting the rotational and fwd-bwd symmetry of the system. Polarization measurement was done in terms of asymmetry measurement of decay positrons of stopped muons in the polarimeter. A longitudinal field method was applied for the ${P}_{T}$ polarization component. In the data analysis a novel technique of the two-analysis method was employed. Two independent analyses were performed following their own policy and criteria and good events were selected. Then, the two analyses were combined. A data quality check was carefully done by looking at the null asymmetry ${A}_{0}$, the sensitivity function ${A}_{N}$, the kinematical attenuation coefficient, and the decay-plane distributions. The asymmetry measurement for finite-size muon stoppers was performed ``differentially'' using the position information by the chamber in front of the polarimeter. From the measurements during 1996--2000, we accumulated $11.8\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{6}$ good events after the two-analysis combination, and deduced ${P}_{T}=\\ensuremath{-}0.0017\\ifmmode\\pm\\else\\textpm\\fi{}0.0023(\\mathrm{stat})\\ifmmode\\pm\\else\\textpm\\fi{}0.0011(\\mathrm{syst})$, corresponding to the $T$-violating parameter $\\mathrm{Im}\\ensuremath{\\xi}=\\ensuremath{-}0.0053\\ifmmode\\pm\\else\\textpm\\fi{}0.0071(\\mathrm{stat})\\ifmmode\\pm\\else\\textpm\\fi{}0.0036(\\mathrm{syst})$. From these results the upper limits of $|{P}_{T}|l0.0050$ (90% C.L.) and $|\\mathrm{Im}\\ensuremath{\\xi}|l0.016$ (90% C.L.) were deduced. Systematic errors were carefully studied and estimated. Almost all of the errors were canceled by the 12-sector summation and/or fwd-bwd subtraction, and the total systematic error was concluded to be as a half of the statistical error. The present result set constraints on model parameters of several theoretical models. For the three-Higgs-doublet model, e.g., a limit $|\\mathrm{Im}({\\ensuremath{\\alpha}}_{1}{\\ensuremath{\\gamma}}_{1}^{*})|l544({M}_{{H}_{1}}/\\mathrm{GeV}{)}^{2}$ was obtained. Implications for several other models are discussed.