An improved search for a T-violating transverse muon polarization ͑P T ͒ in K 1 ! p 0 m 1 n decay was performed using kaon decays at rest. By means of this method, P T was extracted with small systematic errors, P T 20.0042 6 0.0049͑stat͒ 6 0.0009͑syst͒, and the T-violation parameter was determined to be Imj 20.013 6 0.016͑stat͒ 6 0.003͑syst͒.The transverse muon polarization ͑P T ͒ in the K 1 ! p 0 m 1 n decay ͑K 1 m3 ͒ is the polarization component normal to the decay plane, and is a T -odd observable defined by the correlation of the p 0 and m 1 momentum vectors p p 0 and p m 1 and the m 1 spin s m , as P T s m ? ͑p p 0 3 p m 1 ͒͞jp p 0 3 p m 1 j. A nonzero value would be evidence for violation of time reversal invariance ͑T ͒ [1], since any spurious effect from final state interactions is known to be small [2]. Moreover, because the contribution to P T from the standard model (SM) is as small as 10 27 [3], P T would provide important clues to new physics beyond the SM, or in particular, to a CP-violation mechanism from non-SM origins [4] assuming CPT invariance. It is in contrast to the SM T -violation recently observed in the neutral kaon system [5]. The previous limit of P T along with that from K 0 L ! p 2 m 1 n decay ͑K 0 m3 ͒ come from Brookhaven National Laboratory (BNL) experiments [6,7] to obtain the T -violation physics parameter, Imj 20.016 6 0.025 ͑K 1 m3 ͒ and Imj 0.009 6 0.030 ͑K 0 m3 ͒, where j is defined as the ratio of two form factors, f 1 ͑q 2 ͒ and f 2 ͑q 2 ͒ [8].In this Letter we report an improved search for P T . The present experiment (KEK E246) uses stopped K 1 as opposed to the previous BNL experiment [6] which used in-flight decay. The decay products are emitted in all directions and detected with a setup in a 12-sector superconducting toroidal magnet (Figs. 1a and 1b). P T is measured as the azimuthal ͑f͒ polarization of m 1 emitted radially ͑r͒ when a p 0 is tagged in the forward (fwd) or the backward (bwd) direction relative to the detector ͑z͒ axis. The signature of nonzero P T is an asymmetry between clockwise (cw) and counterclockwise (ccw) Michel e 1 (Fig. 1c). Summation over the twelve sectors plays an important role in reducing systematic error. For finite P T , events from fwd and bwd p 0 's have opposite asymmetries. By taking their difference, the P T signal is doubled and most systematic errors are reduced.A separated K 1 beam ͑p 1 ͞K 1 ഠ 6͒ of 660 MeV͞c was produced at the 12 GeV proton synchrotron with a 0031-9007͞99͞83(21)͞4253(4)$15.00

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The ratio of the K + → π 0 µ + ν (K + µ3 ) and K + → π 0 e + ν (K + e3 ) decay widths, Γ(K µ3 )/Γ(K e3 ), has been measured with stopped positive kaons. K + µ3 and K + e3 samples containing 2.4×10 4 and 4.0×10 4 events, respectively, were analyzed. The Γ(K µ3 )/Γ(K e3 ) ratio was obtained to be 0.671±0.007(stat.)±0.008(syst.) calculating the detector acceptance by a Monte Carlo simulation. The coefficient of the q 2 dependent term of the f 0 form factor was also determined to be λ 0 =0.019±0.005(stat.)±0.004(syst.) with the assumption of µ-e universality in K + l3 decay. The agreement of our result with the λ 0 value obtained from K + µ3 Dalitz plot analyses supports the validity of the µ-e universality.