Abstract
In this work, we study the C P asymmetry in the angular distribution of τ → KSπντ decays, taking into account the known C P violation in {K}^0-{overline{K}}^0 mixing. It is pointed out for the first time that, once the well-measured C P violation in the neutral kaon system is invoked, a non-zero C P asymmetry would appear in the angular observable of the decays considered, even within the Standard Model. By employing the reciprocal basis, which is most convenient when a KS(L) is involved in the final state, the C P -violating angular observable is derived to be two times the product of the time-dependent C P asymmetry in K → π+π− and the mean value of the angular distribution in {tau}^{pm}to {K}^0left({overline{K}}^0right){pi}^{pm }{overline{nu}}_{tau}left({nu}_{tau}right) decays. Compared with the Belle results measured in four different bins of the K π invariant mass, our predictions lie within the margins of these measurements, except for a 1.7 σ deviation for the lowest mass bin. While being below the current Belle detection sensitivity that is of mathcal{O} (10−3), our predictions are expected to be detectable at the Belle II experiment, where sqrt{70} times more sensitive results will be obtained with a 50 ab−1 data sample.
Highlights
JHEP05(2020)151 but is detected as a difference in the τ ± decay angular distributions, without requiring information about the τ polarization or the determination of the τ rest frame [15, 35– 38]
It is pointed out for the first time that, once the well-measured CP violation in the neutral kaon system is invoked, a non-zero CP asymmetry would appear in the angular observable of the decays considered, even within the Standard Model
We shall investigate for the first time whether an observable CP asymmetry in the angular distribution of τ → KSπντ decays could be generated by the well-measured CP violation in K0 − K 0mixing
Summary
Before presenting our numerical results, we firstly collect in table 1 all the input parameters used throughout this work. Notice that the mass threshold used by the Belle collaboration for the lowest mass bin, sKπ = 0.625 GeV [21], lies slightly below the theoretical one, sKπ = MK +Mπ = 0.637 GeV. As such a numerical difference has only a marginal impact on our prediction, we shall use. As mentioned already in last section, in order to get a as large as possible for a given time interval, we present two more predictions with the Kπ invariant mass intervals selected at the vicinities of the two negative extrema of cos α τ−:. We suggest the experimental τ physics groups at Belle II to measure the CP -violating angular observable in this mass interval
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