Abstract
Motivated by the $2.8\sigma$ discrepancy observed between the BaBar measurement and the Standard Model prediction of the CP asymmetry in $\tau\to K_S\pi\nu_\tau$ decays, as well as the prospects of future measurements at Belle II, we revisit this observable in this paper. Firstly, we reproduce the known CP asymmetry due to $K^0 -\bar{K}^0$ mixing by means of the reciprocal basis, which is convenient when a $K_{S(L)}$ is involved in the final state. As the $K\pi$ tensor form factor plays a crucial role in generating a non-zero direct CP asymmetry that can arise only from the interference of vector and tensor operators, we then present a dispersive representation of this form factor, with its phase obtained in the context of chiral theory with resonances, which fulfills the requirements of unitarity and analyticity. Finally, the $\tau\to K_S\pi\nu_\tau$ decays are analyzed both within a model-independent low-energy effective theory framework and in a scalar leptoquark scenario. It is observed that the CP anomaly can be accommodated in the model-independent framework, even at the $1\sigma$ level, together with the constraint from the branching ratio of $\tau^-\to K_S\pi^-\nu_\tau$ decay; it can be, however, marginally reconciled only at the $2\sigma$ level, due to the specific relation between the scalar and tensor operators in the scalar leptoquark scenario. Once the combined constraints from the branching ratio and the decay spectrum of this decay are taken into account, these possibilities are however both excluded, even without exploiting further the stronger bounds from the (semi-)leptonic kaon decays under the assumption of lepton-flavour universality, as well as from the neutron electric dipole moment and $D-\bar{D}$ mixing under the assumption of $SU(2)$ invariance of the weak interactions.
Highlights
As the Kobayashi-Maskawa ansatz [1] for CP violation in the quark sector of the standard model (SM) is far too small to explain the observed baryon asymmetry of the Universe [2,3,4,5], we need to look for other sources of CP violation in different ways
As only the interference between vector and tensor operators can provide a potential new physics (NP) explanation of the CP anomaly observed in τ → KSπντ decays [21,24], we focus on the tensor coupling εT
In this paper, motivated by the 2.8σ discrepancy observed between the BABAR measurement and the SM prediction of the CP asymmetry in τ → KSπντ decays, as well as the prospects of future measurements at Belle II, we have studied this observable within the model-independent low-energy effective theory framework and in the scalar LQ scenario, both of which contain a nonstandard tensor operator that is necessary to produce a nonvanishing direct CP asymmetry in the decays considered
Summary
As the Kobayashi-Maskawa ansatz [1] for CP violation in the quark sector of the standard model (SM) is far too small to explain the observed baryon asymmetry of the Universe [2,3,4,5], we need to look for other sources of CP violation in different ways. After taking into account the KS → πþπ− decay-time dependence of the event selection efficiency, the BABAR Collaboration obtained a multiplicative correction factor, 1.08 Æ 0.01, for the CP asymmetry, with the resulting experimental data given by Eq (1.1) and the corresponding SM prediction changed to ASCMP 1⁄4 ð0.36 Æ 0.01Þ% [13]. In order to obtain sensible constraints on nonstandard interactions from τ → KSπντ decays, the exact distributions of the Kπ form factors, including both their moduli and phases, as a function of s 1⁄4 q2, the invariant mass squared of the Kπ final state, are needed. We shall discuss AτCP in a scalar LQ scenario, which contains the relevant operators
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