CP asymmetry in $\tau\to K_S\pi\nu_\tau$ decays within the Standard Model and beyond

TL;DR

This paper investigates the CP asymmetry in tau decays to K_S pi nu, revisiting the Standard Model prediction and exploring potential new physics explanations, including scalar leptoquarks, in light of experimental discrepancies.

Contribution

It provides a dispersive representation of the K pi tensor form factor and analyzes CP asymmetry within both model-independent and scalar leptoquark frameworks, addressing the observed anomaly.

Findings

CP asymmetry can be explained within a model-independent approach at 1σ

Scalar leptoquark scenario marginally reconciles the anomaly at 2σ

Combined constraints exclude new physics explanations under certain assumptions

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.