Forward backward CP asymmetry in $\tau^- \to K \pi \nu_{\tau}$ in the Left-Right Inverse seesaw model

TL;DR

This paper explores CP asymmetry in tau decays within the Left-Right Inverse Seesaw model, highlighting a significant differential asymmetry signal despite a small integrated effect, offering new experimental probes.

Contribution

It identifies a dominant scalar operator in the LRIS model that enhances differential CP asymmetry in tau decays, providing novel observable signatures.

Findings

Integrated CP asymmetry remains small, insufficient to explain BaBar results.

Differential forward-backward CP asymmetry shows a pronounced signal near resonances.

Scalar operator contributions significantly affect angular observables, testable at Belle II.

Abstract

Recent measurements of the integrated CP asymmetry in $\tau \to K\pi\nu_\tau$ decays by the BaBar collaboration exhibit a $2.8\sigma$ deviation from the Standard Model (SM) prediction. In this work, we investigate CP-violating effects in $\tau \to K\pi\nu_\tau$ within the model of the Left--Right Inverse Seesaw (LRIS) model. We show that, although the integrated asymmetry remains too small to account for the BaBar result, the model nevertheless predicts a pronounced signal in the \emph{differential} forward--backward CP asymmetry, $A_{\rm CP}^{\rm FB}(s)$. We derive the effective $|\Delta S| = 1$ Hamiltonian relevant for these decays and identify a dominant non-decoupling scalar operator, $g_S$, generated by a top-quark flavor-changing neutral current box diagram involving heavy neutrinos and scalar exchange. Our numerical analysis demonstrates that, while this contribution largely cancels in the integrated $A_{\rm CP}$, it significantly enhances $A_{\rm CP}^{\rm FB}(s)$ through interference with the SM vector current, leading to distinctive kinematic features near the $K^*(892)$ and $K_0^*(1430)$ resonances. These angular and differential observables provide a sensitive probe of the LRIS scalar sector at current and future flavor experiments, in particular Belle~II.