A no-go theorem for non-standard explanations of the $\tau\to K_S\pi\nu_\tau$ CP asymmetry

Vincenzo Cirigliano,Andreas Crivellin,Martin Hoferichter

doi:10.21468/scipostphysproc.1.007

Abstract

A new tensor interaction is the only possibility to explain the \boldsymbol{2.8\sigma}2.8𝛔 tension observed by the BaBar collaboration in the CP asymmetry in \boldsymbol{\tau\to K_S\pi\nu_\tau}𝛕→𝐊𝐒𝛑𝛎𝛕 with physics beyond the Standard Model (BSM) realized above the electroweak scale. However, the strong phase generated by the interference between vector and tensor phases is suppressed by at least two orders of magnitude due to Watson’s final-state-interaction theorem, and the strength of the CP-violating tensor interaction is strongly constrained by bounds from the neutron electric dipole moment and \boldsymbol{D}𝐃–\boldsymbol{\bar{D}}𝐃‾ mixing. As a result, a confirmation of the tension at Belle II would point to light BSM physics.

Highlights

CP-violating observables are interesting because of their potential connections to baryogenesis mechanisms
In this note we summarize our arguments why this tension cannot be resolved by beyond the Standard Model (BSM) physics above the electroweak scale [4]
While the normalization is known from lattice QCD [6], it had been assumed in previous work that the tensor form factor stays constant as a function of s [5]

Summary

Introduction

CP-violating observables are interesting because of their potential connections to baryogenesis mechanisms. We consider the asymmetry of the decay width for τ → KSπντ. This asymmetry is non-vanishing already in the Standard Model (SM), driven by indirect CP violation in K0–K 0 mixing [1, 2], and can be predicted accurately from the CP violation as measured in semileptonic kaon decays. Including corrections from the experimental conditions and time-dependent efficiencies, the corresponding prediction AτC,PSM = 3.6(1) × 10−3 [2]. In this note we summarize our arguments why this tension cannot be resolved by BSM physics above the electroweak scale [4]

Effective Lagrangian and decay rate

Hadronic form factors

Limits on Im cT

Conclusions