The time-dependent angular analysis of $B_d\to K_S\ell\ell$, a new benchmark for new physics

TL;DR

This paper introduces a time-dependent angular analysis of B_d→K_Sℓℓ decays, identifying new observables that serve as robust tests for new physics, independent of form factors and charm-loop effects.

Contribution

It proposes six new observables in B_d→K_Sℓℓ decays, accessible via time-dependent or time-integrated measurements, providing powerful tests for various new physics scenarios.

Findings

Six new angular observables identified.

Predictions provided for SM and NP models.

Observables are form-factor independent.

Abstract

We consider the time-dependent analysis of $B_d\to K_S\ell\ell$ taking into account the time-evolution of the $B_d$ meson and its mixing into $\bar{B}_d$. We discuss the angular conventions required to define the angular observables in a transparent way with respect to CP conjugation. The inclusion of time evolution allows us to identify six new observables, out of which three could be accessed from a time-dependent tagged analysis. We also show that these observables could be obtained by time-integrated measurements in a hadronic environment if flavour tagging is available. We provide simple and precise predictions for these observables in the SM and in NP models with real contributions to SM and chirally flipped operators, which are independent of form factors and charm-loop contributions. As such, these observables provide robust and powerful cross-checks of the New Physics scenarios currently favoured by global fits to $b\to s\ell\ell$ data. In addition, we discuss the sensitivity of these observables with respect to NP scenarios involving scalar and tensor operators, or CP-violating phases. We illustrate how these new observables can provide a benchmark to discriminate among the various NP scenarios in $b\to s\mu\mu$. We discuss the extension of these results for $B_s$ decays into $f_0$, $\eta$ or $\eta'$.