Time dependence in $B\to V\ell\ell$ decays

TL;DR

This paper develops a theoretical framework for analyzing time-dependent angular distributions in $B_{d,s} o V o M_1M_2 \,\ell\ell$ decays with neutral-meson mixing, proposing new observables for probing New Physics.

Contribution

It introduces two theoretically clean observables, $Q_8^-$ and $Q_9$, for $B\to V\ell\ell$ decays, enhancing the potential to detect New Physics effects.

Findings

Derived expressions for time-dependent angular distributions.

Identified observables $Q_8^-$ and $Q_9$ with high sensitivity to New Physics.

Analyzed the Standard Model predictions for these observables.

Abstract

We discuss the theory and phenomenology of $B_{d,s}\to V(\to M_1M_2)\ell\ell$ decays in the presence of neutral-meson mixing. We derive expressions for the time-dependent angular distributions for decays into CP eigenstates, and identify the relevant observables that can be extracted from time-integrated and time-dependent analyses with or without tagging, with a focus on the difference between measurements at $B$-factories and hadronic machines. We construct two observables of interest, which we call $Q_8^-$ and $Q_9$, and which are theoretically clean at large recoil. We compute these two observables in the Standard Model, and show that they have good potential for New Physics searches by considering their sensitivity to benchmark New Physics scenarios consistent with current $b\to s\ell\ell$ data. These results apply to decays such as $B_d\to K^*(\to K_S\pi^0)\ell\ell$, $B_s\to \phi (\to K_SK_L)\ell\ell$ and $B_s\to \phi(\to K^+K^-)\ell\ell$.