Rare decays of $B_d$ mesons into four charged leptons in the Standard Model

TL;DR

This paper provides the first theoretical predictions within the Standard Model for the decay of B_d mesons into four charged leptons, including branching ratios, distributions, and asymmetries, considering various resonance and non-resonance contributions.

Contribution

It offers the first detailed Standard Model predictions for B_d to four leptons decay observables, incorporating multiple resonance effects and the vector meson dominance model.

Findings

Predicted branching ratios with and without resonance contributions.

Analyzed differential distributions and forward-backward asymmetries.

Quantified resonance and non-resonance effects on decay observables.

Abstract

We present first theoretical predictions for various observables related to the $\bar B_d \to \mu^+ \mu^- e^+ e^-$ decay within the framework of the Standard Model. Our study encompasses the branching ratios, differential distributions, and forward-backward leptonic asymmetries. To obtain these predictions, we account for several contributions: resonance contribution from $\rho(770)$ and significant contribution $\omega(782)$; contributions from four charmonium resonances: $\psi(3770)$, $\psi(4040)$, $\psi(4160)$, and $\psi(4415)$; additional contributions from the "tails" of $J/\psi$ and $\psi(2S)$ resonances; non-resonant contributions arising from virtual photon emission by a $b$-quark of $B_d$ meson, bremsstrahlung, and weak annihilation. In our calculations we employ the model of vector meson dominance (VMD) to assess the resonance contributions accurately. We provide the predictions for the branching ratio of the $\bar B_d \to \mu^+ \mu^- e^+ e^-$ decay both with and without the resonant contribution from $\omega(782)$.