$B^0_s \to \ell^+ \ell^- \gamma$ as a Test of Lepton Flavor Universality

TL;DR

This paper proposes new strategies to measure the decay $B^0_s o ext{leptons}^+ ext{leptons}^- ext{gamma}$ with reduced theoretical uncertainties, creating a sensitive test for lepton flavor universality violations in flavor physics.

Contribution

It introduces a novel ratio $R_ ext{gamma}$ that minimizes form-factor dependence and bremsstrahlung effects, providing a new probe for lepton-universality violation in $B_s$ decays.

Findings

The ratio $R_ ext{gamma}$ is close to unity under Standard Model assumptions.

Strategies to reduce theoretical errors in $B_s o ext{leptons}^+ ext{leptons}^- ext{gamma}$ measurements.

Potential to detect new physics effects through lepton flavor universality tests.

Abstract

We discuss a number of strategies to reduce the $\mathcal B(B^0_s \to \ell^{+} \ell^{-} \gamma)$ theoretical error, and make such a measurement a new probe of the interactions that are interesting in the light of present-day flavor discrepancies. In particular, for low di-lepton invariant mass we propose to exploit the close parenthood between $\mathcal B(B^0_s \to \ell^{+} \ell^{-} \gamma)$ and the measured $\mathcal B(B^0_s \to \phi (\to K^+ K^-) \gamma)$. For high $q^2$, conversely, we exploit the fact that the decay is dominated by two form-factor combinations, plus contributions from broad charmonium that we model accordingly. We construct the ratio $R_\gamma$, akin to $R_K$ and likewise sensitive to lepton-universality violation. Provided the two rates in this ratio are integrated in a suitable region that minimises bremsstrahlung contributions while maximising statistics, the ratio is very close to unity and the form-factor dependence cancels to an extent that makes it a new valuable probe of lepton-universality violating contributions in the effective Hamiltonian. We finally speculate on additional ideas to extract short-distance information from resonance regions, which are theoretically interesting but statistically limited at present.