New physics effects in purely leptonic $B^*_s$ decays

TL;DR

This paper explores how new physics could influence purely leptonic $B^*_s$ decays, proposing the muon polarization asymmetry as a discriminant between different new physics solutions and examining correlations with $b ightarrow c au ar{ u}$ anomalies.

Contribution

It identifies the muon polarization asymmetry in $B^*_s ightarrow au^+ au^-$ as a key observable to distinguish new physics solutions in $b ightarrow s l^+l^-$ anomalies and analyzes their impact on $b ightarrow s au^+ au^-$ decays.

Findings

Muon polarization asymmetry can discriminate between new physics solutions if measured with 10% precision.

Theoretical uncertainties limit the asymmetry's discriminative power if Wilson coefficients are complex.

Branching ratio of $B^*_s ightarrow au^+ au^-$ can be enhanced by up to three orders of magnitude due to new physics.

Abstract

Recently several measurements in the neutral current sector $b\rightarrow s l^+l^-$ ($l=e$ or $\mu$) as well as in the charged current sector $b \rightarrow c \tau \bar{\nu}$ show significant deviations from their Standard Model predictions. It has been shown that two different new physics solutions can explain all the anomalies in $b\rightarrow s l^+l^-$ sector. Both these solutions are in the form of linear combinations of the two operators $(\bar{s}\gamma^{\alpha}P_Lb)(\bar{\mu}\gamma_{\alpha}\mu)$ and $(\bar{s}\gamma^{\alpha}P_Lb)(\bar{\mu}\gamma_{\alpha}\gamma_5\mu)$. We show that the longitudinal polarization asymmetry of the muons in $B^*_s\rightarrow \mu^+\,\mu^-$ decay is a good discriminant between the two solutions if it can be measured to a precision of $10\%$, provided the new physics Wilson coefficients are real. If they are complex, the theoretical uncertainties in this asymmetry are too large to provide effective discrimination. We also investigate the potential impact of $b \rightarrow c \tau \bar{\nu}$ anomalies on $b \rightarrow s \tau^+ \tau^-$ transitions. We consider a model where the new phyics contributions to these two transitions are strongly correlated. We find that the branching ratio of $B^*_s\rightarrow \tau^+\,\tau^-$ can be enhanced by three orders of magnitude.