$\tau _{B_{s}}/\tau _{B_{d}}$ and $\Delta \Gamma _{s}$ confront new physics in $b\rightarrow s\tau \tau $

Several new physics scenarios that address anomalies in B-physics predict an enhancement of $b \rightarrow s \tau \tau $ with respect to its Standard Model prediction. Such scenarios necessarily imply modifications of the lifetime ratio $\tau _{B_{s}}/\tau _{B_{d}}$ and the lifetime difference $\Delta \Gamma _{s}$. In this work, we explore indirect bounds provided by these observables over new physics scenarios. We also estimate future projections, showing that future experimental and theoretical improvements on both $\tau _{B_{s}}/\tau _{B_{d}}$ and $\Delta \Gamma _{s}$ have the potential to provide bounds competitive with those directly extracted from $b\rightarrow s \tau \tau $ transitions. After performing a model-independent analysis, we apply our results to the particular case of leptoquark mediators proposed to address the $R_{D^{(*)}}$ anomalies.