$\tau_{B_{s}}/\tau_{B_{d}}$ and $\Delta\Gamma_{s}$ confront new physics in $b\to s\tau\tau$

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.