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Several new physics scenarios that address anomalies in $B$-physics predictan enhancement of $b \rightarrow s \tau \tau$ with respect to its StandardModel prediction. Such scenarios necessarily imply modifications of thelifetime ratio $\tau_{B_{s}}/\tau_{B_{d}}$ and the lifetime difference$\Delta\Gamma_{s}$. In this work, we explore indirect bounds provided by theseobservables 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 toprovide bounds competitive with those directly extracted from $b\rightarrow s\tau \tau$ transitions. After performing a model-independent analysis, we applyour results to the particular case of leptoquark mediators proposed to addressthe $R_{D^{(*)}}$ anomalies.

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