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Enhanced $B_s$--$\bar{B}_s$ lifetime difference and anomalous like-sign dimuon charge asymmetry from new physics in $B_s \to τ^+ τ^-$

New physics models that increase the decay rate of $B_s \to τ^+ τ^-$ contribute to the absorptive part of $B_s$--$\bar{B}_s$ mixing, and may enhance $ΔΓ_s$ all the way up to its current experimental bound. In particular, the model with a scalar leptoquark can lead to a significant violation of the expectation $ΔΓ_s \leq ΔΓ_s$ (SM). It can even allow regions in the $ΔΓ_s$-$β_s$ parameter space that are close to the best fit obtained by CDF and D\{O} through $B_s \to J/ψϕ$. In addition, it can help explain the anomalous like-sign dimuon charge asymmetry observed recently by DØ. A measurement of $BR(B_s \to τ^+ τ^-)$ is thus crucial for a better understanding of new physics involved in $B_s$--$\bar{B}_s$ mixing.