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Inspired by the recently observed tensions between the experimental data andthe theoretical predictions, based on QCD factorisation, for severalcolour-allowed non-leptonic $B$-meson decays, we study the potential size ofnew physics (NP) effects in the decay channels $b \to c \bar{u} d(s)$. Startingfrom the most general effective Hamiltonian describing the $b \to c \bar{u}d(s)$ transitions, we compute NP contributions to the theoretical predictionsof $B$-meson lifetime and of $B$-mixing observables. The well-known lifetimeratio $\tau (B^+)/\tau (B_d)$ and the experimental bound on the semi-leptonicCP asymmetry $a_{sl}^d$, provide strong, complementary constraints on some ofthe NP Wilson coefficients.

Taming New Physics in $b \to c \bar u d (s) $ with $\tau (B^+)/\tau(B_d)$ and $a_{sl}^d$