| Summary: | We review the validity of the assumption of having no new physics in tree level b quark transitions $b\rightarrow q q' d$ and $b\rightarrow q q' s$ ($q, q'= u,c$). In particular we test for possible deviations on the Wilson coefficients of the corresponding effective current-current operators with respect to their Standard Model values. The allowed new physics regions are determined using a global fit. We take into account constraints from different flavour observables calculated from the hadronic decays $B^0_d\rightarrow \pi\pi$, $B^0_d\rightarrow \rho\pi$, $B^0_d\rightarrow \rho\rho$, $B\rightarrow X_s \gamma$ and $B\rightarrow X_d \gamma$. We also include observables from neutral B meson mixing such as $\Delta \Gamma_s$ and the semileptonic asymmetries $a^{s,d}_{sl}$. We show that deviations in the tree level Wilson coefficients of the order $\mathcal{O}(10\%)$ are consistent with state of the art experimental measurements. We study the implications of these deviations over the decay width $\Delta \Gamma_d$ of $B^0_d$ meson mixing, not measured yet by experiments, and over the precision of the CKM phase $\gamma$. Our results show that enhancements on $\Delta \Gamma_d$ by up to a factor of 3.6 with respect to the Standard Model value are allowed by data. Moreover the effects on $\gamma$ can compete with the corresponding experimental precision $\mathcal{O}(6^{\circ})$. Finally we explore for possible hadron-quark duality violations in the neutral $B$ and $D$ meson sectors. This analysis includes constraints from mixing observables and from the lifetimes of $B^0_d$ and $B^0_s$ mesons. We find that duality violations of $\mathcal{O}(20\%)$ can provide an explanation to the tension of several orders of magnitude between the Heavy Quark Expansion and experimental data in the observable $\Delta \Gamma_D$ of neutral $D$ meson mixing.
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