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We present a considerably improved analysis of model-independent bounds onnew physics effects in non-leptonic tree-level decays of B-mesons. Our mainfinding is that contributions of about $\pm 0.1 $ to the Wilson coefficient ofthe colour-singlet operator $Q_2$ of the effective weak Hamiltonian andcontributions in the range of $\pm 0.5$ (both for real and imaginary part) to$Q_1$ can currently not be excluded at the $90\%$ C.L.. Effects of such a sizecan modify the direct experimental extraction of the CKM angle $\gamma$ by upto $10^{\circ}$ and they could lead to an enhancement of the decay ratedifference $\Delta \Gamma_d$ of up to a factor of 5 over its SM value - a sizethat could explain the D0 dimuon asymmetry. Future more precise measurements ofthe semi-leptonic asymmetries $a_{sl}^q$ and the lifetime ratio $\tau (B_s) /\tau (B_d)$ will allow to shrink the bounds on tree-level new physics effectsconsiderably. Due to significant improvements in the precision of thenon-perturbative input we update all SM predictions for the mixing obervablesin the course of this analysis, obtaining: $\Delta M_s = (18.77 \pm 0.86 ) \,\mbox{ps}^{-1}$, $\Delta M_d = (0.543 \pm 0.029) \, \mbox{ps}^{-1}$, $\Delta\Gamma_s = (9.1 \pm 1.3 ) \cdot 10^{-2} \, \mbox{ps}^{-1}$, $\Delta \Gamma_d =(2.6 \pm 0.4 ) \cdot 10^{-3} \, \mbox{ps}^{-1}$, $a_{sl}^s = (2.06 \pm 0.18)\cdot 10^{-5}$ and $a_{sl}^d = (-4.73 \pm 0.42) \cdot 10^{-4}$.

Model-independent bounds on new physics effects in non-leptonic tree-level decays of B-mesons