We update the theory predictions for the mass difference $\dm_s$, the width difference $\dg_s$ and the CP asymmetry in flavour-specific decays, $a_{ \rm fs}^{ s}$, for the \bbs system. In particular we present a new expression for the element $\Gamma_{ 12}^s$ of the decay matrix, which enters the predictions of $\dg_s$ and $a_{ \rm fs}^{ s}$. To this end we introduce a new operator basis, which reduces the troublesome sizes of the $1/m_b$ and $\alpha_s$ corrections and diminishes the hadronic uncertainty in $\dg_s/\dm_s$ considerably. Logarithms of the charm quark mass are summed to all orders. We find $\dg_s/\dm_s= (49.7 \pm 9.4) \cdot 10^{ -4}$ and $\dg_s =(f_{ B_s}/240 { \rm MeV})^2 [(0.105 \pm 0.016) B + (0.024 \pm 0.004) \tilde{ B}_S' - 0.027 \pm 0.015] { ps}^{ -1}$ in terms of the bag parameters $B$, $\tilde{ B}_S'$ in the NDR scheme and the decay constant $f_{ B_s}$. The improved result for $\Gamma_{ 12}^s$ also permits the extraction of the CP-violating \bbms phase from $a_{ \rm fs}^{ s}$ with better accuracy. We show how the measurements of $\Delta M_s$, $\Delta\Gamma_s$, $a_{ \rm fs}^{ s}$, $A_{ \rm CP}^{ \rm mix}(B_s\to J/\psi \phi)$ and other observables can be efficiently combined to constrain new physics. Applying our new formulae to data from the D{ \O}experiment, we find a 2$\sigma$ deviation of the \bbms phase from its Standard Model value. We also briefly update the theory predictions for the \bbd system and find $\dg_d/\dm_d = \lt(52.6 \epm{ 11.5}{ 12.8} \rt) \cdot 10^{ -4}$ and $a_{ \rm fs}^d = \lt(-4.8\epm{ 1.0}{ 1.2} \rt) \cdot 10^{ -4}$ in the Standard Model.
Categories: hep-ph