Lifetime Difference of Neutral $B_s$ Mesons and its Implications

We discuss the calculation of the width difference $\Delta\Gamma_{B_s}$ between the $B_s$ mass eigenstates to next-to-leading order in the heavy quark expansion. $1/m_b$-corrections are estimated to reduce the leading order result by typically $30\%$. The error of the present estimate $(\Delta\Gamma/\Gamma)_{B_s} = 0.16^{+0.11}_{-0.09}$ could be substantially improved by pinning down the value of $\langle \bar{B}_s |(\bar b_is_i)_{S-P}(\bar b_js_j)_{S-P}| B_s\rangle$ and an accuracy of $10\%$ in $(\Delta\Gamma/\Gamma)_{B_s}$ should eventually be reached. We briefly mention strategies to measure $(\Delta\Gamma/\Gamma)_{B_s}$, and its implications for constraints on $\Delta M_{B_s}$, CKM parameters and the observation of CP violation in untagged $B_s$ samples.