Penguin Contributions in the Lifetime Difference between $B_s$ and $B_d$, and a Possible New Physics

We consider penguin contributions to the lifetime splitting between the $B_s$ and the $B_d$ meson. In the Standard Model the penguin effects are found to be opposite in sign, but of similar magnitude as the contributions of the current-current operators, despite of the smallness of the penguin coefficients. We predict \begin{eqnarray} \frac{\tau(B_s)}{\tau(B_d)} -1 &=& \lt(-1.2 \pm 10.0 \rt) \cdot 10^{-3} \cdot \lt(\frac{f_{B_s}}{190 \mathrm{MeV}} \rt)^2, \no \end{eqnarray} where the error stems from hadronic uncertainties. Since penguin coefficients are sensitive to new physics and poorly tested experimentally, we analyze the possibility to extract them from a future precision measurement of $\tau \lt(B_s \rt)/\tau\lt(B_d\rt)$. Anticipating progress in the determination of the hadronic parameters $\epsilon_1$, $\epsilon_2$ and $f_{B_s}/f_{B_d}$ we find that the coefficient $C_4$ can be extracted with an uncertainty of order $|\Delta C_4|\simeq 0.1$ from the double ratio $[\tau(B_s)-\tau(B_d)]/[\tau(B^+)-\tau(B_d)]$, if $|\epsilon_1-\epsilon_2|$ is not too small.