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

Abstract

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{τ(B_s)}{τ(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 $τ\lt(B_s \rt)/τ\lt(B_d\rt)$. Anticipating progress in the determination of the hadronic parameters $ε_1$, $ε_2$ and $f_{B_s}/f_{B_d}$ we find that the coefficient $C_4$ can be extracted with an uncertainty of order $|ΔC_4|\simeq 0.1$ from the double ratio $[τ(B_s)-τ(B_d)]/[τ(B^+)-τ(B_d)]$, if $|ε_1-ε_2|$ is not too small.