A theoretical prediction of the $B_s$ meson lifetime difference

Abstract. We present the results of a quenched lattice calculation of the operator matrix elements relevant for predicting the $B_s$ width difference. Our main result is $\left(\Delta\Gamma_{B_s}/\Gamma_{B_s}\right)= (4.7 \pm 1.5 \pm 1.6) \times 10^{-2}$, obtained from the ratio of matrix elements ${\cal R}(m_b)= \langle \bar B_s^0\vert Q_{S}\vert B_s^0\rangle/$$\langle \bar B_s^0\vert Q_{L}\vert B_s^0\rangle =-0.93(3)^{+0.00}_{-0.01}$. ${\cal R}(m_b)$ was evaluated from the two relevant B parameters $B_{S}^{\overline{\mathrm{MS}}} (m_b) = 0.86(2)^{+0.02}_{-0.03}$ and $B_{B_s}^{\overline{\mathrm{MS}}} (m_b) =0.91(3)^{+0.00}_{-0.06}$, which we computed in our simulation.