Measurement of the Lifetime Difference in theBs0System

We present a study of the decay $B_s^0\to J/\psi \varphi$. We obtain the $CP$-odd fraction in the final state at time zero, $R_{\perp }=0.16\pm 0.10(\mathrm{stat})\pm 0.02(\mathrm{syst})$, the average lifetime of the ($B_s^0$, ${\overline{B}}_s^0$) system, $\overline{\tau }(B_s^0)={1.39}_{-0.16}^{+0.13}(\mathrm{stat}{)}_{-0.02}^{+0.01}(\mathrm{syst})\mathrm{ps}$, and the relative width difference between the heavy and light mass eigenstates, $\Delta \Gamma /\overline{\Gamma }\equiv ({\Gamma }_L-{\Gamma }_H)/\overline{\Gamma }={0.24}_{-0.38}^{+0.28}(\mathrm{stat}{)}_{-0.04}^{+0.03}(\mathrm{syst})$. With the additional constraint from the world average of the $B_s^0$ lifetime measurements using semileptonic decays, we find $\overline{\tau }(B_s^0)=1.39\pm 0.06\mathrm{ps}$ and $\Delta \Gamma /\overline{\Gamma }={0.25}_{-0.15}^{+0.14}$. For the ratio of the $B_s^0$ and $B^0$ lifetimes we obtain $\frac{\overline{\tau }(B_s^0)}{\tau (B^0)}=0.91\pm 0.09(\mathrm{stat})\pm 0.003(\mathrm{syst})$.