Measurement of the Lifetime Difference betweenBsMass Eigenstates

We present measurements of the lifetimes and polarization amplitudes for $B_s^0\to J/\psi \varphi$ and $B_d^0\to J/\psi K^{*0}$ decays. Lifetimes of the heavy and light mass eigenstates in the $B_s^0$ system are separately measured for the first time by determining the relative contributions of amplitudes with definite $CP$ as a function of the decay time. Using $203\pm 15$ $B_s^0$ decays we obtain ${\tau }_L=({1.05}_{-0.13}^{+0.16}\pm 0.02)\mathrm{p}\mathrm{s}$ and ${\tau }_H=({2.07}_{-0.46}^{+0.58}\pm 0.03)\mathrm{p}\mathrm{s}$. Expressed in terms of the difference $\Delta {\Gamma }_s$ and average ${\Gamma }_s$, of the decay rates of the two eigenstates, the results are $\Delta {\Gamma }_s/{\Gamma }_s=({65}_{-33}^{+25}\pm 1)\%$ and $\Delta {\Gamma }_s=({0.47}_{-0.24}^{+0.19}\pm 0.01)\mathrm{p}{\mathrm{s}}^{-1}$.