$b$-hadron lifetime measurements with exclusive $b\to J/\psi X$ decays reconstructed in the 2010 data

We report on absolute lifetime measurements in the exclusive decays $B^+ \to J/\psi K^+$, $B^0 \to J/\psi K^{*0}$, $B^0 \to J/\psi K_S$, $B_s^0 \to J/\psi \phi$ and $\Lambda_b \to J/\psi \Lambda$ using 36$pb^{-1}$ of data collected in 2010 with the LHCb detector and a muon trigger at a centre-of-mass energy of $7 TeV$. From a maximum likelihood fit to the proper time distribution of fully reconstructed candidates in each decay mode, we measure \begin{align} \tau(B^+ \to J/\psi K^+)& = & 1.689 \pm 0.022 (stat.) \pm 0.047 (syst.) ps\,,&\\ \tau(B^0 \to J/\psi K^{*0}) & = & 1.512 \pm 0.032 (stat.) \pm 0.042 (syst.) ps\,,&\\ \tau(B^0 \to J/\psi K_S) & = & 1.558 \pm 0.056 (stat.) \pm 0.022 (syst.) ps\,,&\\ \tau^{\rm single}(B_s^0 \to J/\psi \phi) & = & 1.447 \pm 0.064 (stat.) \pm 0.056 (syst.) ps\,,&\\ \tau(\Lambda_b \to J/\psi \Lambda) & = & 1.353 \pm 0.108 (stat.) \pm 0.035 (syst.) ps\,, & \end{align} where $\tau^{\rm single}(B_s^0 \to J/\psi \phi)$ is the lifetime measured with $B_s^0 \to J/\psi \phi$ using a single exponential to model the proper time distribution, i.e., ignoring the non-zero decay-width difference of the $B_s^0$ system.