Lifetime measurements of beauty hadrons at the LHCb experiment

This thesis presents several lifetime measurements of $b$-flavoured hadrons at the LHCb experiment. They represent an important test of the theoretical approach to $b$-hadron observables known as Heavy Quark Expansion (HQE). This analysis uses data corresponding to an integrated luminosity of 1 fb $^{-1}$ collected in proton-proton collisions at a centre-of-mass energy of $\sqrt{s} =$ 7 $\text {TeV}$. For the decays $B^+ \rightarrow J/\psi K^+$, $B^0 \rightarrow J/\psi K^{*0}$, $B^0 \rightarrow J/\psi K^0_S$, $\Lambda^0_b \rightarrow J/\psi \Lambda$ and $B^0_s \rightarrow J/\psi \phi$, the lifetimes are measured to be \begin{eqnarray}\nonumber \tau_{B^+ \rightarrow J/\psi K^+} & = & 1.637 \pm 0.004 \pm 0.003 \: \text {ps},\\ \nonumber \tau_{B^0 \rightarrow J/\psi K^{*0}} & =& 1.524 \pm 0.006 \pm 0.004 \: \text {ps},\\ \nonumber \tau_{B^0 \rightarrow J/\psi K^0_S} & =& 1.499 \pm 0.013 \pm 0.005 \: \text {ps},\\ \nonumber \tau_{\Lambda^0_b \rightarrow J/\psi \Lambda} & =& 1.415 \pm 0.027 \pm 0.006 \: \text {ps},\\ \nonumber \tau_{B^0_s \rightarrow J/\psi \phi} & =& 1.480 \pm 0.011 \pm 0.005 \: \text {ps}, \end{eqnarray} where the first uncertainty is statistical and the second is systematic. These are the most precise lifetime measurements in these decay modes to date. Ratios of these lifetimes also are reported in this thesis, as they are well-defined quantities where many theoretical or experimental uncertainties cancel. The ratio of the decay width difference, $\Delta\Gamma_d$, to the average width, $\Gamma_d$, in the $B^0$ system is found to be $\Delta \Gamma_d/\Gamma_d = -0.044 \pm 0.025 \pm 0.011$. Using data corresponding to an integrated luminosity of 3 fb$^-1$ collected at centre-of-mass energies of 7 $\text {TeV}$ and 8 $\text {TeV}$, the measurements of the decay width difference, $\Delta\Gamma_s$, and the average width, $\Gamma_s$, in the $B^0_s$ system are performed. Using the decay $B^0_s \rightarrow J/\psi \phi$, they are measured to be \begin{eqnarray}\nonumber \Delta \Gamma_s & = & 0.0805 \pm 0.0091 \pm 0.0033 \: \text {ps}^{-1}, \\ \nonumber \Gamma_s & = & 0.6603 \pm 0.0027 \pm 0.0015 \: \text {ps}^{-1}. \end{eqnarray} These are the most precise determinations of these observables to date. All measurements are consistent with HQE predictions.