Measurement of the $B_c^+$ meson lifetime using $B_c^+ \to J/\psi\mu^+\nu_\mu X$ decays with the LHCb detector at CERN

The precision measurement of the $B_c^+$ meson lifetime provides an essential test of the models describing the unique open-flavour state composed of two heavy quarks. It is also a necessary input for all measurements of $B_c^+$ production and decay branching fractions. The first measurement of the $B_c^+$ lifetime achieved by the LHCb Collaboration is presented in this Thesis. The data sample collected in 2012, in $pp$ collisions at a centre-of-mass energy of 8 TeV, and corresponding to an integrated luminosity of 2 fb$^{-1}$, is analysed to select $B_c^+ \to J/\psi\mu^+\nu_\mu X$ decays. A two-dimensional data-model is developed combining the information on the invariant mass of the $J/\psi\mu^+$ combination and the decay time, as measured in the rest-frame of the $J/\psi \mu^+$ combination. Data-driven techniques are proposed to model the background sources, including the candidates selected because of the misidentification of a hadron as the muon produced in a $B_c^+$ decay, for which an original technique has been developed. The template distribution for $B_c^+ \to J/\psi\mu^+\nu_\mu X$ decays relies on realistic dynamical models including feed-down decays, and depends on the $B_c^+$ lifetime through a statistical correction between the $B_c$ and $J/\psi \mu^+$ rest frames, known as $k$-factor. Data-driven cross-checks are used to test the dynamical model and assess the related uncertainties. The measured lifetime is $\tau_{B_c^+} = 509 \pm 8 (\mathrm{stat}) \pm 12 (\mathrm{syst}) \ \mathrm{fs},$ where the largest systematic uncertainty is due to the statistical model used to describe the combinatorial background, which is the only one relying on simulation.