Semitauonic $B_c^+$ Decays and Quark Flavor Identification Methods

The LHCb experiment at the Large Hadron collider is a unique laboratory for studying the properties of heavy quarks. The physics program of the experiment includes studies of CP violation, measurements of CKM matrix parameters, searches for rare decays, quarkonia studies, and other flavor physics, forward physics, and new physics topics. This thesis presents an analysis of the semitauonic branching fraction $\mathcal{B}(B_c^+ \to J/\psi \tau^+ \nu_\tau)$ of the doubly-heavy $B_c^+$ meson, which serves as a powerful probe of the universality of the couplings of leptons ($e$, $\mu$ and $\tau$) in electroweak interactions. The ratio of this branching fraction to the semimuonic branching fraction $\mathcal{B}(B_c^+ \to J/\psi \mu^+ \nu_\mu)$ is measured to be $\mathcal{R}(J/\psi) = 0.71 \pm 0.17 \mathrm{\,(stat)} \pm 0.18\mathrm{\,(syst)}$. A second topic of the thesis is the creation of a new algorithm for tagging the flavor of neutral mesons in CP violation studies, and a powerful method for calibrating these flavor tagging algorithms via binomial regression.