Studies of Excited $D$ mesons in $B$ meson decays

This thesis documents the studies of several three-body B + meson decays, each with a charged charmed meson in the final state. All analyses presented use a data sample recorded by the LHCb detector in 2011 and 2012, corresponding to an integrated luminosity of 3.0 $fb^{-1}$ of $pp$ collision data. The $B^{+} \to D^{-}K^{+}\pi^{+}$ and $B^{+} \to D^{+}K^{+}\pi^{-}$ decay modes are observed for the first time. The branching fraction of the favoured $B^{+} \to D^{-}K^{+}\pi^{+}$ decay mode is measured relative to the topologically similar $B^{+} \to D^{-}\pi^{+}\pi^{+}$ decay and the $B^{+} \to D^{-}K^{+}\pi^{+}$ final state is used as a normalisation channel for the suppressed $B^{+} \to D^{+}K^{+}\pi^{-}$ decay branching fraction measurement. Searches are performed for the quasi-two-body decays $B^{+} \to D^{+}K^{*}(892)^{0}$ and $B^{+} \to D_{2}^{*}(2460)^{0}K^{+}$, using the sample of $B^{+} \to D^{+}K^{+}\pi^{-}$ candidate decays. No significant signals are observed for either decay mode and upper limits are set on their branching fractions. Excited charmed mesons decaying to $D^{-}\pi^{+}$ are studied by performing fits to the Dalitz plots of $B^{+} \to D^{-}K^{+}\pi^{+}$ and $B^{+} \to D^{-}\pi^{+}\pi^{+}$ candidates. A structure at $m(D^{-}\pi^{+}) \sim 2.78$ GeV/$c^{2}$ in the $D^{-}K^{+}\pi^{+}$ data sample is determined to have spin-1 for the first time. Evidence from the $B^{+} \to D^{-}\pi^{+}\pi^{+}$ Dalitz plot suggests that the states at $m(D^{-}\pi^{+}) \sim 2.76$ GeV/$c^{2}$ and 3.00 GeV/$c^{2}$, have spin-3 and spin-2, respectively. The mass and width parameters of these states are measured precisely, as are those of the well known $D^{*}_{2}(2460)^{0}$ resonance. Fit fractions and product branching fractions are calculated for all contributions in the $B^{+} \to D^{-}K^{+}\pi^{+}$ and $B^{+} \to D^{-}\pi^{+}\pi^{+}$ amplitude models.