A study of $B \rightarrow DK$ and $D^{0}$ production using $D^{0} \rightarrow K^{+}\pi^{-}\pi^{+}\pi^{-}$ decays at LHCb

A precision measurement of the CKM angle $\gamma$ from tree-level processes is one of the principal goals of the LHCb experiment. Two important channels for the extraction of $\gamma$ are $B^{\pm}\rightarrow D^{0}K^{\pm}$ and $B^{\pm}\rightarrow\kern 0.2em\overline{\kern -0.2em D}{}^{0}K^{\pm}$; a first study of these modes is presented using an integrated luminosity of $\mathcal{L}_{\rm{int}}={35.6}\pm3.6\,\mathrm{\,pb^{-1}}$ at a $pp$ centre-of-mass collision energy of $\sqrt{s}=7\mathrm{\,TeV}$. A measurement is made of the ratio of branching fractions $\mathcal{B}_{DK}/\mathcal{B}_{D\pi}=\Gamma(B^{\pm}\rightarrow DK^{\pm})/\Gamma(B^{\pm}\rightarrow D\pi^{\pm}) = 0.057\pm0.007\pm0.004$ using $B^{\pm}\rightarrow\left(K^{\pm}\pi^{\mp}\pi^{\pm}\pi^{\mp}\right)_{D}K^{\pm}$ and $B^{\pm}\rightarrow\left(K^{\pm}\pi^{\mp}\pi^{\pm}\pi^{\mp}\right)_{D}\pi^{\pm}$ four-body $D$ decay modes. This has an uncertainty competitive with the previous world average of $\left(7.6\pm0.6\right)\%$. A measurement is also made of the rate asymmetry between $B^{-} \rightarrow \left(K^{-}\pi^{+}\pi^{-}\pi^{+}\right)_{D}K^{-}$ and $B^{+} \rightarrow \left(K^{+}\pi^{-}\pi^{+}\pi^{-}\right)_{D}K^{+}$ decays, $A_{fav}^{K3\pi}=\frac{\Gamma\left(B^{-}\rightarrow\left(K^{-}\pi^{+}\pi^{-}\pi^{+}\right)_{D}K^{-}\right)-\Gamma\left(B^{+}\rightarrow\left(K^{+}\pi^{-}\pi^{+}\pi^{-}\right)_{D}K^{+}\right)} {\Gamma\left(B^{-}\rightarrow\left(K^{-}\pi^{+}\pi^{-}\pi^{+}\right)_{D}K^{-}\right)+\Gamma\left(B^{+}\rightarrow\left(K^{+}\pi^{-}\pi^{+}\pi^{-}\right)_{D}K^{+}\right)} = 0.01\pm0.11\pm0.06$. As expected, this result is consistent with zero within statistical and systematic uncertainties. The $D^{0}/\kern 0.2em\overline{\kern -0.2em D}{}^{0}$ production cross-section in bins of transverse momentum and rapidity from prompt $D^{0} \rightarrow K^{-} \pi^{+}\pi^{-}\pi^{+}$ decays (and its charge conjugate) is presented, using $\mathcal{L}_{\rm{int}}={14.96}\pm0.52\,\mathrm{\,nb^{-1}}$ of $\sqrt{s}=7\mathrm{\,TeV}$ LHCb $pp$ collision data. This measurement is important for testing predictions of QCD theoretical models, and determining LHCb's sensitivity to measurements of $C\!P$ violation, mixing measurements and rare decays of charmed hadrons. The results are compared to predictions from two different theoretical models and from the default LHCb tuning of the \mbox{\textsc{Pythia}} Monte Carlo event generator, and the results shown to be in good agreement. The cross-section results are also compared to an independent LHCb measurement in the $D^{0} \rightarrow K^{-} \pi^{+}$ decay channel. LHCb analyses rely on the ability to identify kaons and pions with a high efficiency and low mis-identification rate, achieved by two Ring Imaging Cherenkov (RICH) detectors. To ensure optimal performance of the RICH detectors, the time alignment of the Level\mbox{-}0 (L0) front-end electronics modules has been optimised using a combination of a pulsed laser system installed in the LHCb cavern and $pp$ collision data. After the time-alignment procedure, the L0 modules have been time-aligned to within approximately $\pm 1\mathrm{\,ns}$ across both detectors.