The first observation of the decay $kstarkstar$ is reported using 35invpb of data collected by LHCb in proton-proton collisions at a centre-of-mass energy of 7 TeV. A total of $49.8 pm 7.5$ $B^0_s rightarrow (K^+pi^-)(K^-pi^+)$ events are {observed within $pm 50 mevcc$ of the Bs mass and $746 mevcc < m_{Kpi}< 1046 mevcc$, mostly coming from a resonant $kstarkstar$ signal.} The branching fraction and the CP-averaged Kstarz longitudinal polarization fraction are measured to be {$BR(kstarkstar) = (2.81 pm 0.46 ({rm stat.}) pm 0.45 ({rm syst.}) pm 0.34, (f_s/f_d))times10^{-5}$} and $f_L = 0.31 pm 0.12 ({rm stat.}) pm 0.04 ({rm syst.})$.
The first observation of the decay $B_s^0 rightarrow phi bar{K}^{*0}$ is reported. The analysis is based on a data sample corresponding to an integrated luminosity of 1.0 fb$^{-1}$ of $pp$ collisions at $sqrt{s} = 7 TeV$, collected with the LHCb detector. A yield of $30 pm 6$ $B_s^0 rightarrow (K^+K^-)(K^-pi^+)$ decays is found in the mass windows $1012.5 < M(K^+K^-) < 1026.5 MeV/c^2$ and $746 < M(K^-pi^+)< 1046 MeV/c^2$. The signal yield is found to be dominated by $B_s^0 rightarrow phi bar{K}^{*0}$ decays, and the corresponding branching fraction is measured to be ${cal B}(B_s^0 rightarrow phi bar{K}^{*0}) = (1.10 pm 0.24 (stat) pm 0.14 (syst) pm 0.08 (f_d/f_s)) times 10^{-6}$, where the uncertainties are statistical, systematic and from the ratio of fragmentation fractions $f_d/f_s$ which accounts for the different production rate of $B^0$ and $B_s^0$ mesons. The significance of $B_s^0 rightarrow phi bar{K}^{*0}$ signal is 6.1 standard deviations. The fraction of longitudinal polarization in $B_s^0 rightarrow phi bar{K}^{*0}$ decays is found to be $f_0 = 0.51 pm 0.15 (stat) pm 0.07 (syst)$.
The first observation of the decay $bar{B}^0_s to D^0 K^{*0}$ using $pp$ data collected by the LHCb detector at a centre-of-mass energy of 7 TeV, corresponding to an integrated luminosity of 36 pb$^{-1}$, is reported. A signal of $34.4 pm 6.8$ events is obtained and the absence of signal is rejected with a statistical significance of more than nine standard deviations. The $bar{B}^0_s to D^0 K^{*0}$ branching fraction is measured relative to that of $bar{B}^0 to D^0 rho^0$: $frac{{cal B}(bar{B}^0_s to D^0 K^{*0})}{{cal B}(bar{B}^0 to D^0 rho^0)} = 1.48 pm 0.34 pm 0.15 pm 0.12$, where the first uncertainty is statistical, the second systematic and the third is due to the uncertainty on the ratio of the $B^0$ and $B^0_s$ hadronisation fractions.
The first observation of the decay $B^0 rightarrow D^0 overline{D}{}^0 K^+ pi^-$ is reported using proton-proton collision data corresponding to an integrated luminosity of 4.7 $mathrm{fb}^{-1}$ collected by the LHCb experiment in 2011, 2012 and 2016. The measurement is performed in the full kinematically allowed range of the decay outside of the $D^{*-}$ region. The ratio of the branching fraction relative to that of the control channel $B^0 rightarrow D^{*-} D^0 K^+$ is measured to be $mathcal{R} = (14.2 pm 1.1 pm 1.0)%$, where the first uncertainty is statistical and the second is systematic. The absolute branching fraction of $B^0 rightarrow D^0 overline{D}{}^0 K^+ pi^-$ decays is thus determined to be $mathcal{B}(B^0 rightarrow D^0 overline{D}{}^0 K^+ pi^-) = (3.50 pm 0.27 pm 0.26 pm 0.30) times 10^{-4}$, where the third uncertainty is due to the branching fraction of the control channel. This decay mode is expected to provide insights to spectroscopy and the charm-loop contributions in rare semileptonic decays.
The first observation of the $B^0_stobar{D}^0 K^0_S$ decay mode and evidence for the $B^0_stobar{D}^{*0} K^0_S$ decay mode are reported. The data sample corresponds to an integrated luminosity of 3.0 $text{fb}^{-1}$ collected in $pp$ collisions by LHCb at center-of-mass energies of 7 and 8 TeV. The branching fractions are measured to be begin{align*} mathcal{B}(B^0_stobar{D}^0 bar{K}^0) &= (4.3pm0.5(text{stat})pm0.3(text{syst})pm0.3(text{frag})pm0.6(text{norm}))times10^{-4}, mathcal{B}(B^0_stobar{D}^{*0} bar{K}^0) &= (2.8pm1.0(text{stat})pm0.3(text{syst})pm0.2(text{frag})pm0.4(text{norm}))times10^{-4}, end{align*} where the uncertainties are due to contributions coming from statistical precision, systematic effects, and the precision of two external inputs, the ratio $f_s/f_d$ and the branching fraction of $B^0tobar{D}^0 K^0_S$, which is used as a calibration channel.
The Dalitz plot distribution of $B^0 rightarrow bar{D}^0 K^+ pi^-$ decays is studied using a data sample corresponding to $3.0rm{fb}^{-1}$ of $pp$ collision data recorded by the LHCb experiment during 2011 and 2012. The data are described by an amplitude model that contains contributions from intermediate $K^*(892)^0$, $K^*(1410)^0$, $K^*_2(1430)^0$ and $D^*_2(2460)^-$ resonances. The model also contains components to describe broad structures, including the $K^*_0(1430)^0$ and $D^*_0(2400)^-$ resonances, in the $Kpi$ S-wave and the $Dpi$ S- and P-waves. The masses and widths of the $D^*_0(2400)^-$ and $D^*_2(2460)^-$ resonances are measured, as are the complex amplitudes and fit fractions for all components included in the amplitude model. The model obtained will be an integral part of a future determination of the angle $gamma$ of the CKM quark mixing matrix using $B^0 rightarrow D K^+ pi^-$ decays.