Using protonproton collision data corresponding to an integrated luminosity of 3.0 fb$^{1}$, recorded by the LHCb detector at centreofmass energies of 7 and 8 TeV, the $B_{c}^{+} \rightarrow D^{0} K^{+}$ decay is observed with a statistical significance of 5.1 standard deviations. By normalising to $B^{+} \rightarrow \bar{D}^{0} \pi^{+}$ decays, a measurement of the branching fraction multiplied by the production rates for $B_{c}^{+}$ relative to $B^{+}$ mesons in the LHCb acceptance is obtained, $$ R_{D^{0} K} = \frac{f_{c}}{f_{u}}\times\mathcal{B}(B_{c}^{+} \rightarrow D^{0} K^{+}) = (9.3 ^{+2.8}_{2.5} \pm 0.6) \times 10^{7} , $$ where the first uncertainty is statistical and the second is systematic. This decay is expected to proceed predominantly through weak annihilation and penguin amplitudes, and is the first $B_{c}^{+}$ decay of this nature to be observed.
Tree (a), penguin (b), and weak annihilation (c) diagrams for the decays studied. In each case, the meson appearing before the comma denotes the favoured decay. 
Diagrams.pdf [193 KiB] HiDef png [78 KiB] Thumbnail [50 KiB] *.C file 

Results of the simultaneous fit to the $ D ^0 K ^+ $ (top plot) and $ D ^0 \pi ^+ $ (bottom plot) invariant mass distributions in the $ B _ c ^+ $ mass region, including the $ D ^0 \rightarrow K ^ \pi ^+ $ and $ D ^0 \rightarrow K ^ \pi ^+ \pi ^ \pi ^+ $ final states. Inclusion of the charge conjugate decays is implied. The red solid curve illustrates $ B _ c ^+ \rightarrow D ^0 K^+$ decays, the red dashed curve illustrates $ B _ c ^+ \rightarrow D ^{*0} K^+$ decays, the green dashed curve represents $ B _ c ^+ \rightarrow D ^{*0} \pi^+$ decays, the grey shaded region represents partially reconstructed background decays, the cyan dashed line represents the combinatorial background, and the total PDF is displayed as a blue solid line. The small drop visible in the total $ B _ c ^+ \rightarrow D^{(*)0} \pi ^+ $ PDF around the $ B _ c ^+$ mass arises from the fact that the fit finds a small negative value for the $ B _ c ^+ \rightarrow D ^0 \pi ^+ $ yield. 
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CL$_{\text{s}}$ $p$value distributions for the $R_{ D ^0 h}$ observables. The dashed line represents the expected CL$_{\text{s}}$ values, where the $1\sigma$ and $2\sigma$ contours are indicated by the green (dark) and yellow (light) shaded regions, respectively. Upper limits are determined by the points at which the observed $\text{CL}_{\text{s+b}}$ $p$values (black points connected by straight lines) fall below 5% (red solid line). Also displayed are the corresponding $\text{CL}_{\text{s}} = \text{CL}_{\text{s+b}} / \text{CL}_{\text{b}}$ values (blue points connected by straight dotted lines). 
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CLS_r_[..].pdf [10 KiB] HiDef png [147 KiB] Thumbnail [108 KiB] *.C file 

Animated gif made out of all figures. 
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Supplementary material full pdf 
supple[..].pdf [110 KiB] 

Supplementary material for LHCbPAPER2016058 Contains the invariant mass fits to the B > (D0 > K π+) π and B > (D0 > K π+ π π+) π modes, in Fig. 1 and Fig. 2, respectively. The normalisation yield used in this paper is taken from the sum of the signal yields measured in both of these fits. 
Fig1.pdf [29 KiB] HiDef png [561 KiB] Thumbnail [283 KiB] *C file 

Fig2.pdf [29 KiB] HiDef png [494 KiB] Thumbnail [273 KiB] *C file 
Created on 18 October 2019.