First observation of the rare $B^{+}\to D^{+}{K}^{+}{\pi }^{-}$ decay

The $B^{+}\to D^{+}{K}^{+}{\pi }^{-}$ decay is observed in a data sample corresponding to $3.0{\mathrm{fb}}^{-1}$ of $pp$ collision data recorded by the LHCb experiment during 2011 and 2012. The signal significance is $8\sigma$ and the branching fraction is measured to be $\mathcal{B}(B^{+}\to D^{+}{K}^{+}{\pi }^{-})=(5.31\pm 0.90\pm 0.48\pm 0.35)\times {10}^{-6}$, where the uncertainties are statistical, systematic and due to the normalization mode $B^{+}\to D^{-}{K}^{+}{\pi }^{+}$, respectively. The Dalitz plot appears to be dominated by broad structures. Angular distributions are exploited to search for quasi-two-body contributions from $B^{+}\to D_2^{*}(2460{)}^0{K}^{+}$ and $B^{+}\to D^{+}{K}^{*}(892{)}^0$ decays. No significant signals are observed and upper limits are set on their branching fractions.

Figure 1

Decay diagrams for (a) $B^{+}\to {\overline{D}}_2^{*}(2460{)}^0{K}^{+}$, (b) $B^{+}\to D_2^{*}(2460{)}^0{K}^{+}$ and (c) $B^{+}\to D^{+}{K}^{*}(892{)}^0$ channels.

Figure 2

Weighted invariant mass distribution of candidates in the (left) $B^{+}\to D^{-}{K}^{+}{\pi }^{+}$ and (right) $B^{+}\to D^{+}{K}^{+}{\pi }^{-}$ data samples. Data points and fit functions are weighted as described in the text. The components are as detailed in the legend.

Figure 3

Background-subtracted Dalitz plot distribution of $B^{+}\to D^{+}{K}^{+}{\pi }^{-}$ candidates in the region $5260<m(D^{+}{K}^{+}{\pi }^{-})<5310\mathrm{MeV}/c^2$ from all NN2 bins. Areas of boxes are proportional to signal yields. Negative yields are indicated by crosses.

Figure 4

Results of binned minimum ${\chi }^2$ fits to the $B^{+}$ candidate invariant mass distributions of (left) $B^{+}\to D^{-}{K}^{+}{\pi }^{+}$ and (right) $B^{+}\to D^{+}{K}^{+}{\pi }^{-}$ candidates with efficiency corrections and angular weights applied. Candidates in the ranges (top) $2217.6<m(D^{\pm }{\pi }^{\mp })<2315.6\mathrm{MeV}/c^2$ and (bottom right) $801.0<m(K^{+}{\pi }^{-})<990.6\mathrm{MeV}/c^2$ are shown, while in the bottom left plot the whole $m(K^{+}{\pi }^{+})$ range is included. The components are as described in the legend.