First observation and amplitude analysis of the $B^{-}\to D^{+}{K}^{-}{\pi }^{-}$ 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. Its branching fraction is measured to be $\mathcal{B}(B^{-}\to D^{+}{K}^{-}{\pi }^{-})=(7.31\pm 0.19\pm 0.22\pm 0.39)\times 10^{-5}$ where the uncertainties are statistical, systematic and from the branching fraction of the normalization channel $B^{-}\to D^{+}{\pi }^{-}{\pi }^{-}$, respectively. An amplitude analysis of the resonant structure of the $B^{-}\to D^{+}{K}^{-}{\pi }^{-}$ decay is used to measure the contributions from quasi-two-body $B^{-}\to D_0^{*}(2400{)}^0{K}^{-}$, $B^{-}\to D_2^{*}(2460{)}^0{K}^{-}$, and $B^{-}\to D_J^{*}(2760{)}^0{K}^{-}$ decays, as well as from nonresonant sources. The $D_J^{*}(2760{)}^0$ resonance is determined to have spin 1.

Figure 1

Results of the fit to the $B^{-}\to D^{+}{\pi }^{-}{\pi }^{-}$ candidate invariant mass distribution for the (left) TOS and (right) TIS-only subsamples. Data points are shown in black, the full fitted model as solid blue lines and the components as shown in the legend.

Figure 2

Results of the fit to the $B^{-}\to D^{+}{K}^{-}{\pi }^{-}$ candidate invariant mass distribution for the (left) TOS and (right) TIS-only subsamples. Data points are shown in black, the full fitted model as solid blue lines and the components as shown in the legend.

Figure 3

Signal efficiency across the SDP for (left) TOS and (right) TIS-only $B^{-}\to D^{+}{K}^{-}{\pi }^{-}$ decays. The relative uncertainty at each point is typically 5%.

Figure 4

The first seven Legendre-polynomial-weighted moments for background-subtracted and efficiency-corrected $B^{-}\to D^{+}{K}^{-}{\pi }^{-}$ data (black points) as a function of $m(D^{+}{\pi }^{-})$ in the range 2.0–3.0 GeV. Candidates from both TOS and TIS-only subsamples are included. The blue line shows the result of the DP fit described in Sec. 7.

Figure 5

Distribution of $B^{-}\to D^{+}{K}^{-}{\pi }^{-}$ candidates in the signal region over (left) the DP and (right) the SDP. Candidates from both TOS and TIS-only subsamples are included.

Figure 6

Square Dalitz plot distributions used in the Dalitz plot fit for (top) combinatorial background, (middle) $B^{-}\to D^{(*)+}{\pi }^{-}{\pi }^{-}$ decays and (bottom) $B^{-}\to D_s^{+}{K}^{-}{\pi }^{-}$ decays. Candidates from the TOS (TIS-only) subsamples are shown in the left (right) column.

Figure 7

Differences between the data SDP distribution and the fit model across the SDP, in terms of the per-bin pull.

Figure 8

Projections of the data and amplitude fit onto (a) $m(D\pi )$, (c) $m(DK)$ and (e) $m(K\pi )$, with the same projections shown in (b), (d) and (f) with a logarithmic $y$-axis scale. Components are described in the legend.

Figure 9

Projections of the data and amplitude fit onto $m(D\pi )$ in (a) the threshold region, (b) the $D_2^{*}(2460{)}^0$ region and (c) the $D_1^{*}(2760{)}^0$ region. Components are as shown in Fig. 8.

Figure 10

Projections of the data and amplitude fit onto the cosine of the helicity angle for the $D\pi$ system in (a) the threshold region, (b) the $D_2^{*}(2460{)}^0$ region and (c) the $D_1^{*}(2760{)}^0$ region. Components are as shown in Fig. 8.