Observation of Overlapping Spin-1 and Spin-3 ${\overline{D}}^0{K}^{-}$ Resonances at Mass $2.86\mathrm{GeV}/c^2$

The resonant substructure of $B_s^0\to {\overline{D}}^0{K}^{-}{\pi }^{+}$ decays is studied using a data sample corresponding to an integrated luminosity of $3.0{\mathrm{fb}}^{-1}$ of $pp$ collision data recorded by the LHCb detector. An excess at $m({\overline{D}}^0{K}^{-})\approx 2.86\mathrm{GeV}/c^2$ is found to be an admixture of spin-1 and spin-3 resonances. Therefore, the $D_{sJ}^{*}(2860{)}^{-}$ state previously observed in inclusive $e^{+}{e}^{-}\to {\overline{D}}^0{K}^{-}X$ and $pp\to {\overline{D}}^0{K}^{-}X$ processes consists of at least two particles. This is the first observation of a heavy flavored spin-3 resonance, and the first time that any spin-3 particle has been seen to be produced in $B$ decays. The masses and widths of the new states and of the $D_{s2}^{*}(2573{)}^{-}$ meson are measured, giving the most precise determinations to date.

Figure 1

Fit to the $B_s^0\to {\overline{D}}^0{K}^{-}{\pi }^{+}$ candidate invariant mass distribution. Data points are shown in black, the result of the fit as a solid blue line, and the components as detailed in the legend.

Figure 2

Dalitz plot distribution of $B_s^0\to {\overline{D}}^0{K}^{-}{\pi }^{+}$ candidates in the signal region. The effect of the $D^0$ veto can be seen as an unpopulated horizontal band.

Figure 3

Projections of the data and the Dalitz plot fit result onto (a) $m(K^{-}{\pi }^{+})$, (b) $m({\overline{D}}^0{K}^{-})$, and (c) $m({\overline{D}}^0{\pi }^{+})$, with zooms into $m({\overline{D}}^0{K}^{-})$ around (d) the $D_{s2}^{*}(2573{)}^{-}$ resonance and (e) the $D_{sJ}^{*}(2860{)}^{-}$ region. The data are shown as black points, the total fit result as a solid black curve, and the contributions from different resonances as detailed in the legend (small components, including the background contributions, are not shown).

Figure 4

Projections of the data and Dalitz plot fit results with alternative models onto the cosine of the helicity angle of the ${\overline{D}}^0{K}^{-}$ system, $\cos \theta ({\overline{D}}^0{K}^{-})$, for $2.77<m({\overline{D}}^0{K}^{-})<2.91\mathrm{GeV}/c^2$, where $\theta ({\overline{D}}^0{K}^{-})$ is the angle between the ${\pi }^{+}$ and the ${\overline{D}}^0$ meson momenta in the ${\overline{D}}^0{K}^{-}$ rest frame. The data are shown as black points, with the fit results with different models as detailed in the legend. The dip at $\cos \theta ({\overline{D}}^0{K}^{-})\approx -0.6$ is due to the ${\overline{D}}^0$ veto. Comparisons of the data and the different fit results in the 50 bins of this projection give ${\chi }^2$ values of 47.3, 214.0, and 150.0 for the default, spin-1 only, and spin-3 only models, respectively.