Observation of overlapping spin-1 and spin-3 $\overline{D}^0 K^-$ resonances at mass $2.86 {\rm GeV}/c^2$

The resonant substructure of $B_s^0 \rightarrow \overline{D}^0 K^- \pi^+$ decays is studied using a data sample corresponding to an integrated luminosity of $3.0\,{\rm fb}^{-1}$ of $pp$ collision data recorded by the LHCb detector. An excess at $m(\overline{D}^0 K^-) \approx 2.86 {\rm GeV}/c^2$ is found to be an admixture of spin-1 and spin-3 resonances. Therefore the $D^*_{sJ}(2860)^-$ state previously observed in inclusive $e^+e^- \rightarrow \overline{D}^0 K^- X$ and $pp \rightarrow \overline{D}^0 K^- X$ processes consists of at least two particles. This is the first observation of a heavy flavoured 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.