Observation of new charmonium(-like) states in $B^{+}\to D^{\ast \pm }{D}^{\mp }{K}^{+}$ decays

A study of resonant structures in $B^{+}\to D^{\ast +}{D}^{-}{K}^{+}$ and $B^{+}\to D^{\ast -}{D}^{+}{K}^{+}$ decays is performed, using proton-proton collision data at centre-of-mass energies of $\sqrt{s}=7,8$, and $13$ TeV recorded by the LHCb experiment, corresponding to an integrated luminosity of 9 fb${}^{-1}$. A simultaneous amplitude fit is performed to the two channels with contributions from resonances decaying to $D^{\ast -}{D}^{+}$ and $D^{\ast +}{D}^{-}$ states linked by $C$ parity. This procedure allows the $C$-parities of resonances in the $D^{\ast \pm }{D}^{\mp }$ mass spectra to be determined. Four charmonium(-like) states are observed decaying into $D^{\ast \pm }{D}^{\mp }$: ${\eta }_c(3945)$, $h_c(4000)$, ${\chi }_{c1}(4010)$ and $h_c(4300)$, with quantum numbers $J^{PC}$ equal to $0^{-+}$, $1^{+-}$, $1^{++}$ and $1^{+-}$, respectively. At least three of these states have not been observed previously. In addition, the existence of the $T_{\bar{c}\bar{s}0}^{\ast }(2870{)}^0$ and $T_{\bar{c}\bar{s}1}^{\ast }(2900{)}^0$ resonances in the $D^{-}{K}^{+}$ mass spectrum, already observed in the $B^{+}\to D^{+}{D}^{-}{K}^{+}$ decay, is confirmed in a different production channel.