Study of charmonium decays to $K_S^{0}K\pi$ in the $B\to (K_S^{0}K\pi )K$ channels

A study of the $B^{+}\to K_S^0{K}^{+}{K}^{-}{\pi }^{+}$ and $B^{+}\to K_S^0{K}^{+}{K}^{+}{\pi }^{-}$ decays is performed using proton-proton collisions at center-of-mass energies of 7, 8 and 13 TeV at the LHCb experiment. The $K_S^{0}K\pi$ invariant mass spectra from both decay modes reveal a rich content of charmonium resonances. New precise measurements of the ${\eta }_c$ and ${\eta }_c(2S)$ resonance parameters are performed and branching fraction measurements are obtained for $B^{+}$ decays to ${\eta }_c$, $J\mathrm{/}\psi$, ${\eta }_c(2S)$ and ${\chi }_{c1}$ resonances. In particular, the first observation and branching fraction measurement of $B^{+}\to {\chi }_{c0}{K}^0{\pi }^{+}$ is reported as well as first measurements of the $B^{+}\to K^0{K}^{+}{K}^{-}{\pi }^{+}$ and $B^{+}\to K^0{K}^{+}{K}^{+}{\pi }^{-}$ branching fractions. Dalitz plot analyses of ${\eta }_c\to K_S^{0}K\pi$ and ${\eta }_c(2S)\to K_S^{0}K\pi$ decays are performed. A new measurement of the amplitude and phase of the $K\pi$ $S$-wave as functions of the $K\pi$ mass is performed, together with measurements of the $K_0^{\ast }(1430)$, $K_0^{\ast }(1950)$ and $a_0(1700)$ parameters. Finally, the branching fractions of ${\chi }_{c1}$ decays to $K^{\ast }$ resonances are also measured.