Study of charmonium decays to $K^0_S K π$ in the $B \to (K^0_S K π) K$ channels
A study of the $B^+\to K^0_SK^+K^-π^+$ and $B^+\to K^0_SK^+K^+π^-$ decays is performed using proton-proton collisions at center-of-mass energies of 7, 8 and 13 TeV at the LHCb experiment. The $K^0_SK π$ invariant mass spectra from both decay modes reveal a rich content of charmonium resonances. New precise measurements of the $η_c$ and $η_c(2S)$ resonance parameters are performed and branching fraction measurements are obtained for $B^+$ decays to $η_c$, $J/ψ$, $η_c(2S)$ and $χ_{c1}$ resonances. In particular, the first observation and branching fraction measurement of $B^+ \to χ_{c0} K^0 π^+$ is reported as well as first measurements of the $B^+\to K^0K^+K^-π^+$ and $B^+\to K^0K^+K^+π^-$ branching fractions. Dalitz plot analyses of $η_c \to K^0_SKπ$ and $η_c(2S) \to K^0_SKπ$ decays are performed. A new measurement of the amplitude and phase of the $K π$ $S$-wave as functions of the $K π$ mass is performed, together with measurements of the $K^*_0(1430)$, $K^*_0(1950)$ and $a_0(1700)$ parameters. Finally, the branching fractions of $χ_{c1}$ decays to $K^*$ resonances are also measured.