Study of light-meson resonances decaying to $K^0_{\rm S} K \pi$ in the $B \to (K^0_{\rm S} K \pi) K$ channels

Abstract

A study is presented of $B^+ \to K^0_{\rm S} K^- \pi^+ K^-$ and $B^+ \to K^0_{\rm S} K^+ \pi^- K^+$ decays based on the analysis of proton-proton collision data collected with the LHCb detector at centre-of-mass energies of 7, 8 and 13 TeV, corresponding to an integrated luminosity of $9 fb^{-1}$. The $K^0_{\rm S} K \pi$ invariant-mass distributions of both $B^+$ decay modes show, in the $m(K^0_{\rm S} K \pi)<1.85$ GeV mass region, large activity which is resolved using an amplitude analysis. A simple model, were $J^{PC}$ amplitudes are described by multiple Breit--Wigner functions with appropriate angular distributions provides a good description of the experimental data. In this approach a complex mixture of $J^{PC}=0^{-+}, 1^{++}$ and $1^{+-}$ amplitudes is observed that is dominated by $\eta(1405)$, $\eta(1470)$, $\eta(1760)$, $f_1(1285)$, $f_1(1420)$ and $h_1(1405)$ resonances. The $K^0_{\rm S} K \pi$ Dalitz plots are dominated by asymmetric crossing $K^* \bar{K}$ bands which are different for the two $B^+$ decay modes. This is due to a different interference pattern between the $1^{++}$ and $1^{+-}$ amplitudes in the two channels. Branching fractions are measured for each resonant contribution.