Study of light-meson resonances decaying to $K_{\mathrm{S}}^{0}K\ddot{I}€$ in the $B\to (K_{\mathrm{S}}^{0}K\ddot{I}€)K$ channels

Abstract

A study is presented of $B^{+}\to K_{\mathrm{S}}^0{K}^{-}\ddot{I}{€}^{+}{K}^{-}$ and $B^{+}\to K_{\mathrm{S}}^0{K}^{+}\ddot{I}{€}^{-}{K}^{+}$ 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 $9f{b}^{-1}$. The $K_{\mathrm{S}}^{0}K\ddot{I}€$ invariant-mass distributions of both $B^{+}$ decay modes show, in the $m(K_{\mathrm{S}}^{0}K\ddot{I}€)<1.85$ 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 $\hat{I}\cdot (1405)$, $\hat{I}\cdot (1470)$, $\hat{I}\cdot (1760)$, $f_1(1285)$, $f_1(1420)$ and $h_1(1405)$ resonances. The $K_{\mathrm{S}}^{0}K\ddot{I}€$ Dalitz plots are dominated by asymmetric crossing $K^{\ast }\bar{K}$ 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.

All figures and tables, along with any supplementary material and additional information, are available at https://lbfence.cern.ch/alcm/public/analysis/full-details/3220