Study of light-meson resonances decaying to 𝐾0 S⁢𝐾⁢𝜋 in the 𝐵 →(𝐾0 S⁢𝐾⁢𝜋)⁢𝐾 channels

A study is presented of 𝐵+ →𝐾0S⁢𝐾−⁢𝜋+⁢𝐾+ and 𝐵+ →𝐾0S⁢𝐾+⁢𝜋−⁢𝐾+ decays based on the analysis of proton-proton collision data collected with the LHCb detector at center-of-mass energies of 7, 8 and 13 TeV, corresponding to an integrated luminosity of 9  fb−1. The 𝐾0S⁢𝐾⁢𝜋 invariant-mass distributions of both 𝐵+ decay modes show, in the 𝑚⁡(𝐾0S⁢𝐾⁢𝜋) <1.85  GeV mass region, large activity which is resolved using an amplitude analysis. A simple model, where 𝐽𝑃⁢𝐶 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 𝐽𝑃⁢𝐶 =0−+, 1++ and 1+− amplitudes is observed that is dominated by 𝜂⁡(1405), 𝜂⁡(1470), 𝜂⁡(1760), 𝑓1⁡(1285), 𝑓1⁡(1420) and ℎ1⁡(1405) resonances. The 𝐾0S⁢𝐾⁢𝜋 Dalitz plots are dominated by asymmetric crossing 𝐾*⁢¯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.