Method to study $CP$ violation in $B_s^0\to K_S K^\pm π^\mp$ decays

Abstract

The $B_s^0\to K_S K^\pm π^\mp$ decays are of interest to test the Standard Model and search for new sources of $CP$ violation. A full study of these decays requires a tagged decay-time-dependent Dalitz-plot analysis performed simultaneously in the two final states. Such an analysis has never previously been performed. The method to carry out such an analysis, relating the amplitudes for decays to resonances in the two final-states to each other, is set out and its feasibility is demonstrated using pseudoexperiments. The sensitivity to the weak phase difference, $ϕ_s^{\rm eff}$, between $B_s^0 \to K_S K^*(892)^0$ decays with and without $B_s^0$-$\bar{B}_s^0$ mixing is studied. Good precision on $ϕ_s^{\rm eff}$ is found to be achievable with a dataset corresponding to LHCb Runs 1-3, with further improvement expected with datasets to be collected in future. The method is implemented in the Laura++ Dalitz-plot analysis package, and can be applied to other multibody decays with multiple final states.