Study of charm mixing and CP violation with D⁰ → K^±π^∓π^±π^∓ decays

A study of charm mixing and CP violation in D⁰ → K^±π^∓π^±π^∓ decays is performed using data collected by the LHCb experiment in proton-proton collisions from 2015 to 2018, corresponding to an integrated luminosity of 6 fb⁻¹. The ratio of promptly produced D⁰ → K⁺π^-π⁺π^- to D⁰ → K^-π⁺π^-π⁺ decay rates is measured as a function of D⁰ decay time, both inclusive over phase space and in bins of phase space. Taking external inputs for the D⁰ – D̄⁰ mixing parameters x and y allows constraints to be obtained on the hadronic parameters of the charm decay. When combined with previous measurements from charm-threshold experiments and at LHCb, improved knowledge is obtained for these parameters, which is valuable for studies of the angle γ of the Unitarity Triangle. An alternative analysis is also performed, in which external inputs are taken for the hadronic parameters, and the mixing parameters are determined, including Δx and Δy, which are nonzero in the presence of CP violation. It is found that x = (0.85^+0.15_−0.24)%, y = (0.21^+0.29_−0.27)%, Δx = (−0.02 ± 0.04)% and Δy = (0.02^+0.04_−0.03)%. These results are consistent with previous measurements and the hypothesis of CP conservation.