Study of charm mixing and CP violation with D ⁰→ K ^±π ^∓π ^±π ^∓ decays

A study of charm mixing and CP violation in D ⁰ → 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 D ⁰ → K ⁺π ⁻π ⁺π ⁻ to D ⁰ → K ⁻π ⁺π ⁻π ⁺ decay rates is measured as a function of D ⁰ decay time, both inclusive over phase space and in bins of phase space. Taking external inputs for the D0−D¯0 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 ∆x and ∆y, which are nonzero in the presence of CP violation. It is found that x=0.85−0.24+0.15%, y=0.21−0.27+0.29%, ∆x = (−0.02 ± 0.04) % and Δy=0.02−0.03+0.04%. These results are consistent with previous measurements and the hypothesis of CP conservation.