Measurement of D⁰-D̄⁰ mixing and search for $CP$ violation with D⁰→ K⁺π⁻ decays

A measurement of the time-dependent ratio of the D⁰→ K⁺π⁻ to D̄⁰→ K⁺π⁻ decay rates is reported. The analysis uses a sample of proton-proton collisions corresponding to an integrated luminosity of 6 fb⁻1 recorded by the LHCb experiment from 2015 through 2018 at a center-of-mass energy of 13 TeV. The D⁰ meson is required to originate from a D*+→ D⁰π⁺ decay, such that its flavor at production is inferred from the charge of the accompanying pion. The measurement is performed simultaneously for the K⁺π⁻ and K⁻π⁺ final states, allowing both mixing and $CP$-violation parameters to be determined. The value of the ratio of the decay rates at production is determined to be RKπ = (343.1 ± 2.0) × 10⁻⁵. The mixing parameters are measured to be cKπ = (51.4 ± 3.5) × 10⁻⁴ and cKπ^ = (13 ± 4) × 10⁻⁶, where √RKπcKπ is the linear coefficient of the expansion of the ratio as a function of decay time in units of the D⁰ lifetime, and cKπ^ is the quadratic coefficient, both averaged between the K⁺π⁻ and K⁻π⁺ final states. The precision is improved relative to the previous best measurement by approximately 60%. No evidence for $CP$ violation is found.