Study of charm mixing and CP violation with $D^0\to K^\pm\pi^\mp\pi^\pm\pi^\mp$ decays

Abstract

A study of charm mixing and CP violation in $D^0\to K^\pm\pi^\mp\pi^\pm\pi^\mp$ 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$\text{fb}^{-1}$. The ratio of promptly produced $D^0\to K^+\pi^- \pi^+\pi^-$ to $D^0\to K^-\pi^+ \pi^-\pi^+$ 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 $D^0 -\overline{D}^0$ 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 $\gamma$ 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 $\Delta x$ and $\Delta y$, which are nonzero in the presence of CP violation. It is found that $x=\left(0.85^{+0.15}_{-0.24}\right)\%$, $y=\left( 0.21^{+0.29}{-0.27} \right)\%$, $\Delta x=\left( -0.02\pm {0.04} \right)\% $ and $\Delta y=\left( 0.02^{+0.04}_{-0.03} \right)\%$. These results are consistent with previous measurements and the hypothesis of CP conservation.