Mixing and $CP$ violation in $D^0\to K^{-}{\pi }^{+}$ decays

Abstract

We review the experimental methods to measure mixing and time-dependent $CP$ violation in $D^0$ decays into two hadrons. While these phenomena are usually neglected for $D^0\to K^{-}{\pi }^{+}$ decays, this approximation is not always justified. In particular, it produces a bias on the measurement of the parameter $y_{CP}$, when this is performed by relying on $D^0\to K^{-}{\pi }^{+}$ decays as a normalisation channel, whose size is around 40% of the precision of the current world average. Finally, we estimate the sensitivity to the weak mixing phases achievable by studying $D^0\to K^{-}{\pi }^{+}$ and untagged $D\to K^{-}{\pi }^{+}$ decays, where $D$ stands for either of the $D^0$ and ${\bar{D}}^0$ mesons. Contrary to Cabibbo-suppressed $D^0\to h^{+}{h}^{-}$ decays, these decay channels allow to measure these phases without final-state dependent nuisance contributions from the decay amplitudes, but their sensitivity is lower by a factor of six.

Comments: 19 pages, 2 figures; fitting code available at https://github.com/tpajero/charm-fitter; v2 prepared for submission to JHEP (added 2 figures, fixed minor typos in equations, updated the values of charm mixing parameters); v3 prepared for publication in JHEP (text adds clarifications on the formalism)