Improved determination of the $D \to K^-\pi^+\pi^+\pi^-$ coherence factor and associated hadronic parameters from a combination of $e^+e^-\to \psi(3770)\to c\bar{c}$ and $pp \to c \bar{c} X$ data

Measurements of the coherence factor $R_{K3\pi}$, the average strong-phase difference $\delta^{K3\pi}_D$ and mean amplitude ratio $r_D^{K3\pi}$ for the decay $D \to K^-\pi^+\pi^+\pi^-$ are presented. These parameters are important inputs to the determination of the unitarity triangle angle $\gamma$ in $B^- \to DK^-$ decays, where $D$ designates a superposition of $D^0$ and $\bar{D}{}^0$ mesons decaying to a common final state. The results are based on a combined fit to observables obtained from a re-analysis of the CLEO-c $\psi(3770)$ data set and those measured in a $D^0\bar{D}^0$ mixing study performed by the LHCb collaboration.