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

Abstract

Measurements of the coherence factor $R_{K3\pi }$, the average strong-phase difference ${\delta }_D^{K3\pi }$ 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 $B^{-}\to D{K}^{-}$ 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.

Error corrected in Eq.(5) and fit results relying on this expression updated. Typo corrected in Eq.(1) - no other consequences

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