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

Abstract

Measurements of the coherence factor $R_{K3π}$, the average strong-phase difference $δ^{K3π}_D$ and mean amplitude ratio $r_D^{K3π}$ for the decay $D \to K^-π^+π^+π^-$ are presented. These parameters are important inputs to the determination of the unitarity triangle angle $γ$ 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 $ψ(3770)$ 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