Abstract
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.
Highlights
IntroductionKnowledge of the D → K −π +π +π − coherence factor and associated hadronic parameters is necessary for a measurement of the unitarity triangle angle γ ( denoted φ3) in B− → D K −, D → K −π +π +π − decays. (The symbol D is used to denote a neutral charm-meson that is not in a flavour eigenstate, or where the flavour eigenvalue is not relevant for the discussion.)
This Letter reports a new analysis of D → K −π +π +π − decays in the CLEO-c data set, and benefits from an updated Monte Carlo simulation sample to correct a biased estimate of the background contamination in several sets of double tags that afflicted the results reported in Refs. [4,5]
A re-analysis of the CLEO-c ψ(3770) data set has yielded an updated set of observables sensitive to the hadronic parameters of the decay D → K −π +π +π −, some of which are significantly different to those reported previously [4,5]. These observables have been input to a combined fit, together with measurements from a recent LHCb D0 D 0 mixing analysis [12]
Summary
Knowledge of the D → K −π +π +π − coherence factor and associated hadronic parameters is necessary for a measurement of the unitarity triangle angle γ ( denoted φ3) in B− → D K −, D → K −π +π +π − decays. (The symbol D is used to denote a neutral charm-meson that is not in a flavour eigenstate, or where the flavour eigenvalue is not relevant for the discussion.). A double-tag technique is employed where one meson is reconstructed in the signal decay D → K −π +π +π −, and the other in a tagging mode, for example, a CP eigenstate This method was applied by the CLEO Collaboration to obtain first constraints on R K 3π and δDK 3π , together with R K ππ0 and δDK ππ0 , the analogous parameters for D → K −π +π 0 decays [4]. A and b can either be used to determine x and y, given external information on R K 3π and δDK 3π , or employed to set constraints on the latter parameters, provided x and y are known D → π +π −π 0 [14] is included as a new tagging mode to augment the sensitivity of the analysis The observables from this new analysis are used to determine updated constraints on the hadronic parameters. Since one of the re-measured ψ(3770) observables couples the K −π +π +π − and K −π +π 0 systems, it is possible to determine updated values of RKππ0, δ π π and r
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