Improved measurements of the coherence factors and strong-phase differences in $D\to K^-π^+π^+π^-$ and $D\to K^-π^+π^0$ with quantum-correlated $D\bar{D}$ decays

TL;DR

This work delivers improved measurements of the coherence factors and strong-phase differences for $D\to K^-\pi^+\pi^+\pi^-$ and $D\to K^-\pi^+\pi^0$ using quantum-correlated $D\bar{D}$ decays at the BESIII experiment, based on $7.93~\mathrm{fb^{-1}}$ of data at $\sqrt{s}=3.773$ GeV. Through global and phase-space-binned analyses of CP-tag, like-sign, and self-conjugate double-tags, it extracts $R_{K3\pi}=0.51\pm0.04$, $\delta_D^{K3\pi}=(182^{+14}_{-13})^\circ$, $R_{K\pi\pi^0}=0.75\pm0.03$, and $\delta_D^{K\pi\pi^0}=(209^{+7}_{-8})^\circ$, with improved precision over previous measurements. A four-bin, phase-space-resolved analysis of $D\to K^-\pi^+\pi^+\pi^-$ provides bin-specific $R$ and $\delta_D$ values and shows consistency with amplitude-model predictions within uncertainties. These refined hadronic parameters will reduce the systematic uncertainty in $\gamma$ measurements in $B^-\to DK^-$ decays, contributing an estimated $\sim3.5^\circ$ to the $\gamma$ precision in future high-luminosity experiments, and they bolster charm-mixing and CP-violation studies in charm decays.

Abstract

Improved measurements of the coherence factors and strong-phase differences in $D\to K^-π^+π^+π^-$ and $D\to K^-π^+π^0$ decays are reported, using quantum-correlated $D\bar{D}$ pairs produced in $e^+e^-$ annihilation at a center-of-mass energy of $3.773\,\mathrm{GeV}$, where $D$ denotes a quantum superposition of the flavour-specific $D^{0}$ and $\bar{D}^{0}$ mesons. The analysis employs a dataset collected by the BESIII experiment, corresponding to an integrated luminosity of $7.93~\rm fb^{-1}$. The observables sensitive to the coherence factors and strong-phase differences are measured by reconstructing one $D$ meson in the signal mode and the other in a tag mode. These parameters provide essential inputs to the measurement of the angle $γ$ of the Cabibbo-Kobayashi-Maskawa Unitarity Triangle in the LHCb and Belle II experiments. The coherence factors are determined to be $R_{K3π}=0.51\pm0.04$ and $R_{Kππ^0}=0.75\pm0.03$, and the strong-phase differences are $δ_D^{K3π}=\left(182^{+14}_{-13}\right)^\circ$ and $δ_D^{Kππ^0}=\left(209^{+7}_{-8}\right)^\circ$, where the uncertainties include both statistical and systematic contributions. For $D\to K^-π^+π^+π^-$, the parameters have been further determined in four phase-space bins with improved precision compared to the previous BESIII results. The uncertainty on future $γ$ measurements from the knowledge of $D\to K^-π^+π^+π^-$ parameters is expected to be reduced to approximately 3.5$^\circ$.

Figures (10)

• Figure 1: The Dalitz plot of $D \to K^{0}_{S}\pi^+\pi^-$ illustrating the equal-$\Delta \delta_D$ binning scheme.
• Figure 2: The $M_{\rm BC}$ distributions for the like-sign and opposite-sign flavour tags. The data are shown as points with error bars. The red lines represent the total fit; the long-dashed cyan lines indicate the $D \to K_S^0 K^\mp \pi^\pm$ background; the misidentified opposite-sign background in like-sign case is shown as the dashed browm lines, and other $D^0\bar{D}^0$ backgrounds are shown as the dashed green lines. The dashed magenta lines represent the combinatorial background, which is very small.
• Figure 3: The $M_{\rm BC}$ distributions for a selection of $C\!P$-tagged decays. The points with error bars are data; the red lines indicate the total fit; the dashed brown and green lines show the peaking-background contributions from $D\to K_S^0 K^\mp \pi^\pm$ and other $D^{0}\bar{D}^{0}$ process, respectively; the combinatorial-background contributions are shown as the dashed magenta line.
• Figure 4: The $M_{\rm miss}^2$ distributions for double tags involving a $K^0_L$ meson. The points with error bars represent the data; the red lines denote the total fit; the dashed blue lines indicate the signal component; the dashed brown lines correspond the $D\to K_S^0 K^\mp \pi^\pm$ background; dashed green curves represent the combined $\pi^0 X$, $\eta X$, and $K^0_{S} X$ peaking backgrounds; and the dashed yellow and magenta curves represent the unmatched and other $D^{0}\bar{D}^0$ background, respectively.
• Figure 5: Efficiencies of $K \to \pi$ (top) and $\pi \to K$ (bottom) misidentifications in bins of momentum, as measured in data and Monte Carlo simulation.