A novel measurement of the strong-phase difference between $D^0\to K^-π^+$ and $\bar{D}^0\to K^-π^+$ decays using $C$-even and $C$-odd quantum-correlated $D\bar{D}$ pairs

TL;DR

This work presents a novel method to determine the relative strong phase between $D^0\to K^-\pi^+$ and ${\overline{D}}^0\to K^-\pi^+$ decays by exploiting quantum-correlated ${D}\overline{D}$ pairs produced above the charm threshold in both $C$-even and $C$-odd states. Using BESIII data corresponding to $7.13\ \mathrm{fb}^{-1}$, the paper demonstrates quantum coherence, measures CP-tagged observables, and extracts the strong-phase difference $\delta_{K\pi}^{D}$ with two independent channels: CP eigenstate tags and the ${D}\to K_S^0\pi^+\pi^-$ Dalitz region. The reported values are $\delta_{K\pi}^{D} = (192.8^{+11.0+1.9}_{-12.4-2.4})^{\circ}$ (from this measurement with fixed $r$) and $\delta_{K\pi}^{D} = (189.2^{+6.9+3.4}_{-7.4-3.8})^{\circ}$ when combined with the prior analysis, consistent with global fits. The results validate the use of above-threshold $D\overline{D}$ data for precision charm-physics inputs and open avenues for time-integrated mixing and CP-violation studies with quantum correlations.

Abstract

A novel measurement technique of strong-phase differences between the decay amplitudes of $D^0$ and $\bar{D}^0$ mesons is introduced which exploits quantum-correlated $D\bar{D}$ pairs produced by $e^+e^-$ collisions at energies above the $ψ(3770)$ production threshold, where $D\bar{D}$ pairs are produced in both even and odd eigenstates of the charge-conjugation symmetry. Employing this technique, the first determination of a $D^0$-$\bar{D^0}$ relative strong phase is reported with such data samples. The strong-phase difference between $D^0\to K^-π^+$ and $\bar{D}^0\to K^-π^+$ decays, $δ^{D}_{Kπ}$, is measured to be $δ^{D}_{Kπ}=\left(192.8^{+11.0 + 1.9}_{-12.4 -2.4}\right)^\circ$, using a dataset corresponding to an integrated luminosity of 7.13 $\text{fb}^{-1}$ collected at center-of-mass energies between $4.13-4.23 \text{ GeV}$ by the BESIII experiment.

Figures (11)

• Figure 1: The (a) $E_{\text{miss}}$, (b) $M_{\text{rec,}D}$, (c) $M_{\text{miss,${D}\xspace\overline{ {D}}\xspace\;\xspace$}}^2$, (d) $M_{\text{miss,$\gamma{D}\xspace\overline{ {D}}\xspace\;\xspace$}}^2$ distributions of ${D}\xspace\overline{ {D}}\xspace\;\xspace\to{{\textit{K}}\xspace^-}\xspace{{\pi\xspace}\xspace^+}\xspace\ \mathrm{vs.}\ {{\textit{K}}\xspace^+}\xspace{{\pi\xspace}\xspace^-}\xspace$ candidates in MC simulation samples. The $\Delta M_{{{D}\xspace^*}\xspace}$ vs. $M_{\text{rec,}{{D}\xspace^*}\xspace}$ distribution of simulated ${{D}\xspace \overline{ {D}}\xspace}\xspace\to {{\textit{K}}\xspace^-}\xspace{{\pi\xspace}\xspace^+}\xspace\ \text{vs.}\ {{\textit{K}}\xspace^+}\xspace{{\pi\xspace}\xspace^-}\xspace$ decays which originate from the (e) ${{D}\xspace^*}\xspace{{\overline{ D\xspace}}\xspace{}^*}\xspace\xspace\to\gamma\gamma{D}\xspace\overline{ {D}}\xspace\;\xspace$ and ${{D}\xspace^*}\xspace{{\overline{ D\xspace}}\xspace{}^*}\xspace\xspace\to\gamma{{\pi\xspace}\xspace^0}\xspace{D}\xspace\overline{ {D}}\xspace\;\xspace$ and (f) ${{D}\xspace^*}\xspace{{\overline{ D\xspace}}\xspace{}^*}\xspace\xspace\to{{\pi\xspace}\xspace^0}\xspace{{\pi\xspace}\xspace^0}\xspace{D}\xspace\overline{ {D}}\xspace\;\xspace$ processes are also shown. The vertical dashed lines are used to distinguish between production mechanisms and correspond to the requirements in Table \ref{['table:sels']}.
• Figure 2: Comparisons between the (a) $E_{\text{miss}}$, (b) $M_{\text{rec,}D}$, (c) $M_{\text{miss,${D}\xspace\overline{ {D}}\xspace\;\xspace$}}^2$, (d) $M_{\text{miss,$\gamma{D}\xspace\overline{ {D}}\xspace\;\xspace$}}^2$, (e) $M_{\text{rec,}{{D}\xspace^*}\xspace}$ and (f) $\Delta M_{{{D}\xspace^*}\xspace}$ distributions of ${D}\xspace\overline{ {D}}\xspace\;\xspace\to{{\textit{K}}\xspace^-}\xspace{{\pi\xspace}\xspace^+}\xspace\ \mathrm{vs.}\ {{\textit{K}}\xspace^+}\xspace{{\pi\xspace}\xspace^-}\xspace$ candidates in data and MC simulation samples that contain signal and background contributions.
• Figure 3: Comparisons between the $M_{\text{miss,${D}\xspace\overline{ {D}}\xspace\;\xspace$}}^2$ distributions in data and MC simulation samples for each of the final states used to demonstrate the $C$-coherence of the ${D}\xspace\overline{ {D}}\xspace\;$ pairs. The data are enhanced or suppressed relative to the MC samples, which does not account for quantum correlations, depending on the final state and the expected $C$-eigenvalue of the ${D}\xspace\overline{ {D}}\xspace\;$ pairs that can be found in a particular region.
• Figure 4: Comparisons between the $M_{\text{miss,$\gamma{D}\xspace\overline{ {D}}\xspace\;\xspace$}}^2$ distributions in data and MC simulation samples for each of the final states used to demonstrate the $C$-coherence of the ${D}\xspace\overline{ {D}}\xspace\;$ pairs. The data are enhanced or suppressed relative to the MC samples, which does not account for quantum correlations, depending on the final state and the expected $C$-eigenvalue of the ${D}\xspace\overline{ {D}}\xspace\;$ pairs that can be found in a particular region.
• Figure 5: Projections of the fits to the ${D}\xspace\overline{ {D}}\xspace\;\xspace\to{{\textit{K}}\xspace^-}\xspace{{\pi\xspace}\xspace^+}\xspace\ \mathrm{vs.}\ {{\textit{K}}\xspace^+}\xspace{{\pi\xspace}\xspace^-}\xspace$ decays passing the requirements which isolate the (top) $D^{*}\bar{D}\to {\gamma} {D}\xspace\overline{ {D}}\xspace$, (center) $D^{*}\bar{D}\to{\pi^0} {D}\xspace \overline{ {D}}\xspace$ and (bottom) $D^{*}\bar{D}^{*}\to{\gamma\pi^0}{D}\xspace \overline{ {D}}\xspace$ production mechanisms.