Improved measurement of the strong-phase difference $\delta _D^{K\pi }$ in quantum-correlated $D{\overline{D}}$ decays
The decay D → K - π + is studied in a sample of quantum-correlated D$\overline{D}$ pairs, based on a data set corresponding to an integrated luminosity of 2.93 fb -1 collected at the ψ(3770) resonance by the BESIII experiment. The asymmetry between CP-odd and CP-even eigenstate decays into K - π + is determined to be A Kπ = 0.132 ± 0.011 ± 0.007, where the first uncertainty is statistical and the second is systematic. This measurement is an update of an earlier study exploiting additional tagging modes, including several decay modes involving a $K^{0}_{L}$ meson. The branching fractions of the $K^{0}_{L}$ modes are determined as input to the analysis in a manner that is independent of any strong phase uncertainty. Using the predominantly CP-even tag D → π + π - π 0 and the ensemble of CP-odd eigenstate tags, the observable $A^{πππ^0}_{Kπ}$ is measured to be 0.130 ± 0.012 ± 0.008. The two asymmetries are sensitive to $r^{Kπ}_{D}$ cos $δ^{Kπ}_{D}$ where $r^{Kπ}_{D}$ and $δ^{Kπ}_{D}$ are the ratio of amplitudes and phase difference, respectively, between the doubly Cabibbo-suppressed and Cabibbo-favoured decays. In addition, events containing D → K - π + tagged by D → $K^{0}_{S,L}$π + π - are studied in bins of phase space of the three-body decays. This analysis has sensitivity to both $r^{Kπ}_{D}$ cos $δ^{Kπ}_{D}$ and $r^{Kπ}_{D}$, sin $δ^{Kπ}_{D}$. A fit to A Kπ , $A^{πππ^0}_{Kπ}$ and the phase-space distribution of the D → $K^{0}_{S,L}$π + π - tags yields $δ^{Kπ}_{D}$ = ($187.6^{+8.9+5.4}_{-9.7-6.4}$)°, where external constraints are applied for $r^{Kπ}_{D}$ and other relevant parameters. This is the most precise measurement of $δ^{Kπ}_{D}$ in quantum-correlated D$\overline{D}$ decays.