Improved measurement of the strong-phase difference $$\delta _D^{K\pi }$$ in quantum-correlated $$D{\bar{D}}$$ decays

The decay D -> K-pi(+) is studied in a sample of quantum-correlated D (D) over bar pairs, based on a data set corresponding to an integrated luminosity of 2.93 fb(-1) collected at the psi(3770) resonance by the BESIII experiment. The asym- metry between CP-odd and CP-even eigenstate decays into K-pi(+) is determined to be A(K pi) = 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-L(0) meson. The branching fractions of the K-L(0) 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 -> pi(+)pi(-)pi(0) and the ensemble of CP-odd eigenstate tags, the observable A(K pi)(pi pi pi 0) is measured to be 0.130 +/- 0.012 +/- 0.008. The two asymmetries are sensitive to r(D)(K pi) delta(K)(pi)(D), where r(D)(K pi) and S-D(K pi) are the ratio of amplitudes and phase difference, respectively, between the doubly Cabibbo-suppressed and Cabibbofavoured decays. In addition, events containing D -> K-pi(+) tagged by D -> K-S,L(0) pi(+)pi(-) are studied in bins of phase space of the three-body decays. This analysis has sensitivity to both r(D)(K pi) cos delta(K)(pi)(D) and r(D)(K pi) sin delta(K)(pi)(D). A fit to A(K pi), A(K pi)(pi pi pi 0) and the phase-space distribution of the D -> K-S,L(0) pi(+)pi(-) tags yields delta(K)(pi)(D) = (187.6(-9.7-6.4)(+8.9+5.4))degrees , where external con- straints are applied for r(D)(K pi) and other relevant parameters. This is the most precise measurement of delta(K)(pi)(D) in quantumcorrelated D (D) over bar decays.