Strong and electromagnetic amplitudes, direct $CP$ and isospin asymmetries in the decays $J/\ddot{I}ˆ\to K_S^0{K}^{+}\ddot{I}{€}^{-}+c.c.$

Abstract

Using $e^{+}{e}^{-}$ annihilation data collected at 26 center-of-mass energy points between 3000.00 and $3119.88\text{MeV}$ with the BESIII detector, corresponding to a total integrated luminosity of about $440.7{\text{pb}}^{-1}$, we study the cross section lineshape of $e^{+}{e}^{-}\to K_S^0{K}^{+}\ddot{I}{€}^{-}+c.c.$. The relative phases and magnitudes between $J/\ddot{I}ˆ$ strong and electromagnetic decay amplitudes are measured to be $(123.7\pm 5.3{)}^{\circ };4.31\pm 0.22$ or $(-123.1\pm 5.2{)}^{\circ };4.38\pm 0.22$, with corresponding branching fractions $\mathcal{B}(J/\ddot{I}ˆ\to K_S^0{K}^{+}\ddot{I}{€}^{-}+c.c.)=(5.17\pm 0.20)$ or $(5.36\pm 0.20)\times 10^{-3}$. Based on a partial wave analysis, the cross sections of $e^{+}{e}^{-}\to {\bar{K}}^0{K}^{\ast }(892{)}^0+c.c.$ and $e^{+}{e}^{-}\to K^{+}{K}^{\ast }(892{)}^{-}+c.c.$ are obtained. For these subprocesses, the relative phases and magnitudes are determined as $(155.2\pm 15.5{)}^{\circ };3.67\pm 0.27$ or $(-154.1\pm 15.5{)}^{\circ };3.71\pm 0.25$ and $(180.1\pm 31.8{)}^{\circ };25.06\pm 2.51$, respectively. The large relative phases deviate from the orthogonality relation expected from experiment and from the assumption of purely real amplitudes by more than $3\ddot{I}ƒ$. The measured branching fractions $\mathcal{B}(J/\ddot{I}ˆ\to {\bar{K}}^0{K}^{\ast }(892{)}^0)+c.c.=(4.18\pm 0.18)$ or $(4.31\pm 0.19)\times 10^{-3}$, $\mathcal{B}(J/\ddot{I}ˆ\to K^{+}{K}^{\ast }(892{)}^{-}+c.c.)=(7.09\pm 0.28)\times 10^{-3}$ are all consistent with the world average values, but achieve better than a twofold improvement in precision. The ratios between the branching fractions of $J/\ddot{I}ˆ\to {\bar{K}}^0{K}^{\ast }(892{)}^0+c.c.$ and $J/\ddot{I}ˆ\to {\bar{K}}^{+}{K}^{\ast }(892{)}^{-}+c.c.$ are ${\mathcal{R}}_{K^{\ast }\bar{K}}=0.589\pm 0.012$ or $0.612\pm 0.013$. After subtracting the electromagnetic contribution, the corresponding strong amplitude ratios are ${\mathcal{R}}_{K^{\ast }\bar{K}}^{3g}=0.884\pm 0.050$ or $0.909\pm 0.044$, which deviate $2.3$ or $2.1\ddot{I}ƒ$ from the unity. No evidence for direct $CP$ violation is observed.