Strong and electromagnetic amplitudes, direct $CP$ and isospin asymmetries in the decays $J/\psi \to K^0_SK^+\pi^-+c.c.$

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 $e^+e^-\to K_S^0 K^+\pi^-+c.c.$. The relative phases and magnitudes between $J/\psi$ strong and electromagnetic decay amplitudes are measured to be $(123.7\pm5.3)^\circ;4.31\pm0.22$ or $(-123.1\pm5.2)^\circ;4.38\pm0.22$, with corresponding branching fractions $\mathcal{B}(J/\psi\to K_S^0 K^+\pi^-+c.c.)=(5.17\pm0.20)$ or $(5.36\pm0.20)\times10^{-3}$. Based on a partial wave analysis, the cross sections of $e^+e^-\to\bar K^0 K^*(892)^0+c.c.$ and $e^+e^-\to K^+ K^*(892)^-+c.c.$ are obtained. For these subprocesses, the relative phases and magnitudes are determined as $(155.2\pm15.5)^{\circ};3.67\pm0.27$ or $(-154.1\pm15.5)^{\circ};3.71\pm0.25$ and $(180.1\pm31.8)^{\circ};25.06\pm2.51$, respectively. The large relative phases deviate from the orthogonality relation expected from experiment and from the assumption of purely real amplitudes by more than $3\sigma$. The measured branching fractions $\mathcal{B}(J/\psi\to\bar K^0 K^*(892)^0)+c.c.=(4.18\pm0.18)$ or $(4.31\pm0.19)\times10^{-3}$, $\mathcal{B}(J/\psi\to K^+ K^*(892)^-+c.c.)=(7.09\pm0.28)\times10^{-3}$ are all consistent with the world average values, but achieve better than a twofold improvement in precision. The ratios between the branching fractions of $J/\psi\to\bar K^0 K^*(892)^0+c.c.$ and $J/\psi\to\bar K^+ K^*(892)^-+c.c.$ are $\mathcal{R}_{K^*\bar{K}}=0.589\pm0.012$ or $0.612\pm0.013$. After subtracting the electromagnetic contribution, the corresponding strong amplitude ratios are $\mathcal{R}^{3g}_{K^*\bar{K}}=0.884\pm0.050$ or $0.909\pm0.044$, which deviate $2.3$ or $2.1\sigma$ from the unity. No evidence for direct $CP$ violation is observed.