Study of CP violation and CPT violation in $K^{\ast}(892)\rightarrow K_{S,L}^{0}\pi$ decays at BESIII

The decays $K^{\ast}(892)\rightarrow K_{S,L}^{0}\pi$ can be used to study CP violation and CPT violation. The $K^{\ast}(892)$ meson can be produced via $J/\psi$ decays at BESIII. In this paper, we study CP violation and CPT violation in $K^{\ast}(892)\rightarrow K_{S,L}^{0}\pi$ decays at BESIII. Basing on two cases: the samples of $10^{10}$ and $10^{12}$$J/\psi$ events, we calculate the expected numbers of the observed signal events on the CP violation in $J/\psi$ decays with $K^{\ast}(892)$ meson in the final states, we find that the BESIII experiment may be able to unambiguously observe CP violation for each of these two cases. Under the assumption that the observed event on CPT violation is absent, we discuss the upper limits on the absolute value of the CPT violation parameter $Re(z)$ in $J/\psi$ decays involving $K^{\ast}(892)$ meson in the final states with $10^{10}$$J/\psi$ events and $10^{12}$$J/\psi$ events, respectively. By using the accumulated $10^{10}$$J/\psi$ events, the upper limits on $\left|Re(z)\right|$ can be obtained at the $90\%$ confidence level of $10^{-4}-10^{-5}$, which is competitive with the current best result, if the detection efficiency $\varepsilon_{K^0_{L}}$ is assumed to be at the level of $8\times 10^{-3}$ at BESIII. And besides, the upper limits on $\left|Re(z)\right|$ will be improved by about two orders of magnitude compared with the current best result with $10^{12}$$J/\psi$ events.