Study of CP violation and CPT violation in $K^{\ast}(892)\rightarrow K_{S,L}^{0}π$ decays at BESIII
The decays $K^{\ast}(892)\rightarrow K_{S,L}^{0}π$ can be used to study CP violation and CPT violation. The $K^{\ast}(892)$ (hereinafter referred to as $K^{\ast}$) meson can be produced via $J/ψ$ decays at BESIII. In this paper, we study CP violation and $K_S^0-K_L^0$ asymmetry in the $J/ψ$ decays involving the $K^{\ast}$ meson in the final states and obtain the following results \begin{align} {\mathcal A}_{CP}\left(J/ψ\rightarrow K^{\ast}f_{J/ψ}\rightarrow K^0_{S}πf_{J/ψ}\right)=\left(3.64\pm0.04\right)\times 10^{-3},\nonumber\\ {\mathcal A}_{CP}\left(J/ψ\rightarrow K^{\ast}f_{J/ψ}\rightarrow K^0_{L}πf_{J/ψ}\right)=\left(-3.32\pm0.04\right)\times 10^{-3},\nonumber \end{align} and \begin{align} &R\left(J/ψ\rightarrow K^{\ast}f_{J/ψ}\rightarrow K^0_{S,L}πf_{J/ψ} \right)=\left(3.51\pm0.03\right)\times 10^{-3},\nonumber\\ &R\left(J/ψ\rightarrow \bar{K}^{\ast} \bar{f}_{J/ψ}\rightarrow K^0_{S,L}π\bar{f}_{J/ψ} \right)=\left(-3.45\pm0.03\right)\times 10^{-3}.\nonumber \end{align} Basing on two cases: the samples of $10^{10}$ and $10^{12}$ $J/ψ$ events, we calculate the expected numbers of the observed signal events on the CP violation and the $K_S^0-K_L^0$ asymmetry in the $J/ψ$ decays with $K^{\ast}$ meson in the final states, we find that the BESIII experiment may be able to unambiguously observe CP violation and $K_S^0-K_L^0$ asymmetry for each of these two cases. We study the possibility to constraint the CPT violation parameter $z$ and discuss the sensitivity for the measurement of $z$ in $J/ψ$ decays with $K^{\ast}$ meson in the final states at BESIII. The sensitivity of the measurement of $z$ depend on the measured precision of the parameters $m_L-m_S$, $Γ_L$, $Γ_S$, $p$ and $q$ and the consistence between the values of $t_0$ and $t_1$ and the event selection criteria in experiment.