Summary
The decays K*(892) -> K-S,L(0)pi can be used to study CP violation and CPT violation. The K*(892) (hereinafter referred to as K*) meson can be produced via J/psi decays at BESIII. In this paper, we study CP violation and K-S(0) - K-L(0) asymmetry in the J/psi decays involving the K* meson in the final states and obtain the following results: ACP(J/psi -> K*f(J/psi) -> K-S(0)pi f(J/psi)) = (3.64 +/- 0.04) x 10(-3), ACP(J/psi -> K*f(J/psi) -> K-L(0) pi f(J/psi)) = (-3.32 +/- 0.04) x 10(-3), and R(J/psi -> K*f(J/psi) -> K-S,L(0)pi f(J/psi)) = (3.51 +/- 0.03) x 10(-3), R(J/psi -> over bar K* f(J/psi) -> K-S,L(0)pi f(J/psi)) = (-3.451 +/- 0.03) x 10(-3). Based 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 and the K-S(0) - K-L(0) asymmetry in the J/psi decays with K* meson in the final states, and 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 constrain the CPT violation parameter z and discuss the sensitivity for the measurement of z in J/psi decays with K* meson in the final states at BESIII. The sensitivity of the measurement of z depends on the measured precision of the parameters m(L) - m(S), Gamma(L), Gamma(S), p, and q and the consistence between the values of t(0) and t(1) and the event selection criteria in experiment.