Effect of K 0 − K ¯ 0 mixing on C P and C P T violations in B c ± → B ± K S , L 0 decays

The large data sample of the ${B}_{c}$ meson collected at the LHC experiment and the HL-LHC experiment provides us the opportunity to study the ${B}_{c}$ decays and the related physics. In this paper, we investigate the effect of ${K}^{0}\ensuremath{-}{\overline{K}}^{0}$ mixing on the branching ratios, $CP$ violations and $CPT$ violations in the ${B}_{c}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{B}^{\ifmmode\pm\else\textpm\fi{}}{K}_{S,L}^{0}$ decays. We find that some of the ${B}_{c}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{B}^{\ifmmode\pm\else\textpm\fi{}}{K}_{S,L}^{0}\ensuremath{\rightarrow}{f}_{{B}^{\ifmmode\pm\else\textpm\fi{}}}{f}_{{K}_{S,L}^{0}}$ decay chains have large branching ratios, whose maximum value can exceed the order of ${10}^{\ensuremath{-}6}$, the minimum number of ${B}_{c}^{\ifmmode\pm\else\textpm\fi{}}$ events times efficiency for observing the decays at three standard deviations ($3\ensuremath{\sigma}$) level is about ${10}^{6}$. We study the $CP$ asymmetries in the ${B}_{c}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{B}^{\ifmmode\pm\else\textpm\fi{}}{K}_{S,L}^{0}$ decays and find that the $CP$ asymmetries can exceed the order of ${10}^{\ensuremath{-}3}$, which are dominated by ${K}^{0}\ensuremath{-}{\overline{K}}^{0}$ mixing. We give the most promising processes to observe the $CP$ violations and the ranges of the numbers of ${B}_{c}^{\ifmmode\pm\else\textpm\fi{}}$ events-times-efficiency needed to observe the $CP$ asymmetries at a significance of $3\ensuremath{\sigma}$ in these decays. We investigate the possibility to constraint the $CPT$ violation parameter $z$ in the ${B}_{c}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{B}^{\ifmmode\pm\else\textpm\fi{}}{K}_{S,L}^{0}\ensuremath{\rightarrow}{f}_{{B}^{\ifmmode\pm\else\textpm\fi{}}}{f}_{{K}_{S,L}^{0}}$ decays and give the most promising processes to constraint the parameter $z$.