Effect of $K^0-{\bar{K}}^0$ Mixing on CP and CPT Violations in $B_c^{\pm }\to B^{\pm }{K}_{S,L}^0$ Decays

Abstract

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 $K^0-{\bar{K}}^0$ mixing on the the branching ratios, CP violations and CPT violations in the $B_c^{\pm }\to B^{\pm }{K}_{S,L}^0$ decays. We find that some of the $B_c^{\pm }\to B^{\pm }{K}_{S,L}^0\to f_{B^{\pm }}{f}_{K_{S,L}^0}$ decay chains have large branching ratios, whose maximum value can exceed the order of $10^{-6}$, the minimum number of $B_c^{\pm }$ events times efficiency for observing the decays at three standard deviations (3$\sigma$) level is about $10^6$. We study the CP asymmetries in the $B_c^{\pm }\to B^{\pm }{K}_{S,L}^0$ decays and find that the CP asymmetries can exceed the order of $10^{-3}$, which are dominated by $K^0-{\bar{K}}^0$ mixing. We give the most promising processes to observe the CP violations and the ranges of the numbers of $B_c^{\pm }$ events-times-efficiency needed to observe the CP asymmetries at a significance of 3$\sigma$ in these decays. We investigate the possibility to constraint the CPT violation parameter $z$ in the $B_c^{\pm }\to B^{\pm }{K}_{S,L}^0\to f_{B^{\pm }}{f}_{K_{S,L}^0}$ decays and give the most promising processes to constraint the parameter $z$.

Comments: 32 pages,2 figures