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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 $B_{c}^{pm}rightarrow B^{pm} K_{S,L}^{0}$ decays. We find that some of the $B_c^{pm}rightarrow B^{pm} K_{S,L}^0rightarrow f_{B^{pm}} f_{K_{S,L}^0}$ 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 $B_c^{pm}rightarrow B^{pm} K_{S,L}^0$ 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 $Re(z)$ in the $B_c^{pm}rightarrow B^{pm} K_{S,L}^0rightarrow f_{B^{pm}} f_{K_{S,L}^0}$ decays and give the most promising processes to extract the parameter $Re(z)$. We find that the sensitivity for the measurement of parameter $Re(z)$ can reach below $10^{-3}$ in the most promising decays if we assume the selection efficiency is $10^{-3}$ and the total number of $B_c^{pm}$ events collected by the LHCb experiment is $10^{12}$ in the HL-LHC era.
We study charmless hadronic decays of charged $B$ mesons to the final states $K^{0}_{S}K^{0}_{S}K^{pm}$ and $K^{0}_{S}K^{0}_{S}pi^{pm}$ using a $711 fb^{-1}$ data sample that contains $772times 10^6$ $Bbar{B}$ pairs, and was collected at the $Upsilon
The first untagged decay-time-integrated amplitude analysis of $B^{0}_{s} rightarrow K^{0}_{textrm{S}} K^{pm}pi^{mp}$ decays is performed using a sample corresponding to $3.0,$fb$^{-1}$ of $pp$ collision data recorded with the LHCb detector during 20
Measurements of the effective lifetimes in the $B_{s}^{0} rightarrow K^{+}K^{-}$, $B^{0} rightarrow K^{+}pi^{-}$ and $B_{s}^{0} rightarrow pi^{+}K^{-}$ decays are presented using $1.0~mathrm{fb^{-1}}$ of $pp$ collision data collected at a centre-of-m
Using an $e^{+}e^{-}$ annihilation data sample corresponding to an integrated luminosity of $3.19~mathrm{fb}^{-1}$ and collected at a center-of-mass energy $sqrt{s} = 4.178~mathrm{GeV}$ with the BESIII detector, we measure the absolute branching frac
A search for charmless three-body decays of $B^0$ and $B_{s}^0$ mesons with a $K_{rm S}^0$ meson in the final state is performed using the $pp$ collision data, corresponding to an integrated luminosity of $1.0,mbox{fb}^{-1}$, collected at a centre-of