Search for pentaquark state and measurement of CP violation with the LHCb detector

Testing the standard model (SM) of particle physics and searching for new physics beyond it, explaining the asymmetry between matter and antimatter in the universe is the frontier of particle physics researches. The LHCb experiment at the Large Hadron Collider (LHC) has collected a large number of proton-proton ($pp$) collision data at the TeV energy scale, provided the possibility for the relative frontier researches. Based on the advantages of $ J/\psi$ particle detection in this experiment,we searched the strangeness hidden-charm pentaquark state, which provides experimental support for the theoretical study of low-energy non-perturbative quantum chromodynamics. We also measured the charge conjugation and parity $CP$ destruction, which provides an experimental basis for the search for new physics outside the SM. The main work described in this dissertation is as follows: 1. We observed the $\Xi_b^-\to J/\psi\Lambda K^-$ decay for the first time by analysing a data sample corresponding to an integrated luminosity of 3 fb$^{-1}$ at 7 TeV and 8 TeV $pp$ collision energy (Run-I). Taking into account the effect of the relative fragmentation fraction between $\Lambda ^0_b$ and $\Xi_b^-$, the relative branching ratio of $\mathcal{B}(\Xi_b^-\to J/\psi\Lambda K^-) / \mathcal{B}(\Lambda ^0_b\to J/\psi\Lambda)$ is measured to be $0.0419\pm 0.0029(\mathrm{ stat.)}\pm0.0015(\mathrm{syst.})$. This decay channel is an ideal channel for searching the predicted $udsc\overline{c}$ pentaquark state. The mass difference between the $\Lambda ^0_b$ and $\Xi_b^-$ baryons is also determined, which is $M(\Xi_b^-)-M(\Lambda ^0_b)=177.08\pm0.47(\mathrm{stat})\pm0.16(\mathrm{syst})\ \mathrm{MeV}/c^{2}$. This measurement gives one of the best results on this parameter in the world. 2.We analysed two different $B^0_s$ decay channels containing $J/\psi$ final states that could be used in the searches of \textit{CP} violation. Using the LHC Run-I data, a measurement of \textit{CP}-violating phase $\phi_s$ is first time performed in the $m(K^+ K^-)$ higher than $\phi(1020)$ region of $B^0_s\to J/\psi K^+ K^-$ decay channel. $\phi_s$ is measured to be $0.119\pm0.107(\mathrm{stat})\pm0.034(\mathrm{syst})$ rad, which is consistent with result obtained in $B^0_s\to J/\psi\phi(1020)$ channel. As the $B^0_s$ production cross-section increases with the colliding energy, another data set of $B^0_s\ to J/\psi\pi^+\pi^-m$ decay channel corresponding to an integrated luminosity of 1.9 fb$^{-1}$ at 13 TeV $pp$ collision energy (Run-II) is used to measurement $\phi_s$, this results in $\phi_s=-0.057\pm0.060(\mathrm{stat})\pm0.011(\mathrm{syst})$ rad, which is consistent with Run-I result from the same decay channel. Both of the measurements are in line with the SM calculations of $\phi_s=-0.0368^{+0.0096}_{-0.0068}$ rad in one standard deviation.