Measurement of the CP violating weak phase $\phi_s$ in the $\mathrm{B}^0_\mathrm{s}\to\mathrm{J}/\psi\phi \to \mu^{+}\mu^{-}\mathrm{K^+K^-}$ decay process using the data collected by CMS in proton-proton collision at $\sqrt{s} = 13\,\text{TeV}$

The invariance of the decay rate ( the amplitude square) of a decay process $|\mathcal{M}|^2(|{\psi_1}\rangle\to |{\psi_2}\rangle) $ under the simultaneous operation of discrete symmetry operators such as charge conjugation ($\hat{C}$), and parity ($\hat{P}$) is defined as the CP-symmetry i.e., $|\mathcal{M}|^2(|{\psi_1}\rangle\to |{\psi_2}\rangle) = |\bar{\mathcal{M}}|^2(|{\bar{\psi}_1}\rangle\to |{\bar{\psi}_2}\rangle) $. The violation of such invariance $|\mathcal{M}|^2 \neq |\bar{\mathcal{M}}|^2 $ is termed as the CP violation (CPV). In the high energy particle physics, the first CP violation was discovered at Brookhaven National Laboratory (1963); the current SM describes the appearance of CP violation in the Yukawa sector via flavor changing transitions of quarks ($q_i \to Wq_j$) as a complex phase in the Cabibbo-Kobayashi-Maskawa (CKM) matrix. Given that the value of the CP-violating phase predicted by the SM is very small, makes it too sensitive toward the new physics. In addition to this, baryogenesis (leptogenesis) can be probed through the window of CP-violation as postulated by Sakharov in 1967. This thesis describes the theory, and the details of the measurement procedure of the CP-violating weak phase using time dependent flavour tagged angular analysis in the $\mathrm{B_s^0\to J/\psi\phi}$ decay process. The total data correspond to an integrated luminosity of $96.4\,\text{fb}^{-1}$ is used, which is collected during 2017-2018 data taking period in proton-proton collisions at center of mass energy $\sqrt{s} = 13\, \text{TeV}$. This analysis makes the use of robust efficiency estimating algorithms, a DNN based flavour tagger by deploying a dedicated trigger, and an state-of-the-art model building technique toward the extraction of weak phase $\phi_s$ , decay width difference $\Delta\Gamma_s$ . The obtained results are $\phi_s = -11\pm 50\,\text{(stat)}\pm 10\,\text{(syst)}\, \text{mrad}$ and $\Delta\Gamma_s = 0.114 \pm 0.014\,\text{(stat)}\pm 0.007\,\text{(syst)}\, \text{ps}^{-1}$ which are extracted from 48500 reconstructed $\mathrm{B_s^0\to J/\psi\phi}$ events. Finally the $\sqrt{s} = 13\, \text{TeV}$ results are combined with the previous $8\,\text{TeV}$ results, and the combined results are : $\phi_s = -21\pm 44\,\text{(stat)}\pm 10\,\text{(syst)}\, \text{mrad}$, $\Delta\Gamma_s = 0.1032 \pm 0.0095\,\text{(stat)}\pm 0.0048\,\text{(syst)}\, \text{ps}^{-1}$. The overall improvement is significant when compared to the $8\,\text{TeV}$ result.