Measurement of the CP-violating phase $\phi_s$ in $B_s^0 \rightarrow J/\psi \left(\mu^+\mu^-\right) + \phi\left(K^+K^-\right)$ decays

The CP violating phase $\phi_s$ arises from the interference between the $B_s^0$ direct decays and decays with the $B_s^0 - \bar{B_s^0}$ mixing. The $\phi_s$ is defined as the weak phase difference between $B_s^0- \bar{B_s^0}$ mixing amplitude and $b \rightarrow c \bar{c} s$ decay amplitude and it is related to the CKM quark mixing matrix. Its theoretically predicted value is small in the Standard Model, $\phi_s = -0.0363^{+0.0016}_{-0.0015}$. Any measured deviations from this value can indicate New Physics not described in SM. The decay of $B_s^0 \rightarrow J/\psi (\mu^+ \mu^-) + \phi(K^+K^-)$ is considered to be one of the most sensitive channels for studying the NP. Next advantage of this channel is its high yield. A decay-time-dependent angular analysis determine not only $\phi_s$, but also the decay width difference and the average decay width of the $B_s^0$ mass eigenstates, $\Delta \Gamma_s$ and $\Gamma_s$. This contribution presents the $B_s^0 \rightarrow J/\psi (\mu^+ \mu^-) + \phi(K^+K^-)$ oscillation parameters using $80.5 ~\mathrm{fb^{-1}}$ collected by the ATLAS detector in $pp$ collisions at the energy $13 ~\mathrm{TeV}$ at the LHC.