The new physics (NP) is parametrized with four model-independent quantities: the magnitudes and phases of the dispersive part $M_{12}$ and the absorptive part $\Gamma_{12}$ of the NP contribution to the effective Hamiltonian. We constrain these parameters using the four observables $\Delta M_{\text{s}}$, $\Delta \Gamma_{\text{s}}$, the mixing phase $\beta_{\text{s}}^{J/\psi \phi}$ and $A_{\text{sl}}^{b}$. This formalism is extended to include charge-parity-time reversal (CPT) violation, and it is shown that CPT violation by itself, or even in the presence of CPTconserving NP without an absorptive part, helps only marginally in the simultaneous resolution of these anomalies.