Quantum decoherence signatures in charmless non-leptonic $B$ decays

Quantum coherence plays a crucial role in the dynamics of neutral meson systems, aiding in the extraction of various Standard Model parameters. However, real physical systems always interact with their surroundings, which causes decoherence. In case of time dependent analysis of non-leptonic neutral $B$ meson decays, this decoherence can be modeled using a single parameter, $\lambda$. Since decoherence can affect the observed dynamics of flavor oscillations and CP violation, it becomes essential to revisit the key SM parameters such as the CKM angles $(\alpha, \beta, \gamma)$ and the mass differences of neutral $B$ mesons ($\Delta m_{d,s}$). In this work, we study the CKM phase $\beta$ as well as the penguin contributions in the $B_d^0 \to J/\psi K_S$ decay mode in the presence of decoherence. We employ the pseudo-experiment (Toy Monte-Carlo) technique and perform an $SU(3)_F$ analysis using the $B_d^0 \to J/\psi \pi^0$ process. Furthermore, we investigate the $B_d^0 \to \pi^+ \pi^-$ decay mode to understand how the decoherence influences the CP violating observables. Our findings reveal that the presence of decoherence can affect crucially the measured values of the observables.