Quantum Correlations in the Decay of $B^0$ meson and Entanglement Entropy

We present a phenomenological study of quantum correlations in the decay of $B^0$ mesons into a system of two vector mesons. The decay of the $B^0$ meson into two vector mesons constitutes a bipartite system of two qutrits. The entanglement entropy is used as a measure of quantum correlations in the system of decaying particles. We study the variation of the R\'enyi entropy with R\'enyi order ($\alpha$) for the decay channels $B_s^0 \rightarrow \phi\, \phi$, $B_d^0 \rightarrow J/\psi\, K^{*}(892)^0$, $B_d^0 \rightarrow \phi\, K^{*}(892)^0$ and $B_s^0 \rightarrow J/\psi\, \phi$ and discuss the significance of entanglement entropy at different R\'enyi order regimes. The LHCb, ATLAS and Belle collaborations experimental measurements of complex polarization amplitudes and relative phases are used as input for our analysis. A comparison of entanglement entropy for all the $B^0$ meson decay processes, with both vanishing and non-vanishing phases, reveals a strong phase dependence of the entropy. We further present the results of Hartley entropy (Max-Entropy), von Neumann entropy, collision entropy, and min-entropy, each corresponding to different values and limits of the R\'enyi order. The comparison between the branching fractions of the decay processes and the von Neumann entropy shows a connection between entanglement and decay dynamics, indicating the role of weak and strong interaction in generating quantum entanglement. In addition, we evaluate several other entanglement measures, including linear entropy, I-concurrence, tangle, negativity, logarithmic negativity, Schmidt coefficients, and Schmidt rank for different $B^0$ meson decay processes. Our study demonstrates that entanglement measures provide useful insights into the underlying decay dynamics and may serve as important tools for understanding quantum correlations in high-energy particle physics processes.