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 Rényi entropy with Rényi order ( $α$ ) for the decay channels $B_s^0 \rightarrow φ\, φ$ , $B_d^0 \rightarrow J/ψ\, K^{*}(892)^0$ , $B_d^0 \rightarrow φ\, K^{*}(892)^0$ and $B_s^0 \rightarrow J/ψ\, φ$ and discuss the significance of entanglement entropy at different Rényi 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 Rényi 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.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 Rényi entropy with Rényi order ($α$) for the decay channels $B_s^0 \rightarrow φ\, φ$, $B_d^0 \rightarrow J/ψ\, K^{*}(892)^0$, $B_d^0 \rightarrow φ\, K^{*}(892)^0$ and $B_s^0 \rightarrow J/ψ\, φ$ and discuss the significance of entanglement entropy at different Rényi 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 Rényi 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.

hep-phCross-listedarXiv:2606.28034Jun 29, 20260 citations

Theory of Entanglement Entropy

Durrani, Ijaz

Jan 1, 20250 citations

Entanglement Entropy Distributions of a Muon Decay

Shanmuka Shivashankara

Divergences that occur in density matrices of decay and scattering processes are shown to be regularized by tracing and unitarity or the optical theorem.These divergences are regularized by the lifetime of the decaying particle or the total scattering cross section.Also, these regularizations are shown to give the expected helicities of final particles.As an illustration, the density matrix is derived for the weak decay of a polarized muon at rest, µ -→ ν µ (e -νe ), with Lorentz invariant density matrix entries and unitarity upheld at tree level.The electron's von Neumann entanglement entropy distributions are derived with respect to both the electron's emission angle and energy.The angular entropy distribution peaks for an electron emitted backward with respect to the muon's polarization given a minimum volume regularization larger than the cube of the muon's Compton wavelength.The kinematic entropy distribution is maximal at half the muon's rest mass energy.These results are similar to the electron's angular and kinematic decay rate distributions.Both the density matrix and entanglement entropy can be cast in terms of either ratios of areas or volumes.Divergences that occur in density matrices of decay and scattering processes are shown to be regularized by tracing and unitarity or the optical theorem.These divergences are regularized by the lifetime of the decaying particle or the total scattering cross section.Also, these regularizations are shown to give the expected helicities of final particles.As an illustration, the density matrix is derived for the weak decay of a polarized muon at rest, µ -→ ν µ (e -νe ), with Lorentz invariant density matrix entries and unitarity upheld at tree level.The electron's von Neumann entanglement entropy distributions are derived with respect to both the electron's emission angle and energy.The angular entropy distribution peaks for an electron emitted backward with respect to the muon's polarization given a minimum volume regularization larger than the cube of the muon's Compton wavelength.The kinematic entropy distribution is maximal at half the muon's rest mass energy.These results are similar to the electron's angular and kinematic decay rate distributions.Both the density matrix and entanglement entropy can be cast in terms of either ratios of areas or volumes.

arXiv:2312.05712Letters in High Energy PhysicsJan 1, 20242 citations

Entanglement entropy in the scattering process

Chao Zhang

Jan 1, 20200 citations

Parameter Inference from Final-State Entanglement in Higgs Decays

Jia Liu, Masanori Tanaka, Xiao-Ping Wang +2 more

The decay out-states of unstable Standard Model (SM) particles provide a unique, well-defined intrinsic quantum-information probe of the SM parameter space. We use Higgs decays as a test case: after tracing out kinematics, we compute entanglement among final-state spins and colors across all decay channels and impose a near-maximal entanglement-entropy criterion. This criterion yields quantitative indications for fundamental parameters. Within the SM, the entanglement entropy exhibits a global maximum close to the observed Higgs mass and the measured $W$ mass, the latter being equivalent to the $SU(2)_L$ gauge coupling. In a two-parameter kappa framework, applying the same criterion points to an SM-like balance between vector and fermion couplings, constraining the ratio of the sector-wide rescalings. These results suggest that entanglement extremality can serve as a complementary handle on fundamental parameters.The decay out-states of unstable Standard Model (SM) particles provide a unique, well-defined intrinsic quantum-information probe of the SM parameter space. We use Higgs decays as a test case: after tracing out kinematics, we compute entanglement among final-state spins and colors across all decay channels and impose a near-maximal entanglement-entropy criterion. This criterion yields quantitative indications for fundamental parameters. Within the SM, the entanglement entropy exhibits a global maximum close to the observed Higgs mass and the measured $W$ mass, the latter being equivalent to the $SU(2)_L$ gauge coupling. In a two-parameter kappa framework, applying the same criterion points to an SM-like balance between vector and fermion couplings, constraining the ratio of the sector-wide rescalings. These results suggest that entanglement extremality can serve as a complementary handle on fundamental parameters.

hep-phCross-listedarXiv:2511.17321Nov 24, 2025

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 Rényi entropy with Rényi order (

α

) for the decay channels

B_s^0 \rightarrow φ\, φ

B_d^0 \rightarrow J/ψ\, K^{*}(892)^0

B_d^0 \rightarrow φ\, K^{*}(892)^0

and

B_s^0 \rightarrow J/ψ\, φ

and discuss the significance of entanglement entropy at different Rényi 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 Rényi 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.

W

mass, the latter being equivalent to the

SU(2)_L

gauge coupling. In a two-parameter kappa framework, applying the same criterion points to an SM-like balance between vector and fermion couplings, constraining the ratio of the sector-wide rescalings. These results suggest that entanglement extremality can serve as a complementary handle on fundamental parameters.