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arxiv: 2606.28034 · v1 · pith:GWZ7F7ULnew · submitted 2026-06-26 · ✦ hep-ph · hep-ex· hep-th· quant-ph

Quantum Correlations in the Decay of B⁰ meson and Entanglement Entropy

Divya Sharma , Vaibhav Rawoot , Sudip Kumar Haldar This is my paper

Pith reviewed 2026-06-29 03:50 UTC · model grok-4.3

classification ✦ hep-ph hep-exhep-thquant-ph
keywords B meson decayentanglement entropyRényi entropyquantum correlationsvector mesonspolarization amplitudesbranching fractions
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The pith

Entanglement entropy in B0 decays into vector meson pairs depends strongly on relative phases of polarization amplitudes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper models the decay of neutral B mesons into two vector mesons as a bipartite system of two qutrits and computes its entanglement entropy from experimental polarization amplitudes and phases. It tracks how Rényi entropy changes with order alpha across four specific channels and shows that the entropy shifts markedly when phases are present versus set to zero. The work also computes von Neumann entropy, min-entropy, and other measures, finding a correlation between the von Neumann value and the observed branching fractions. This correlation is presented as evidence that weak and strong interactions shape the generated quantum correlations.

Core claim

The final state of B0 to two-vector-meson decays forms a two-qutrit system whose density matrix is fixed by measured complex polarization amplitudes and relative phases; the Rényi entropies of this state, together with von Neumann, collision, and min-entropies, exhibit strong phase dependence and correlate with branching fractions, indicating the role of the underlying interactions in producing the observed quantum correlations.

What carries the argument

Rényi entropy of order alpha applied to the two-qutrit density matrix reconstructed from polarization amplitudes and relative phases.

If this is right

  • The von Neumann entropy tracks the branching fraction, connecting entanglement to the strength of weak and strong interactions.
  • Entropy values rise or fall sharply once nonzero relative phases are included.
  • Different decay channels produce measurably different entanglement levels.
  • Additional quantifiers such as negativity and I-concurrence give consistent diagnostics of the same correlations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The phase sensitivity could be checked against independent amplitude analyses from multiple experiments for internal consistency.
  • If the phases carry CP-violating information, the entropy might serve as an indirect probe of those phases.
  • Time-dependent versions of the same calculation could track how entanglement evolves inside the B meson before decay.

Load-bearing premise

The two-meson final state is a pure bipartite system whose quantum state is completely determined by the measured polarization amplitudes and relative phases.

What would settle it

A direct experimental extraction of Rényi entropy (or von Neumann entropy) from one of the four decay channels that deviates from the numerical value computed from the published amplitudes and phases.

Figures

Figures reproduced from arXiv: 2606.28034 by Divya Sharma, Sudip Kumar Haldar, Vaibhav Rawoot.

Figure 1
Figure 1. Figure 1: FIG. 1. (Color online) Behavior of the function [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (Color online) Plot of the R´enyi entropy as a function of R´enyi order ( [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (Color online) Plot of R´enyi entropy as a function of R´enyi order [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (Color online) R´enyi entropy as a function of R´enyi order ( [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (Color online) Plot of R´enyi entropy as a function of R´enyi order ( [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (Color online) Comparison of the variation of the R´enyi entropy for non-vanishing phases for all the decay process [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (Color online) Comparison of the variation of the R´enyi entropy for vanishing phases ( [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. (Color online) 2D plot of the phase dependence of the von Neumann entropy for all the processes of [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript performs a phenomenological study of quantum correlations in four B^0 (and Bs^0) decay channels to two vector mesons, treating each as a pure two-qutrit state constructed from measured helicity amplitudes and relative phases reported by LHCb, ATLAS, and Belle. Rényi entropies are evaluated as functions of the order α, with limits yielding Hartley, von Neumann, collision, and min-entropies; additional monotones (linear entropy, I-concurrence, tangle, negativity, logarithmic negativity, Schmidt coefficients, and Schmidt rank) are computed. Results are presented for both vanishing and non-vanishing phases, and von Neumann entropy values are compared with branching fractions to argue for a link between entanglement and the roles of weak and strong interactions in the decays.

Significance. The work supplies concrete numerical values of standard entanglement measures for experimentally accessible two-vector-meson final states. Because the two-qutrit state is fixed by the helicity amplitudes, the reported entropies are direct functions of published data; the phase-dependence plots and branching-fraction comparisons therefore constitute a re-expression of existing measurements rather than new dynamical predictions. The approach is technically sound within the helicity formalism but does not yet demonstrate that the entanglement quantities yield independent physical insight beyond what is already contained in the amplitude magnitudes and phases.

minor comments (3)
  1. [numerical results section] §3 (or wherever the numerical tables appear): the manuscript should tabulate the input amplitudes, phases, and their experimental uncertainties together with the resulting entropy values so that readers can reproduce the quoted numbers and assess error propagation.
  2. [discussion of branching fractions] The abstract and §4 claim a 'connection between entanglement and decay dynamics' on the basis of the branching-fraction comparison; this comparison is a direct numerical consequence of the amplitude normalizations and should be presented with the explicit functional relation rather than as an interpretive conclusion.
  3. [figures] Figure captions and axis labels for the Rényi-entropy plots should state the precise values of α used and whether the curves include experimental uncertainties.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript, the accurate summary, and the recommendation for minor revision. We address the principal concern expressed in the significance assessment below.

read point-by-point responses

  1. Referee: Because the two-qutrit state is fixed by the helicity amplitudes, the reported entropies are direct functions of published data; the phase-dependence plots and branching-fraction comparisons therefore constitute a re-expression of existing measurements rather than new dynamical predictions. The approach is technically sound within the helicity formalism but does not yet demonstrate that the entanglement quantities yield independent physical insight beyond what is already contained in the amplitude magnitudes and phases.

    Authors: We agree that the numerical values are obtained directly from published helicity amplitudes and phases. Nevertheless, the manuscript's contribution consists in the systematic computation of a suite of entanglement monotones (including the full Rényi family and its limits) and in the explicit demonstration that these quantities exhibit strong sensitivity to the relative phases and a clear correlation with measured branching fractions. This correlation is interpreted as reflecting the interplay between weak and strong dynamics in generating the observed interference. Such a quantum-information re-analysis is not present in the original experimental publications and supplies a new interpretive framework for the same data. To make this point more explicit we will add a short clarifying paragraph in the conclusions. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper constructs the two-qutrit state |ψ⟩ directly from external experimental helicity amplitudes and phases (LHCb/ATLAS/Belle data) and computes all listed entropies and monotones from the resulting reduced density matrix via standard definitions. No parameters are fitted to the target quantities, no predictions are made that reduce to the inputs by construction, and no load-bearing steps rely on self-citations or imported uniqueness theorems. The derivation is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The analysis rests on the assumption that the two-vector-meson final state is a pure bipartite qutrit system fully characterized by the measured amplitudes and phases; no new free parameters or postulated entities are introduced.

axioms (1)
  • domain assumption The decay of the B0 meson into two vector mesons constitutes a bipartite system of two qutrits.
    Explicitly stated in the abstract as the basis for applying entanglement entropy.

pith-pipeline@v0.9.1-grok · 5902 in / 1177 out tokens · 40302 ms · 2026-06-29T03:50:25.276699+00:00 · methodology

discussion (0)

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Reference graph

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