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arxiv: 2604.21332 · v1 · submitted 2026-04-23 · ✦ hep-ph · hep-th

Recognition: unknown

Disentangling new physics with quantum entanglement in tbar{t} production at future lepton colliders

Kentarou Mawatari, Masato Arai, Nobuchika Okada

Authors on Pith no claims yet

Pith reviewed 2026-05-09 22:00 UTC · model grok-4.3

classification ✦ hep-ph hep-th
keywords quantum entanglementtop-antitop productionnew physicslepton collidersspin correlationsBell inequalityextra dimensions
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The pith

Quantum entanglement in top-antitop pairs at future lepton colliders can reveal new physics from scalars, Z' bosons, and extra dimensions.

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

The paper calculates the degree of spin entanglement between top and antitop quarks produced at proposed lepton colliders such as the ILC and multi-TeV muon machines. In the Standard Model this entanglement comes from s-channel photon and Z exchange and produces measurable patterns. Adding new particles changes those patterns: a neutral scalar mediator usually lowers the entanglement, while a new gauge boson in the U(1)_{B-L} model or Kaluza-Klein gravitons in a Randall-Sundrum setup can produce sizable shifts in the relevant observables. The authors show that these shifts occur in regions of parameter space still allowed by current data, suggesting the observables could serve as new tools to search for physics beyond the Standard Model.

Core claim

In the Standard Model, top-antitop production at lepton colliders proceeds through s-channel gamma and Z exchange and exhibits a non-trivial amount of entanglement. When a neutral scalar mediator is added, the entanglement marker, concurrence, and maximal CHSH parameter are typically reduced relative to the Standard Model. In the minimal U(1)_{B-L} model and in Randall-Sundrum scenarios with massive Kaluza-Klein gravitons, sizable deviations appear for phenomenologically viable values of the new parameters. The authors therefore conclude that quantum-information observables can act as sensitive probes of new neutral interactions and extra-dimensional dynamics.

What carries the argument

The spin-density-matrix observables of the top-antitop system, quantified by the entanglement marker, concurrence, and the maximal Clauser-Horne-Shimony-Holt parameter, which are altered by additional s-channel contributions from new particles.

If this is right

  • Entanglement is reduced relative to the Standard Model expectation in the scalar-mediator scenario.
  • Sizable deviations appear in the U(1)_{B-L} and Randall-Sundrum cases for relevant parameter space.
  • The observables depend on center-of-mass energy, scattering angle, and model parameters and can be evaluated at future lepton colliders.
  • Quantum-information quantities therefore complement traditional searches for new resonances.

Where Pith is reading between the lines

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

  • Precise entanglement measurements could help distinguish which new-physics scenario is realized if a deviation is observed.
  • The same spin-correlation technique might be applied to other heavy-fermion pairs produced at colliders.
  • If the method works, it adds a quantum-information layer to beyond-Standard-Model searches that does not rely on resonance peaks.

Load-bearing premise

That the computed changes in entanglement and Bell parameters stay distinguishable from Standard Model backgrounds and from experimental uncertainties at the energies and luminosities of future lepton colliders.

What would settle it

A precision measurement of the concurrence or CHSH parameter in top-antitop events at the ILC that agrees with the Standard Model prediction within expected errors, even in the parameter regions where the new-physics models predict large deviations.

Figures

Figures reproduced from arXiv: 2604.21332 by Kentarou Mawatari, Masato Arai, Nobuchika Okada.

Figure 1
Figure 1. Figure 1: Orthonormal basis (ˆr, n, ˆ ˆk) in the tt¯ rest frame, defined with respect to the top-quark direction ˆk and beam direction ˆp. 2.2 Entanglement measures and Bell inequality To quantify bipartite entanglement between the two spin-1/2 systems, we use the concur￾rence C introduced by Wootters [48]. For a given two-qubit density matrix ρ, we define the spin-flipped density matrix as ρ˜ = (σy ⊗ σy) ρ ∗ (σy ⊗ … view at source ↗
Figure 2
Figure 2. Figure 2: This behavior originates from interference between the SM and the [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 2
Figure 2. Figure 2: Contours of the entanglement marker in the ( [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Angular dependence of the entanglement marker at fixed center-of-mass energies [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Contours of the concurrence in the (√ s, θ/π) plane. The panel assignments are the same as in [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Angular dependence of the concurrence at fixed center-of-mass energies. The [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Contours of the CHSH Bell parameter in the ( [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Angular dependence of the CHSH Bell parameter at fixed center-of-mass en [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
read the original abstract

We investigate quantum entanglement and Bell-inequality violation in top-antitop pair production at future lepton colliders such as the International Linear Collider (ILC) and multi-TeV muon colliders. Within the Standard Model (SM), the process proceeds through $s$-channel $\gamma$ and $Z$ exchange and exhibits characteristic spin-correlation patterns that encode a non-trivial amount of entanglement. We then examine how these features are modified in several well-motivated extensions of the SM:(i) a neutral scalar mediator that couples to charged leptons and top quarks via Yukawa interactions and contributes as an additional $s$-channel exchange; (ii) the minimal gauged $U(1)_{B-L}$ model, which introduces a new neutral gauge boson $Z'$ coupling vectorially to SM fermions; and (iii) a Randall-Sundrum scenario, in which the exchange of massive Kaluza-Klein gravitons arising from a warped extra dimension induces additional spin-dependent interactions. For all cases, we evaluate quantum-information observables, including the entanglement marker, the concurrence, and the maximal Clauser-Horne-Shimony-Holt parameter, and study their dependence on the center-of-mass energy, scattering angle, and model parameters. We find that, relative to the SM expectation, the entanglement is typically reduced in the scalar-mediator scenario, while sizable deviations can arise in the $U(1)_{B-L}$ and Randall-Sundrum cases for phenomenologically relevant regions of parameter space. These results demonstrate the potential of quantum-information observables as sensitive probes of new neutral interactions and extra-dimensional dynamics in future lepton colliders.

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

1 major / 2 minor

Summary. The paper investigates quantum entanglement and Bell-inequality violation in top-antitop pair production at future lepton colliders (ILC and multi-TeV muon colliders). Within the SM, the process proceeds via s-channel γ/Z exchange; the authors then compute the entanglement marker, concurrence, and maximal CHSH parameter in three BSM extensions—a neutral scalar mediator with Yukawa couplings, the minimal U(1)_{B-L} model with a Z' boson, and a Randall-Sundrum scenario with Kaluza-Klein gravitons—and map their dependence on center-of-mass energy, scattering angle, and model parameters. They report that entanglement is typically reduced relative to the SM in the scalar case while sizable deviations appear in the U(1)_{B-L} and RS cases for phenomenologically relevant parameter regions, arguing that these quantum-information observables can serve as sensitive probes of new neutral interactions and extra-dimensional dynamics.

Significance. If the reported deviations survive experimental effects, the work demonstrates a concrete application of quantum-information observables to distinguish BSM scenarios at lepton colliders, complementing conventional cross-section and spin-correlation analyses. The explicit evaluation across three distinct model classes and the focus on collider-relevant energies constitute a useful contribution to the growing literature on quantum correlations in high-energy processes.

major comments (1)
  1. The central phenomenological claim—that the computed shifts in concurrence, entanglement marker, and CHSH remain 'sizable' and 'distinguishable' at ILC/muon-collider luminosities—rests on parton-level spin-density-matrix calculations. No full simulation chain (e.g., including top decays, acceptance cuts, combinatorial backgrounds, or detector smearing) or quantitative estimate of dilution factors is presented, which directly undermines the assertion that these observables constitute practical probes.
minor comments (2)
  1. The dependence of the quantum observables on the scattering angle is discussed but would benefit from explicit plots or tables showing the angular regions where deviations are maximal for each BSM scenario.
  2. A brief comparison of the computational method (helicity amplitudes or density-matrix formalism) with existing SM spin-correlation literature would help readers assess the novelty of the SM baseline.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive summary and significance assessment of our manuscript. We address the single major comment below.

read point-by-point responses

  1. Referee: The central phenomenological claim—that the computed shifts in concurrence, entanglement marker, and CHSH remain 'sizable' and 'distinguishable' at ILC/muon-collider luminosities—rests on parton-level spin-density-matrix calculations. No full simulation chain (e.g., including top decays, acceptance cuts, combinatorial backgrounds, or detector smearing) or quantitative estimate of dilution factors is presented, which directly undermines the assertion that these observables constitute practical probes.

    Authors: We agree that the calculations are performed at the parton level and that a full experimental simulation chain is absent. The manuscript's goal is to isolate the theoretical impact of new physics on the quantum-information observables via the spin-density matrix, which is a standard first step for such studies. The abstract and conclusions frame the results as demonstrating the 'potential' of these observables rather than claiming immediate experimental readiness. In the revised manuscript we will add an explicit paragraph in the conclusions acknowledging that top decays, acceptance cuts, combinatorial backgrounds, and detector smearing will introduce dilution, and that quantitative dilution factors require a dedicated Monte Carlo study beyond the present scope. At the same time, the deviations we obtain in the U(1)_{B-L} and Randall-Sundrum scenarios reach 20-50% relative to the SM in phenomenologically allowed parameter regions; such magnitudes suggest that the effects could survive moderate dilution and therefore motivate the experimental work the referee correctly identifies as necessary. revision: partial

Circularity Check

0 steps flagged

No circularity in the computation of entanglement observables from production amplitudes

full rationale

The paper derives the quantum-information observables (entanglement marker, concurrence, CHSH parameter) by first computing the spin density matrix from the scattering amplitudes in the SM and the three BSM scenarios, then applying standard definitions of these measures to the resulting density matrix. This chain is self-contained and independent: the amplitudes follow from the Lagrangian terms of each model, and the entanglement quantities are fixed functions of the density matrix elements. No parameter is fitted to the target observables and then re-predicted, no self-citation provides a uniqueness theorem that forces the result, and no ansatz is smuggled in. The calculations are direct evaluations at parton level, making the derivation non-circular by construction.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The paper relies on standard quantum field theory for the Standard Model and three established beyond-Standard-Model scenarios. Free parameters are the masses and couplings of the new mediators in each model. No new entities are postulated by the authors themselves.

free parameters (3)
  • scalar mediator mass and Yukawa couplings
    Dependence on these parameters is studied in the first scenario.
  • Z' mass and vector couplings
    Dependence on these parameters is studied in the U(1)B-L model.
  • Kaluza-Klein graviton masses and couplings
    Dependence on these parameters is studied in the Randall-Sundrum scenario.
axioms (2)
  • standard math Validity of perturbative quantum field theory calculations for the listed processes
    Used for both SM and BSM contributions.
  • domain assumption Standard Model particle content and electroweak interactions as baseline
    Invoked when comparing to new physics effects.

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discussion (0)

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Reference graph

Works this paper leans on

59 extracted references · 58 canonical work pages · 3 internal anchors

  1. [1]

    J. S. Bell, Physics Physique Fizika1(1964), 195-200 doi:10.1103/PhysicsPhysiqueFizika.1.195

    work page doi:10.1103/physicsphysiquefizika.1.195 1964

  2. [2]

    Experimental R ealization of E instein- P odolsky- R osen- B ohm G edankenexperiment: A N ew V iolation of B ell's I nequalities

    A. Aspect, P. Grangier and G. Roger, Phys. Rev. Lett.49(1982), 91-97 doi:10.1103/PhysRevLett.49.91

    work page doi:10.1103/physrevlett.49.91 1982

  3. [3]

    Bloch, J

    I. Bloch, J. Dalibard and S. Nascimb` ene, Nature Phys.8(2012), 267-276 doi:10.1038/nphys2259

    work page doi:10.1038/nphys2259 2012

  4. [4]

    G. L. Kane, G. A. Ladinsky and C. P. Yuan, Phys. Rev. D45(1992), 124-141 doi:10.1103/PhysRevD.45.124

    work page doi:10.1103/physrevd.45.124 1992

  5. [5]

    Bernreuther and A

    W. Bernreuther and A. Brandenburg, Phys. Rev. D49(1994), 4481-4492 doi:10.1103/PhysRevD.49.4481 [arXiv:hep-ph/9312210 [hep-ph]]

    work page doi:10.1103/physrevd.49.4481 1994

  6. [6]

    S. J. Parke and Y. Shadmi, Phys. Lett. B387(1996), 199-206 doi:10.1016/0370- 2693(96)00998-7 [arXiv:hep-ph/9606419 [hep-ph]]. 20

    work page doi:10.1016/0370- 1996

  7. [7]

    Bernreuther, M

    W. Bernreuther, M. Flesch and P. Haberl, Phys. Rev. D58(1998), 114031 doi:10.1103/PhysRevD.58.114031 [arXiv:hep-ph/9709284 [hep-ph]]

    work page doi:10.1103/physrevd.58.114031 1998

  8. [8]

    Bernreuther, A

    W. Bernreuther, A. Brandenburg, Z. G. Si and P. Uwer, Nucl. Phys. B690(2004), 81-137 doi:10.1016/j.nuclphysb.2004.04.019 [arXiv:hep-ph/0403035 [hep-ph]]

    work page doi:10.1016/j.nuclphysb.2004.04.019 2004

  9. [9]

    Uwer, Phys

    P. Uwer, Phys. Lett. B609(2005), 271-276 doi:10.1016/j.physletb.2005.01.005 [arXiv:hep-ph/0412097 [hep-ph]]

    work page doi:10.1016/j.physletb.2005.01.005 2005

  10. [10]

    Baumgart and B

    M. Baumgart and B. Tweedie, JHEP03(2013), 117 doi:10.1007/JHEP03(2013)117 [arXiv:1212.4888 [hep-ph]]

    work page doi:10.1007/jhep03(2013)117 2013

  11. [11]

    Bernreuther, D

    W. Bernreuther, D. Heisler and Z. G. Si, JHEP12(2015), 026 doi:10.1007/JHEP12(2015)026 [arXiv:1508.05271 [hep-ph]]

    work page doi:10.1007/jhep12(2015)026 2015

  12. [12]

    Aaltonenet al.[CDF], Phys

    T. Aaltonenet al.[CDF], Phys. Rev. D83(2011), 031104 doi:10.1103/PhysRevD.83.031104 [arXiv:1012.3093 [hep-ex]]

    work page doi:10.1103/physrevd.83.031104 2011

  13. [13]

    V. M. Abazovet al.[D0], Phys. Rev. Lett.107(2011), 032001 doi:10.1103/PhysRevLett.107.032001 [arXiv:1104.5194 [hep-ex]]

    work page doi:10.1103/physrevlett.107.032001 2011

  14. [14]

    V. M. Abazovet al.[D0], Phys. Lett. B757(2016), 199-206 doi:10.1016/j.physletb.2016.03.053 [arXiv:1512.08818 [hep-ex]]

    work page doi:10.1016/j.physletb.2016.03.053 2016

  15. [15]

    Aadet al.[ATLAS], Phys

    G. Aadet al.[ATLAS], Phys. Rev. Lett.108(2012), 212001 doi:10.1103/PhysRevLett.108.212001 [arXiv:1203.4081 [hep-ex]]

    work page doi:10.1103/physrevlett.108.212001 2012

  16. [16]

    Chatrchyanet al.[CMS], Phys

    S. Chatrchyanet al.[CMS], Phys. Rev. Lett.112(2014) no.18, 182001 doi:10.1103/PhysRevLett.112.182001 [arXiv:1311.3924 [hep-ex]]

    work page doi:10.1103/physrevlett.112.182001 2014

  17. [17]

    Aadet al.[ATLAS], Phys

    G. Aadet al.[ATLAS], Phys. Rev. Lett.114(2015) no.14, 142001 doi:10.1103/PhysRevLett.114.142001 [arXiv:1412.4742 [hep-ex]]

    work page doi:10.1103/physrevlett.114.142001 2015

  18. [18]

    A. M. Sirunyanet al.[CMS], Phys. Rev. D100(2019) no.7, 072002 doi:10.1103/PhysRevD.100.072002 [arXiv:1907.03729 [hep-ex]]

    work page doi:10.1103/physrevd.100.072002 2019

  19. [19]

    Aaboudet al.[ATLAS], Eur

    M. Aaboudet al.[ATLAS], Eur. Phys. J. C80(2020) no.8, 754 doi:10.1140/epjc/s10052-020-8181-6 [arXiv:1903.07570 [hep-ex]]

    work page doi:10.1140/epjc/s10052-020-8181-6 2020

  20. [20]

    Afik and J

    Y. Afik and J. R. M. de Nova, Eur. Phys. J. Plus136(2021) no.9, 907 doi:10.1140/epjp/s13360-021-01902-1 [arXiv:2003.02280 [quant-ph]]

    work page doi:10.1140/epjp/s13360-021-01902-1 2021

  21. [21]

    Fabbrichesi, R

    M. Fabbrichesi, R. Floreanini and G. Panizzo, Phys. Rev. Lett.127(2021) no.16, 16 doi:10.1103/PhysRevLett.127.161801 [arXiv:2102.11883 [hep-ph]]

    work page doi:10.1103/physrevlett.127.161801 2021

  22. [22]

    Severi, C

    C. Severi, C. D. Boschi, F. Maltoni and M. Sioli, Eur. Phys. J. C82(2022) no.4, 285 doi:10.1140/epjc/s10052-022-10245-9 [arXiv:2110.10112 [hep-ph]]

    work page doi:10.1140/epjc/s10052-022-10245-9 2022

  23. [23]

    Afik and J

    Y. Afik and J. R. M. de Nova, Quantum6(2022), 820 doi:10.22331/q-2022-09-29-820 [arXiv:2203.05582 [quant-ph]]

    work page doi:10.22331/q-2022-09-29-820 2022

  24. [24]

    J. A. Aguilar-Saavedra and J. A. Casas, Eur. Phys. J. C82(2022) no.8, 666 doi:10.1140/epjc/s10052-022-10630-4 [arXiv:2205.00542 [hep-ph]]. 21

    work page doi:10.1140/epjc/s10052-022-10630-4 2022

  25. [25]

    Maltoni, C

    F. Maltoni, C. Severi, S. Tentori and E. Vryonidou, JHEP03(2024), 099 doi:10.1007/JHEP03(2024)099 [arXiv:2401.08751 [hep-ph]]

    work page doi:10.1007/jhep03(2024)099 2024

  26. [26]

    A. J. Barr, Phys. Lett. B825(2022), 136866 doi:10.1016/j.physletb.2021.136866 [arXiv:2106.01377 [hep-ph]]

    work page doi:10.1016/j.physletb.2021.136866 2022

  27. [27]

    Fabbrichesi, R

    M. Fabbrichesi, R. Floreanini, E. Gabrielli and L. Marzola, Eur. Phys. J. C83(2023) no.9, 823 doi:10.1140/epjc/s10052-023-11935-8 [arXiv:2302.00683 [hep-ph]]

    work page doi:10.1140/epjc/s10052-023-11935-8 2023

  28. [28]

    Aghaee Rad, T

    G. Aadet al.[ATLAS], Nature633(2024) no.8030, 542-547 doi:10.1038/s41586-024- 07824-z [arXiv:2311.07288 [hep-ex]]

    work page doi:10.1038/s41586-024- 2024

  29. [29]

    Hayrapetyanet al.[CMS], Phys

    A. Hayrapetyanet al.[CMS], Phys. Rev. D110, no.11, 112016 (2024) doi:10.1103/PhysRevD.110.112016 [arXiv:2409.11067 [hep-ex]]

    work page doi:10.1103/physrevd.110.112016 2024

  30. [30]

    Maltoni, C

    F. Maltoni, C. Severi, S. Tentori and E. Vryonidou, JHEP09(2024), 001 doi:10.1007/JHEP09(2024)001 [arXiv:2404.08049 [hep-ph]]

    work page doi:10.1007/jhep09(2024)001 2024

  31. [31]

    Ehat¨ aht, M

    K. Ehat¨ aht, M. Fabbrichesi, L. Marzola and C. Veelken, Phys. Rev. D109(2024) no.3, 032005 doi:10.1103/PhysRevD.109.032005 [arXiv:2311.17555 [hep-ph]]

    work page doi:10.1103/physrevd.109.032005 2024

  32. [32]

    T. Han, M. Low and Y. Su, JHEP10(2025), 217 doi:10.1007/JHEP10(2025)217 [arXiv:2501.04801 [hep-ph]]

    work page doi:10.1007/jhep10(2025)217 2025

  33. [33]

    B. Yang, Y. Zhang, Z. S. Wang and X. Zhou, [arXiv:2603.05846 [hep-ph]]

    work page arXiv

  34. [34]

    Cheng, T

    K. Cheng, T. Han and M. Low, Phys. Lett. B868(2025), 139675 doi:10.1016/j.physletb.2025.139675 [arXiv:2410.08303 [hep-ph]]

    work page doi:10.1016/j.physletb.2025.139675 2025

  35. [35]

    Automated computation of spin-density matrices and quantum observables for collider physics

    V. Durupt, F. Maltoni and O. Mattelaer, [arXiv:2510.17730 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv

  36. [36]

    M. M. Altakach, P. Lamba, F. Maltoni and K. Sakurai, [arXiv:2601.09558 [hep-ph]]

    work page arXiv

  37. [37]

    Cheng, T

    K. Cheng, T. Han and M. Low, Phys. Rev. D111(2025) no.3, 033004 doi:10.1103/PhysRevD.111.033004 [arXiv:2407.01672 [hep-ph]]

    work page doi:10.1103/physrevd.111.033004 2025

  38. [38]

    T. Han, M. Low, N. McGinnis and S. Su, JHEP05(2025), 081 doi:10.1007/JHEP05(2025)081 [arXiv:2412.21158 [hep-ph]]

    work page doi:10.1007/jhep05(2025)081 2025

  39. [39]

    H. W. Zhang, X. Cao and T. F. Feng, [arXiv:2602.10389 [hep-ph]]

    work page arXiv

  40. [40]

    Y. C. Guo, T. Han, M. Low and Y. Su, [arXiv:2602.02719 [hep-ph]]

    work page arXiv

  41. [41]

    R. N. Mohapatra and R. E. Marshak, Phys. Rev. Lett.44(1980), 1316-1319 [erratum: Phys. Rev. Lett.44(1980), 1643] doi:10.1103/PhysRevLett.44.1316

    work page doi:10.1103/physrevlett.44.1316 1980

  42. [42]

    R. E. Marshak and R. N. Mohapatra, Phys. Lett. B91(1980), 222-224 doi:10.1016/0370-2693(80)90436-0

    work page doi:10.1016/0370-2693(80)90436-0 1980

  43. [43]

    Wetterich, Nucl

    C. Wetterich, Nucl. Phys. B187(1981), 343-375 doi:10.1016/0550-3213(81)90279-0

    work page doi:10.1016/0550-3213(81)90279-0 1981

  44. [44]

    Masiero, J

    A. Masiero, J. F. Nieves and T. Yanagida, Phys. Lett. B116(1982), 11-15 doi:10.1016/0370-2693(82)90024-7 22

    work page doi:10.1016/0370-2693(82)90024-7 1982

  45. [45]

    R. N. Mohapatra and G. Senjanovic, Phys. Rev. D27(1983), 254 doi:10.1103/PhysRevD.27.254

    work page doi:10.1103/physrevd.27.254 1983

  46. [46]

    Buchmuller, C

    W. Buchmuller, C. Greub and P. Minkowski, Phys. Lett. B267(1991), 395-399 doi:10.1016/0370-2693(91)90952-M

    work page doi:10.1016/0370-2693(91)90952-m 1991

  47. [47]

    A Large Mass Hierarchy from a Small Extra Dimension

    L. Randall and R. Sundrum, Phys. Rev. Lett.83(1999), 3370-3373 doi:10.1103/PhysRevLett.83.3370 [arXiv:hep-ph/9905221 [hep-ph]]

    work page internal anchor Pith review doi:10.1103/physrevlett.83.3370 1999

  48. [48]

    W. K. Wootters, Phys. Rev. Lett.80(1998), 2245-2248 doi:10.1103/PhysRevLett.80.2245 [arXiv:quant-ph/9709029 [quant-ph]]

    work page doi:10.1103/physrevlett.80.2245 1998

  49. [49]

    J. F. Clauser, M. A. Horne, A. Shimony and R. A. Holt, Phys. Rev. Lett.23(1969), 880-884 doi:10.1103/PhysRevLett.23.880

    work page doi:10.1103/physrevlett.23.880 1969

  50. [50]

    J. S. Bell, Rev. Mod. Phys.38(1966), 447-452 doi:10.1103/RevModPhys.38.447

    work page doi:10.1103/revmodphys.38.447 1966

  51. [51]

    B. S. Cirelson, Lett. Math. Phys.4(1980), 93-100 doi:10.1007/BF00417500

    work page doi:10.1007/bf00417500 1980

  52. [52]

    Horodecki, P

    R. Horodecki, P. Horodecki and M. Horodecki, Phys. Lett. A200(1995) no.5, 340- 344 doi:10.1016/0375-9601(95)00214-N

    work page doi:10.1016/0375-9601(95)00214-n 1995

  53. [53]

    Davoudiasl, J

    H. Davoudiasl, J. L. Hewett and T. G. Rizzo, Phys. Rev. Lett.84(2000), 2080 doi:10.1103/PhysRevLett.84.2080 [arXiv:hep-ph/9909255 [hep-ph]]

    work page doi:10.1103/physrevlett.84.2080 2000

  54. [54]

    Davoudiasl, J

    H. Davoudiasl, J. L. Hewett and T. G. Rizzo, Phys. Rev. D63(2001), 075004 doi:10.1103/PhysRevD.63.075004 [arXiv:hep-ph/0006041 [hep-ph]]

    work page doi:10.1103/physrevd.63.075004 2001

  55. [55]

    Murayama, I

    H. Murayama, I. Watanabe and K. Hagiwara, KEK-91-11

  56. [56]

    Alwall, R

    J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, H. S. Shao, T. Stelzer, P. Torrielli and M. Zaro, JHEP07, 079 (2014) doi:10.1007/JHEP07(2014)079 [arXiv:1405.0301 [hep-ph]]

    work page doi:10.1007/jhep07(2014)079 2014

  57. [57]

    Artoisenet, P

    P. Artoisenet, P. de Aquino, F. Demartin, R. Frederix, S. Frixione, F. Maltoni, M. K. Mandal, P. Mathews, K. Mawatari and V. Ravindran,et al.JHEP11, 043 (2013) doi:10.1007/JHEP11(2013)043 [arXiv:1306.6464 [hep-ph]]

    work page doi:10.1007/jhep11(2013)043 2013

  58. [58]

    A. Das, P. S. B. Dev, Y. Hosotani and S. Mandal, Phys. Rev. D105, no.11, 115030 (2022) doi:10.1103/PhysRevD.105.115030 [arXiv:2104.10902 [hep-ph]]

    work page doi:10.1103/physrevd.105.115030 2022

  59. [59]

    Y. J. Fang, A. Bhoonah, K. Cheng, T. Han, Y. Liu and H. Zhang, [arXiv:2604.11887 [hep-ph]]. 23

    work page internal anchor Pith review Pith/arXiv arXiv