pith. sign in

arxiv: 2605.25015 · v3 · pith:LXMMXHFMnew · submitted 2026-05-24 · ✦ hep-ph · hep-ex· hep-th

Emerging Nonlocal K\"{a}ll\`{e}n-Lehmann Higgs Spectra at the LHC

Stathes Paganis This is my paper

Pith reviewed 2026-06-29 23:45 UTC · model grok-4.3

classification ✦ hep-ph hep-exhep-th
keywords nonlocal HiggsKällén-Lehmann spectral densityhierarchy problemLHC new physicselectroweak symmetry breakingnon-perturbative amplitudesmultiscalar interactions
0
0 comments X

The pith

Nonlocal Källén-Lehmann spectral densities in the Higgs sector suppress scattering amplitudes above a natural scale and suppress the self-energy at large spacelike momenta.

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

The paper argues that electroweak symmetry breaking can arise from emergent nonlocal spectral densities in the Higgs two-point function when Hamiltonians contain multiple interacting scalars. The nonlocality scale appears automatically once the number of mass eigenstates grows exponentially at high momenta. After the nonlocal propagator is renormalized, analytic non-perturbative amplitudes can be written down and are exponentially damped once the collision energy exceeds that scale. The same nonlocality also drives the real part of the Higgs self-energy to zero at deep spacelike momenta, removing the need for fine-tuning to protect the electroweak scale. These effects remain visible in current and future LHC data through combined fits to di-Higgs, diboson, and diphoton final states.

Core claim

Electroweak symmetry breaking may arise from emergent nonlocal Källén-Lehmann spectral densities in Hamiltonians with multiscalar interactions. The nonlocality scale Λ_NL emerges naturally from the exponentially increasing degeneracy of mass eigenstates in the Higgs two-point function at scales p² ≥ Λ²_NL. Following renormalization of the nonlocal Higgs propagator, analytic expressions for non-perturbative scattering amplitudes show exponential suppression for energies above Λ_NL. The real part of the Higgs self-energy is suppressed at p² ∼ −Λ²_NL, providing a solution to the hierarchy problem. Such nonlocal scalar sectors can be constrained at the LHC by a simultaneous global fit to exclusi

What carries the argument

The emergent nonlocal Källén-Lehmann spectral density of the Higgs two-point function, generated by exponential degeneracy of mass eigenstates in multiscalar Hamiltonians.

If this is right

  • Scattering amplitudes become exponentially suppressed once the center-of-mass energy exceeds the nonlocality scale.
  • The real part of the Higgs self-energy vanishes at momenta p² ∼ −Λ²_NL, eliminating quadratic divergences without additional symmetries.
  • The nonlocal effects remain testable at the LHC through simultaneous fits across di-Higgs, diboson, and diphoton channels.
  • Analytic expressions for non-perturbative amplitudes follow directly once the nonlocal propagator is renormalized.

Where Pith is reading between the lines

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

  • The same exponential degeneracy mechanism could appear in other scalar sectors if they also involve multiple interacting fields.
  • High-energy tails of differential distributions at the LHC would show the first deviations rather than sharp resonances.
  • If the degeneracy pattern proves universal across Hamiltonians, the nonlocality scale could be predicted without extra parameters.

Load-bearing premise

Exponential growth in the number of mass eigenstates at high momenta in any multiscalar Hamiltonian automatically produces a finite nonlocality scale.

What would settle it

A global fit to LHC di-Higgs, diboson, and diphoton data that finds no exponential damping of amplitudes or self-energy contributions above a few TeV would rule out the proposed suppression mechanism.

Figures

Figures reproduced from arXiv: 2605.25015 by Stathes Paganis.

Figure 1
Figure 1. Figure 1: FIG. 1. Tree-level Feynman diagrams for VBF di-Higgs pro [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Scalar di-photon resonance search at the LHC. Figure [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Projection of the nonlocality di-photon continuum [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Expected 95% CL cross-section limits for BSM ex [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
read the original abstract

Electroweak symmetry breaking may arise from emergent nonlocal K\"{a}ll\`{e}n-Lehmann spectral densities in Hamiltonians with multiscalar interactions. The nonlocality scale $\Lambda_{NL}$ emerges naturally from the exponentially increasing degeneracy of mass eigenstates in the Higgs two-point function at scales $p^2 \geq \Lambda^2_{NL}$. Following the renormalization of the nonlocal Higgs propagator, we provide a framework for deriving analytic expressions for non-perturbative scattering amplitudes. We demonstrate that for energies exceeding the nonlocality scale, scattering amplitudes are exponentially suppressed. Furthermore, the real part of the Higgs self-energy is suppressed at deep spacelike momenta ($p^2 \sim -\Lambda^2_{NL}$), offering a solution to the Hierarchy problem. Such nonlocal scalar sectors are accessible to current and future LHC runs. We argue that the nonlocal K\"{a}ll\`{e}n-Lehmann spectral density can be constrained through a simultaneous global fit of LHC measurements in exclusive channels, including di-Higgs, electroweak di-boson, and di-photon production. This approach represents a paradigm shift in the search for new physics at high-energy 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

2 major / 1 minor

Summary. The manuscript proposes that electroweak symmetry breaking arises from emergent nonlocal Källén-Lehmann spectral densities in Hamiltonians with multiscalar interactions. The nonlocality scale Λ_NL is asserted to emerge naturally from exponentially increasing degeneracy of mass eigenstates in the Higgs two-point function for p² ≥ Λ²_NL. Following renormalization of the nonlocal Higgs propagator, the paper outlines a framework for analytic non-perturbative scattering amplitudes that are exponentially suppressed above Λ_NL. It further claims that the real part of the Higgs self-energy is suppressed at deep spacelike momenta p² ∼ −Λ²_NL, providing a solution to the hierarchy problem, and argues that the spectral density can be constrained via global fits to LHC data in di-Higgs, electroweak di-boson, and di-photon channels.

Significance. If the emergence of the nonlocal spectral density from multiscalar Hamiltonians is rigorously demonstrated, the framework could offer a new approach to the hierarchy problem and motivate targeted LHC searches for nonlocal Higgs effects through global fits. The emphasis on analytic amplitudes and exponential suppression provides a potentially falsifiable signature distinct from conventional BSM models.

major comments (2)
  1. [Abstract] Abstract, first sentence: The central claim that Λ_NL 'emerges naturally from the exponentially increasing degeneracy of mass eigenstates in the Higgs two-point function at scales p² ≥ Λ²_NL' is load-bearing for the entire framework (renormalized propagator, analytic amplitudes, exponential suppression, and hierarchy solution), yet no explicit multiscalar Hamiltonian, mass matrix, or spectral density computation is supplied to establish the degeneracy or the resulting nonlocal Källén-Lehmann form.
  2. [Abstract] Abstract: The renormalization procedure for the nonlocal Higgs propagator and the derivation of analytic non-perturbative scattering amplitudes are invoked to support exponential suppression above Λ_NL and real-part self-energy suppression at p² ∼ −Λ²_NL, but these steps are not shown; without them the downstream claims cannot be assessed.
minor comments (1)
  1. The abstract states that nonlocal sectors 'are accessible to current and future LHC runs' and can be constrained by global fits, but does not identify concrete observables or background-subtraction strategies that would isolate the nonlocal spectral density from SM or other BSM contributions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment below and will make targeted revisions to improve clarity without altering the core claims.

read point-by-point responses

  1. Referee: [Abstract] Abstract, first sentence: The central claim that Λ_NL 'emerges naturally from the exponentially increasing degeneracy of mass eigenstates in the Higgs two-point function at scales p² ≥ Λ²_NL' is load-bearing for the entire framework (renormalized propagator, analytic amplitudes, exponential suppression, and hierarchy solution), yet no explicit multiscalar Hamiltonian, mass matrix, or spectral density computation is supplied to establish the degeneracy or the resulting nonlocal Källén-Lehmann form.

    Authors: The abstract summarizes the result; the explicit construction of the multiscalar Hamiltonian, the associated mass matrix, and the computation of the spectral density demonstrating the exponential degeneracy for p² ≥ Λ²_NL appear in Section 2 of the full manuscript. We will revise the abstract to include a one-sentence pointer to this derivation and add a short schematic of the mass-matrix structure to the introduction for immediate accessibility. revision: partial

  2. Referee: [Abstract] Abstract: The renormalization procedure for the nonlocal Higgs propagator and the derivation of analytic non-perturbative scattering amplitudes are invoked to support exponential suppression above Λ_NL and real-part self-energy suppression at p² ∼ −Λ²_NL, but these steps are not shown; without them the downstream claims cannot be assessed.

    Authors: The renormalization subtracts the divergent contribution in the Källén-Lehmann integral representation, yielding a finite nonlocal propagator; the analytic scattering amplitudes follow from contour integration of this propagator against the appropriate vertex kernels. These steps are carried out in Sections 3 and 4. We will append a concise outline of both procedures to the abstract and ensure the key integral expressions are displayed early in the revised text. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation chain not shown to reduce to inputs by construction

full rationale

The abstract asserts that Λ_NL emerges naturally from exponential degeneracy in unspecified multiscalar Hamiltonians and that the spectral density can be constrained by global fit to LHC data, with downstream claims of exponential suppression and hierarchy-problem solution following renormalization. No equations, explicit Hamiltonians, or self-citations are supplied in the provided text that would allow a quoted reduction (e.g., a fitted parameter renamed as a prediction or a self-referential definition). The fit is presented as a constraint method rather than the source of the emergence claim, and no load-bearing step is exhibited that collapses to its own inputs by construction. The paper's framework therefore remains self-contained against external benchmarks on the basis of the given material.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claim rests on the emergence of nonlocality from mass-eigenstate degeneracy in multiscalar Hamiltonians and on the subsequent renormalization procedure; these are postulated without independent evidence in the abstract.

free parameters (1)
  • Λ_NL
    Nonlocality scale introduced as emerging from degeneracy but to be constrained by global fit to data.
axioms (1)
  • domain assumption Electroweak symmetry breaking arises from emergent nonlocal Källén-Lehmann spectral densities in Hamiltonians with multiscalar interactions.
    Opening sentence of the abstract states this as the foundational premise.
invented entities (1)
  • nonlocal Källén-Lehmann spectral density no independent evidence
    purpose: To generate the nonlocality scale and produce exponential suppression in amplitudes and self-energy.
    Introduced as emergent from degeneracy but no independent evidence or falsifiable handle is supplied in the abstract.

pith-pipeline@v0.9.1-grok · 5749 in / 1534 out tokens · 41750 ms · 2026-06-29T23:45:59.137866+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

61 extracted references · 45 canonical work pages · 28 internal anchors

  1. [1]

    = Σ 0 h(p2)−Σ 0(N) h (p2) + + Σ0(N) h (p2)− N−1X n=0 δn(p2 −m 2 0) ! ,(27) where the subtraction polynomial is defined as: Σ0(N) h (p2) = Σ 0 h(m2

  2. [2]

    + dΣ0 h dp2 p2=m2 0 (p2 −m 2

  3. [3]

    + 1 (N−1)! d(N−1)Σ0 h dp2(N−1) p2=m2 0 (p2 −m 2 0)N−1

    +. . . + 1 (N−1)! d(N−1)Σ0 h dp2(N−1) p2=m2 0 (p2 −m 2 0)N−1 . Since we possess the freedom to add a polynomial of con- tact terms with arbitrary coefficientsδ n to the two-point function, the (N−1)-degree polynomial Σ 0(N) h (p2) can be canceled term-by-term. The resulting renormalized self-energy for a finite number of subtractionsNis: eΣh(p2;m 2

  4. [4]

    This damping ensures that the theory is renormalizable if the spectral densityρ(m 2) grows no faster than (m 2)N

    = Σ 0 h(p2)−Σ 0(N) h (p2) =− Z ∞ m2 th (p2 −m 2 0)N (m2 −m 2 0)N ρΣ m2 p2 −m 2 +iϵ dm2 =− Z ∞ m2 th g(p2) g(m2) ρΣ m2 p2 −m 2 +iϵ dm2,(28) whereg(m 2) = (m2 −m 2 0)N in the denominator acts as a damping function. This damping ensures that the theory is renormalizable if the spectral densityρ(m 2) grows no faster than (m 2)N. This effectively isolates the ...

    2000

  5. [5]

    Weinberg, Implications of Dynamical Symmetry Breaking, Phys

    S. Weinberg, Implications of Dynamical Symmetry Breaking, Phys. Rev. D13, 974 (1976), [Addendum: Phys. Rev. D 19, 1277–1280 (1979)]

    1976

  6. [6]

    The Hierarchy Problem and New Dimensions at a Millimeter

    N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, The Hierarchy problem and new dimensions at a millimeter, Phys. Lett. B429, 263 (1998), arXiv:hep-ph/9803315

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  7. [7]

    A Large Mass Hierarchy from a Small Extra Dimension

    L. Randall and R. Sundrum, A Large mass hierarchy from a small extra dimension, Phys. Rev. Lett.83, 3370 (1999), arXiv:hep-ph/9905221

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  8. [8]

    G. F. Giudice and M. McCullough, A Clockwork The- ory, Journal of High Energy Physics02, 036 (2017), arXiv:1610.07962 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  9. [9]

    Tasi 2009 lectures: The Higgs as a Composite Nambu-Goldstone Boson

    R. Contino, The Higgs as a Composite Nambu-Goldstone Boson, inTheoretical Advanced Study Institute in Ele- mentary Particle Physics: Physics of the Large and the Small(2011) pp. 235–306, arXiv:1005.4269 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  10. [10]

    Resummation of Massive Gravity

    C. de Rham, G. Gabadadze, and A. J. Tolley, Resum- mation of Massive Gravity, Phys. Rev. Lett.106, 231101 (2011), arXiv:1011.1232 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  11. [11]

    Massive Gravity

    C. de Rham, Massive Gravity, Living Rev. Rel.17, 7 (2014), arXiv:1401.4173 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  12. [12]

    Effective Field Theories from Soft Limits

    C. Cheung, K. Kampf, J. Novotny, and J. Trnka, Effective Field Theories from Soft Limits of Scatter- ing Amplitudes, Phys. Rev. Lett.114, 221602 (2015), arXiv:1412.4095 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  13. [13]

    Nortier, Extra Dimensions and Fuzzy Branes in String- inspired Nonlocal Field Theory, Acta Phys

    F. Nortier, Extra Dimensions and Fuzzy Branes in String- inspired Nonlocal Field Theory, Acta Phys. Polon. B54, 6 (2023), arXiv:2112.15592 [hep-th]

    work page arXiv 2023

  14. [14]

    Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM

    F. Cachazo, S. He, and E. Y. Yuan, Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM, Journal of High Energy Physics07, 149 (2015), arXiv:1412.3479 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  15. [15]

    A Hidden Symmetry of the Galileon

    K. Hinterbichler and A. Joyce, Hidden symmetry of the Galileon, Phys. Rev. D92, 023503 (2015), arXiv:1501.07600 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  16. [16]

    UV properties of Galileons: Spectral Densities

    L. Keltner and A. J. Tolley, UV properties of Galileons: Spectral Densities, arXiv e-prints , arXiv:1502.05706 (2015), arXiv:1502.05706 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  17. [17]

    Boos and C

    J. Boos and C. D. Carone, Asymptotic nonlocality, Phys. Rev. D104, 015028 (2021)

    2021

  18. [18]

    V. V. Khoze and M. Spannowsky, Higgsplosion: Solv- ing the hierarchy problem via rapid decays into mul- tiple Higgs bosons, Nucl. Phys. B926, 95 (2018), arXiv:1704.03447 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  19. [19]

    Kallen, Higher Approximations in the external field for the Problem of Vacuum Polarization, Helv

    G. Kallen, Higher Approximations in the external field for the Problem of Vacuum Polarization, Helv. Phys. Acta22, 637 (1949)

    1949

  20. [20]

    Lehmann, On the Properties of propagation functions and renormalization constants of quantized fields, Nuovo Cim.11, 342 (1954)

    H. Lehmann, On the Properties of propagation functions and renormalization constants of quantized fields, Nuovo Cim.11, 342 (1954). 10

    1954

  21. [21]

    Englert, G

    C. Englert, G. F. Giudice, A. Greljo, and M. McCullough, The ˆH-Parameter: An Oblique Higgs View, JHEP09, 041, arXiv:1903.07725 [hep-ph]

    work page arXiv 1903

  22. [22]

    Banks and M

    H. Banks and M. McCullough, Charting the Fifth Force Landscape, Phys. Rev. D103, 075018 (2021), arXiv:2009.12399 [hep-ph]

    work page arXiv 2021

  23. [23]

    E. T. Tomboulis, Superrenormalizable gauge and gravi- tational theories, (1997), arXiv:hep-th/9702146 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  24. [24]

    Super-renormalizable Quantum Gravity

    L. Modesto, Super-renormalizable Quantum Gravity, Phys. Rev. D86, 044005 (2012), arXiv:1107.2403 [hep- th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  25. [25]

    On the Stability of Infinite Derivative Abelian Higgs

    A. Ghoshal, A. Mazumdar, N. Okada, and D. Villalba, Stability of infinite derivative Abelian Higgs models, Phys. Rev. D97, 076011 (2018), arXiv:1709.09222 [hep- th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  26. [26]

    Ghost-free infinite derivative quantum field theory

    L. Buoninfante, G. Lambiase, and A. Mazumdar, Ghost- free infinite derivative quantum field theory, Nucl. Phys. B944, 114646 (2019), arXiv:1805.03559 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  27. [27]

    Ghoshal, A

    A. Ghoshal, A. Mazumdar, N. Okada, and D. Villalba, Nonlocal non-Abelian gauge theory: Conformal invari- ance andβ-function, Phys. Rev. D104, 015003 (2021), arXiv:2010.15919 [hep-ph]

    work page arXiv 2021

  28. [28]

    Nortier, Exorcizing Ghosts from the Vacuum Spectra in String-inspired Nonlocal Tachyon Condensation, Acta Phys

    F. Nortier, Exorcizing Ghosts from the Vacuum Spectra in String-inspired Nonlocal Tachyon Condensation, Acta Phys. Polon. B54, 9 (2023), arXiv:2307.11741 [hep-th]

    work page arXiv 2023

  29. [29]

    Chattopadhyay and F

    P. Chattopadhyay and F. Nortier, Ghost-free Elec- troweak Symmetry Breaking with Weakly Nonlocal Interactions, Acta Phys. Polon. B55, 8 (2024), arXiv:2311.08311 [hep-ph]

    work page arXiv 2024

  30. [30]

    J. A. Pinedo Soto,Modified Gravity and Regular Black Hole Models, Ph.D. thesis, Alberta U. (2025), arXiv:2511.12902 [gr-qc]

    work page arXiv 2025

  31. [31]

    Abu-Ajamieh and S

    F. Abu-Ajamieh and S. K. Vempati, A proposed renor- malization scheme for non-local QFTs and application to the hierarchy problem, Eur. Phys. J. C83, 1070 (2023), arXiv:2304.07965 [hep-th]

    work page arXiv 2023

  32. [32]

    Biswas and N

    T. Biswas and N. Okada, Towards lhc physics with nonlo- cal standard model, Nuclear Physics B898, 113 (2015)

    2015

  33. [33]

    Su, Y.-Y

    X.-F. Su, Y.-Y. Li, R. Nicolaidou, M. Chen, H.-Y. Wu, and S. Paganis, HighP T Higgs excess as a signal of non- local QFT at the LHC, Eur. Phys. J. C81, 796 (2021), arXiv:2108.10524 [hep-ph]

    work page arXiv 2021

  34. [34]

    A. M. Sirunyanet al.(CMS), Search for physics beyond the standard model in high-mass diphoton events from proton-proton collisions at √s= 13 TeV, Phys. Rev. D 98, 092001 (2018), arXiv:1809.00327 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  35. [35]

    Tumasyanet al.(CMS), Search for high-mass reso- nances decaying to a jet and a Lorentz-boosted resonance in proton-proton collisions at s=13TeV, Phys

    A. Tumasyanet al.(CMS), Search for high-mass reso- nances decaying to a jet and a Lorentz-boosted resonance in proton-proton collisions at s=13TeV, Phys. Lett. B 832, 137263 (2022), arXiv:2201.02140 [hep-ex]

    work page arXiv 2022

  36. [36]

    E. T. Tomboulis, Nonlocal and quasilocal field theories, Phys. Rev. D92, 125037 (2015), arXiv:1507.00981 [hep- th]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  37. [37]

    Buoninfante, Contour prescriptions in string-inspired nonlocal field theories, Phys

    L. Buoninfante, Contour prescriptions in string-inspired nonlocal field theories, Phys. Rev. D106, 126028 (2022)

    2022

  38. [38]

    Matrix Description of M-theory on $T^4$ and $T^5$

    M. Berkooz, M. Rozali, and N. Seiberg, Matrix descrip- tion of M theory on T**4 and T**5, Phys. Lett. B408, 105 (1997), arXiv:hep-th/9704089

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  39. [39]

    Matrix Description of M-theory on $T^5$ and $T^5/Z_2$

    N. Seiberg, New theories in six-dimensions and matrix description of M theory on T**5 and T**5 / Z(2), Phys. Lett. B408, 98 (1997), arXiv:hep-th/9705221

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  40. [40]

    Note on the Quantum Mechanics of M Theory

    O. Aharony and T. Banks, Note on the quantum me- chanics of M theory, Journal of High Energy Physics03, 016 (1999), arXiv:hep-th/9812237

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  41. [41]

    A. W. Peet and J. Polchinski, UV / IR relations in AdS dynamics, Phys. Rev. D59, 065011 (1999), arXiv:hep- th/9809022

    work page arXiv 1999

  42. [42]

    Comments on the IIA NS5-brane

    S. Minwalla and N. Seiberg, Comments on the IIA (NS)five-brane, Journal of High Energy Physics06, 007 (1999), arXiv:hep-th/9904142

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  43. [43]

    A brief Introduction to Dispersion Relations and Analyticity

    R. Zwicky, A brief Introduction to Dispersion Relations and Analyticity, inQuantum Field Theory at the Limits: from Strong Fields to Heavy Quarks(2017) pp. 93–120, arXiv:1610.06090 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  44. [44]

    Paganis, Heavy Particle Towers and Nonlocal QFT, (2024), arXiv:2404.09159 [hep-ph]

    S. Paganis, Heavy Particle Towers and Nonlocal QFT, (2024), arXiv:2404.09159 [hep-ph]

    work page arXiv 2024

  45. [45]

    Briscese, G

    F. Briscese, G. Calcagni, L. Modesto, and G. Nardelli, Form factors, spectral and K¨ all´ en-Lehmann represen- tation in nonlocal quantum gravity, JHEP08, 204, arXiv:2405.14056 [hep-th]

    work page arXiv

  46. [46]

    P. G. O. Freund and E. Witten, Adelic String Ampli- tudes, Phys. Lett. B199, 191 (1987)

    1987

  47. [47]

    Brekke, P

    L. Brekke, P. G. O. Freund, M. Olson, and E. Witten, Non-Archimedean String Dynamics, Nucl. Phys. B302, 365 (1988)

    1988

  48. [48]

    Ostrowski, ¨Uber einige L¨ osungen der Funktionalgle- ichungϕ(x)·ϕ(y) =ϕ(xy), Acta Mathematica41, 271 (1916)

    A. Ostrowski, ¨Uber einige L¨ osungen der Funktionalgle- ichungϕ(x)·ϕ(y) =ϕ(xy), Acta Mathematica41, 271 (1916)

    1916

  49. [49]

    Koblitz,p-adic Numbers, p-adic Analysis, and Zeta- Functions, 2nd ed., Graduate Texts in Mathematics, Vol

    N. Koblitz,p-adic Numbers, p-adic Analysis, and Zeta- Functions, 2nd ed., Graduate Texts in Mathematics, Vol. 58 (Springer-Verlag, 1984)

    1984

  50. [50]

    Hayrapetyanet al.(CMS), Search for new physics in high-mass diphoton events from proton-proton collisions at √s = 13 TeV, JHEP08, 215, arXiv:2405.09320 [hep- ex]

    A. Hayrapetyanet al.(CMS), Search for new physics in high-mass diphoton events from proton-proton collisions at √s = 13 TeV, JHEP08, 215, arXiv:2405.09320 [hep- ex]

    work page arXiv

  51. [51]

    G. Aadet al.(ATLAS), Search for periodic signals in the dielectron and diphoton invariant mass spectra using 139 fb−1 of pp collisions at √s= 13 TeV with the ATLAS detector, Journal of High Energy Physics10, 079 (2023), arXiv:2305.10894 [hep-ex]

    work page arXiv 2023

  52. [52]

    Y.-Y. Li, R. Nicolaidou, and S. Paganis, Exclusion of heavy, broad resonances from precise measurements of W ZandV Hfinal states at the LHC, Eur. Phys. J. C 79, 348 (2019), arXiv:1904.03995 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  53. [53]

    Probing Compositeness with Higgs Boson Decays at the LHC

    M. Hoffmann, A. Kaminska, R. Nicolaidou, and S. Pa- ganis, Probing Compositeness with Higgs Boson De- cays at the LHC, Eur. Phys. J. C74, 3181 (2014), arXiv:1407.8000 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  54. [54]

    G. C. Branco, P. M. Ferreira, L. Lavoura, M. N. Rebelo, M. Sher, and J. P. Silva, Theory and phenomenology of two-Higgs-doublet models, Phys. Rept.516, 1 (2012), arXiv:1106.0034 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  55. [55]

    M. R. Anderson and C. D. Carone, Dijet spectrum in nonlocal and asymptotically nonlocal theories, Phys. Rev. D110, 055018 (2024), arXiv:2406.12073 [hep-ph]

    work page arXiv 2024

  56. [56]

    C. D. Carone and M. R. Musser, Note on scattering in asymptotically nonlocal theories, Phys. Rev. D108, 095015 (2023), arXiv:2308.11051 [hep-th]

    work page arXiv 2023

  57. [57]

    Higgs pair production in vector-boson fusion at the LHC and beyond

    F. Bishara, R. Contino, and J. Rojo, Higgs pair produc- tion in vector-boson fusion at the LHC and beyond, Eur. Phys. J. C77, 481 (2017), arXiv:1611.03860 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  58. [58]

    Wang (ATLAS), Search for new resonances in high- mass diphoton final states using proton-proton colli- sion data collected with the ATLAS detector, PoS ICHEP2020, 109 (2021)

    Y. Wang (ATLAS), Search for new resonances in high- mass diphoton final states using proton-proton colli- sion data collected with the ATLAS detector, PoS ICHEP2020, 109 (2021). 11

    2021

  59. [59]

    Asymptotic formulae for likelihood-based tests of new physics

    G. Cowan, K. Cranmer, E. Gross, and O. Vitells, Asymp- totic formulae for likelihood-based tests of new physics, Eur. Phys. J. C71, 1554 (2011), [Erratum: Eur.Phys.J.C 72, 2123 (2012)], arXiv:1007.1727 [physics.data-an]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  60. [60]

    Paganis and D

    S. Paganis and D. R. Tovey, Background and signal es- timation for a low mass Higgs Boson at the LHC, Eur. Phys. J. C56, 21 (2008)

    2008

  61. [61]

    V. V. Khoze and M. Spannowsky, Consistency of Hig- gsplosion in Localizable QFT, Phys. Lett. B790, 466 (2019), arXiv:1809.11141 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2019