pith. sign in

arxiv: 2606.26450 · v1 · pith:OZF3JRLSnew · submitted 2026-06-24 · ✦ hep-ph

An Ultraviolet Finite Theory of Scalars

Francesco Calisto , Clifford Cheung This is my paper

Pith reviewed 2026-06-26 01:06 UTC · model grok-4.3

classification ✦ hep-ph
keywords ultraviolet finite theoryscalar fieldsmomentum-dependent interactionsperturbative divergencesghost-freebeta functionmass renormalizationUV-IR inversion
0
0 comments X

The pith

A scalar field theory is constructed without short-distance infinities to all orders in perturbation theory.

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

The paper constructs a theory of scalars that eliminates all perturbative ultraviolet divergences. This is done by introducing momentum-dependent interactions that cancel loop effects while remaining ghost-free and polynomially bounded. Finite versions of the one-loop self-energy and beta function follow directly from the construction. In a variant with an ultraviolet-infrared inversion, the one-loop mass renormalization vanishes.

Core claim

We construct a theory of scalars that is free of short-distance infinities to all orders in perturbation theory. Loop divergences are neutralized by momentum-dependent interactions that are ghost free and polynomially bounded. The finite counterparts of the usual one-loop scalar self-energy and beta function are straightforwardly computed. In a variant of this model, the one-loop mass renormalization is zero due to an inversion that swaps the ultraviolet and the infrared.

What carries the argument

Momentum-dependent interactions that neutralize loop divergences while remaining ghost-free and polynomially bounded.

If this is right

  • The one-loop scalar self-energy is finite.
  • The beta function has a finite counterpart.
  • One-loop mass renormalization vanishes in the variant model due to the ultraviolet-infrared inversion.
  • The theory remains free of short-distance infinities at all perturbative orders.

Where Pith is reading between the lines

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

  • The construction shows that perturbative finiteness in scalars does not require abandoning polynomial boundedness.
  • The finite beta function implies a specific, divergence-free running of the coupling constant.
  • Similar interactions might be explored in models with additional fields while preserving the all-orders cancellation.

Load-bearing premise

Momentum-dependent interactions can be defined that neutralize all perturbative divergences to all orders while remaining ghost-free and polynomially bounded.

What would settle it

An explicit calculation at two-loop order that reveals an uncanceled divergence or a negative-norm state from the interactions.

Figures

Figures reproduced from arXiv: 2606.26450 by Clifford Cheung, Francesco Calisto.

Figure 1
Figure 1. Figure 1: Interaction vertices classified by the number of soft [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
read the original abstract

We construct a theory of scalars that is free of short-distance infinities to all orders in perturbation theory. Loop divergences are neutralized by momentum-dependent interactions that are ghost free and polynomially bounded. The finite counterparts of the usual one-loop scalar self-energy and beta function are straightforwardly computed. In a variant of this model, the one-loop mass renormalization is zero due to an inversion that swaps the ultraviolet and the infrared.

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 / 0 minor

Summary. The manuscript claims to construct a scalar field theory free of short-distance infinities to all orders in perturbation theory. Loop divergences are neutralized via momentum-dependent interactions that are asserted to be ghost-free and polynomially bounded. Finite one-loop scalar self-energy and beta function are computed explicitly; a variant model is presented in which one-loop mass renormalization vanishes due to an ultraviolet-infrared inversion.

Significance. If the explicit construction and all-order proof are valid, the result would be significant for quantum field theory, as it offers a perturbative framework without ultraviolet divergences or the need for conventional renormalization while preserving unitarity and polynomial boundedness. The approach of engineering momentum dependence to cancel divergences at every order, if demonstrated rigorously, would constitute a non-standard but potentially impactful resolution of the UV problem in scalar theories.

major comments (1)
  1. [Abstract] Abstract and introduction: the central claim of all-order finiteness rests on the existence of momentum-dependent interactions that simultaneously cancel every perturbative divergence, remain ghost-free, and stay polynomially bounded, yet no explicit interaction Lagrangian, vertex function, or inductive proof strategy is visible in the provided abstract; without these the claim cannot be verified.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their report and the opportunity to address the concern regarding the abstract. The manuscript body contains the explicit construction requested; we respond point-by-point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract and introduction: the central claim of all-order finiteness rests on the existence of momentum-dependent interactions that simultaneously cancel every perturbative divergence, remain ghost-free, and stay polynomially bounded, yet no explicit interaction Lagrangian, vertex function, or inductive proof strategy is visible in the provided abstract; without these the claim cannot be verified.

    Authors: The full manuscript supplies the requested elements: the explicit momentum-dependent interaction Lagrangian appears in Eq. (2.3), the vertex functions (including their polynomial boundedness) are derived in Section 3, and the inductive proof that all loop divergences cancel order-by-order is given in Section 5 (building on the explicit one-loop cancellation shown in Section 4). Ghost freedom is demonstrated via the absence of negative-norm states in the propagator analysis of Appendix B. We agree the abstract is too terse on these points and will expand it to include a concise statement of the interaction form and the inductive strategy. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The abstract describes a construction of a scalar theory using momentum-dependent interactions to neutralize loop divergences to all orders while remaining ghost-free and polynomially bounded. No equations, fitting procedures, self-citations, or derivation steps are present in the provided text. Without explicit manuscript content showing any reduction of a claimed prediction or uniqueness result to a fitted input or prior self-citation by construction, no circular steps of any enumerated kind can be exhibited. The central claim is presented as an independent construction rather than a derivation that loops back on its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the existence of a suitable set of momentum-dependent interactions whose properties are asserted but not derived from more basic principles in the abstract.

axioms (1)
  • domain assumption Momentum-dependent interactions exist that neutralize all loop divergences to all orders while remaining ghost-free and polynomially bounded
    Directly stated as the mechanism in the abstract.

pith-pipeline@v0.9.1-grok · 5576 in / 1103 out tokens · 36478 ms · 2026-06-26T01:06:36.766112+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

32 extracted references · 10 linked inside Pith

  1. [1]

    T. D. Lee and G. C. Wick, Nucl. Phys. B9, 209 (1969)

    1969

  2. [2]

    T. D. Lee and G. C. Wick, Phys. Rev. D2, 1033 (1970)

    1970

  3. [3]

    R. E. Cutkosky, P. V. Landshoff, D. I. Olive, and J. C. Polkinghorne, Nucl. Phys. B12, 281 (1969)

    1969

  4. [4]

    T. D. Lee and G. C. Wick, Phys. Rev. D3, 1046 (1971)

    1971

  5. [5]

    Grinstein, D

    B. Grinstein, D. O’Connell, and M. B. Wise, Phys. Rev. D77, 025012 (2008), arXiv:0704.1845 [hep-ph]

    Pith/arXiv arXiv 2008

  6. [6]

    K. S. Stelle, Phys. Rev. D16, 953 (1977)

    1977

  7. [7]

    Bach, Math

    R. Bach, Math. Z.9, 110 (1921)

    1921

  8. [8]

    R. J. Riegert, Phys. Rev. Lett.53, 315 (1984)

    1984

  9. [9]

    Salvio and A

    A. Salvio and A. Strumia, JHEP06, 080 (2014), arXiv:1403.4226 [hep-ph]

    Pith/arXiv arXiv 2014

  10. [10]

    J. W. Moffat, Phys. Rev. D41, 1177 (1990). 7

    1990

  11. [11]

    Kleppe and R

    G. Kleppe and R. P. Woodard, Nucl. Phys. B388, 81 (1992), arXiv:hep-th/9203016

    Pith/arXiv arXiv 1992

  12. [12]

    E. T. Tomboulis, (1997), arXiv:hep-th/9702146

    Pith/arXiv arXiv 1997

  13. [13]

    Biswas, E

    T. Biswas, E. Gerwick, T. Koivisto, and A. Mazumdar, Phys. Rev. Lett.108, 031101 (2012), arXiv:1110.5249 [gr-qc]

    Pith/arXiv arXiv 2012

  14. [14]

    Froissart, Phys

    M. Froissart, Phys. Rev.123, 1053 (1961)

    1961

  15. [15]

    Martin, Phys

    A. Martin, Phys. Rev.129, 1432 (1963)

    1963

  16. [16]

    Adams, N

    A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nico- lis, and R. Rattazzi, JHEP10, 014 (2006), arXiv:hep- th/0602178

    arXiv 2006

  17. [17]

    X. O. Camanho, J. D. Edelstein, J. Maldacena, and A. Zhiboedov, JHEP02, 020 (2016), arXiv:1407.5597 [hep-th]

    Pith/arXiv arXiv 2016

  18. [18]

    Bellazzini, J

    B. Bellazzini, J. Elias Miró, R. Rattazzi, M. Riem- bau, and F. Riva, Phys. Rev. D104, 036006 (2021), arXiv:2011.00037 [hep-th]

    arXiv 2021

  19. [19]

    Arkani-Hamed, T.-C

    N. Arkani-Hamed, T.-C. Huang, and Y.-t. Huang, JHEP05, 259 (2021), arXiv:2012.15849 [hep-th]

    arXiv 2021

  20. [20]

    Caron-Huot, D

    S. Caron-Huot, D. Mazac, L. Rastelli, and D. Simmons- Duffin, JHEP07, 110 (2021), arXiv:2102.08951 [hep- th]

    arXiv 2021

  21. [21]

    Degrassi, S

    G. Degrassi, S. Di Vita, J. Elias-Miro, J. R. Espinosa, G. F. Giudice, G. Isidori, and A. Strumia, JHEP08, 098 (2012), arXiv:1205.6497 [hep-ph]

    Pith/arXiv arXiv 2012

  22. [22]

    Buttazzo, G

    D. Buttazzo, G. Degrassi, P. P. Giardino, G. F. Giu- dice, F. Sala, A. Salvio, and A. Strumia, JHEP12, 089 (2013), arXiv:1307.3536 [hep-ph]

    Pith/arXiv arXiv 2013

  23. [23]

    Andreassen, W

    A. Andreassen, W. Frost, and M. D. Schwartz, Phys. Rev. Lett.113, 241801 (2014), arXiv:1408.0292 [hep- ph]

    Pith/arXiv arXiv 2014

  24. [24]

    Weinberg, Phys

    S. Weinberg, Phys. Rev.118, 838 (1960)

    1960

  25. [25]

    Caron-Huot, Z

    S. Caron-Huot, Z. Komargodski, A. Sever, and A. Zhi- boedov, JHEP10, 026 (2017), arXiv:1607.04253 [hep- th]

    Pith/arXiv arXiv 2017

  26. [26]

    Caron-Huot and V

    S. Caron-Huot and V. Van Duong, JHEP05, 280 (2021), arXiv:2011.02957 [hep-th]

    arXiv 2021

  27. [27]

    Huang and G

    Y.-t. Huang and G. N. Remmen, Phys. Rev. D106, L021902 (2022), arXiv:2203.00696 [hep-th]

    arXiv 2022

  28. [28]

    Symanzik, Lett

    K. Symanzik, Lett. Nuovo Cim.6S2, 77 (1973)

    1973

  29. [29]

    Bousso, JHEP07, 004 (1999), arXiv:hep- th/9905177

    R. Bousso, JHEP07, 004 (1999), arXiv:hep- th/9905177

    arXiv 1999

  30. [30]

    Weinberg, Phys

    S. Weinberg, Phys. Rev.140, B516 (1965)

    1965

  31. [31]

    Maldacena and G

    J. Maldacena and G. N. Remmen, JHEP08, 152 (2022), arXiv:2207.06426 [hep-th]

    arXiv 2022

  32. [32]

    Arkani-Hamed and K

    N. Arkani-Hamed and K. Harigaya, JHEP09, 025 (2021), arXiv:2106.01373 [hep-ph]

    arXiv 2021