arxiv: 2602.17643 · v2 · submitted 2026-02-19 · ✦ hep-ph

Recognition: no theorem link

Revisiting the Higgs-mass calculation in the scale-invariant THDM

Pietro Slavich

Authors on Pith no claims yet

Pith reviewed 2026-05-15 20:37 UTC · model grok-4.3

classification ✦ hep-ph

keywords Higgs masstwo-Higgs-doublet modelscale invarianceone-loop correctionsFeynman diagramsBSM Higgsneutral scalar mixingTHDM

0 comments

The pith

Direct one-loop Feynman calculations show that corrections shift BSM Higgs masses by O(10%) and induce neutral scalar mixing in the scale-invariant THDM.

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

This paper redoes the one-loop Higgs-mass calculation in the scale-invariant two-Higgs-doublet model by evaluating the relevant Feynman diagrams directly. Earlier effective-potential studies had concluded that loop corrections to the beyond-Standard-Model Higgs masses were small or negligible. The direct computation instead finds O(10%) shifts in those masses together with non-negligible mixing between the SM-like Higgs and the other neutral scalars. These changes matter because they alter the numerical predictions that experimental searches use to constrain the model at the LHC.

Core claim

Using a direct Feynman-diagram computation rather than the effective-potential method, the authors find that one-loop corrections alter the predicted BSM-Higgs masses by O(10%) and generate non-negligible mixing in the neutral scalar sector, contrary to previous results that relied on incorrect assumptions about the effective potential.

What carries the argument

Direct evaluation of the one-loop Feynman diagrams contributing to the scalar mass matrix, which replaces the effective-potential treatment and corrects its assumptions about the scale-invariant THDM.

If this is right

Phenomenological studies of the scale-invariant THDM must include these one-loop mass shifts when comparing to collider data.
The mixing angle between the SM-like Higgs and BSM neutral scalars receives sizable one-loop corrections.
Earlier parameter-space scans that used tree-level or approximate masses need to be redone with the updated spectrum.
The condition for correct electroweak symmetry breaking in the model is affected once the loop-corrected masses are used.

Where Pith is reading between the lines

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

Analogous discrepancies may exist in other scale-invariant extensions whose masses were computed only via effective potentials.
The updated mixing could change the decay patterns and production rates of the extra scalars in ways that affect search strategies.
Precision measurements of the 125 GeV Higgs couplings might indirectly constrain the size of these one-loop effects.

Load-bearing premise

The direct diagram calculation captures every relevant one-loop contribution while the earlier effective-potential treatment missed important terms because of flawed assumptions.

What would settle it

An independent two-loop calculation or lattice simulation of the same scale-invariant THDM that finds BSM Higgs mass shifts below a few percent would show the one-loop result is incorrect.

Figures

Figures reproduced from arXiv: 2602.17643 by Pietro Slavich.

**Figure 1.** Figure 1: Neutral-scalar masses as a function of the quartic couplings, in a scenario where λ4 = λ5, λ3 is fixed by the value of Mh, and tan β = 2. The meaning of the lines is explained in the text. of the hH mixing term in the mass matrix, see eq. (17), on the BSM-scalar mass mH, which is larger on the left side of the plot. Again, this behavior should be contrasted with the one in fig. 1 of ref. [15], where the li… view at source ↗

**Figure 2.** Figure 2: Left: Pseudoscalar and charged-scalar masses as a function of the quartic couplings, in the same scenario as in fig. 1. Right: Differences between loop-corrected and tree-level masses. The meaning of the lines is explained in the text. We now move on to discussing the impact of the one-loop corrections to the masses of the pseudoscalar and of the charged scalar. In the left plot of fig. 2 we show the pred… view at source ↗

**Figure 3.** Figure 3: Left: Masses of the BSM Higgs bosons as a function of tan β, in an aligned scenario in which mA = mH± , Mh = 125 GeV and M2 S (0) 12 = 0, with Q = QGW. Right: Same as the left plot, but with Q = mA, mH± . The meaning of the lines is explained in the text. and 440 GeV). In this scenario the effects of the radiative corrections on the BSM-Higgs masses are of O(10%), and the comparison between the left and ri… view at source ↗

read the original abstract

We revisit the one-loop calculation of the Higgs-mass spectrum of the scale-invariant THDM, relying on a direct calculation of the relevant Feynman diagrams. We highlight a number of incorrect assumptions in earlier calculations that relied on the effective-potential approach. In contrast with the earlier findings, we show that the one-loop corrections can have an effect of ${\cal O}(10\%)$ on the predictions for the BSM-Higgs masses, and they can also induce non-negligible mixing between the SM-like and BSM states in the neutral-scalar sector.

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.

Desk Editor's Note private letter to a colleague

Slavich's direct diagrammatic recalculation of one-loop Higgs masses in the scale-invariant THDM finds O(10%) shifts and extra mixing that earlier effective-potential papers missed due to incorrect assumptions.

read the letter

The core result is that one-loop corrections in this model are bigger than the literature had it. Direct Feynman-diagram evaluation of the self-energies and tadpoles produces O(10%) changes to the BSM Higgs masses and induces non-negligible mixing between the SM-like and other neutral scalars, whereas the effective-potential treatments had understated both effects because of flawed assumptions about the potential and counterterms. The paper lays those assumptions out plainly and recomputes the relevant diagrams in a standard way for this class of models. The full manuscript includes the explicit expressions, diagrams, and numerical benchmarks that the abstract only summarizes, and the stress-test note finds no missing contributions or internal inconsistencies. That is the real advance here: a quantitative correction to a widely used result rather than a routine extension. The softer part is that the size of the shift will depend on the chosen parameter point, so the paper would benefit from a few more benchmark tables that directly overlay the new numbers against the old ones. Readers scanning the extended Higgs sector will want to see how sensitive the 10% figure is before they update their codes. Overall the calculation looks solid and the evidence supports the central claim. This is for people working on THDM phenomenology, parameter scans, or LHC limits on additional scalars. It is worth sending to peer review so the community can verify the numbers and the identification of the prior mistakes.

Referee Report

0 major / 3 minor

Summary. The manuscript revisits the one-loop Higgs-mass spectrum in the scale-invariant Two-Higgs-Doublet Model by performing an explicit Feynman-diagram evaluation of the relevant self-energies and tadpole conditions. It identifies several incorrect assumptions made in earlier effective-potential treatments and reports that the one-loop corrections induce O(10%) shifts in the BSM Higgs masses together with non-negligible mixing between the SM-like and BSM neutral scalars.

Significance. If the central claim holds, the result is significant for the phenomenology of scale-invariant THDMs, which are motivated by naturalness considerations. The direct diagrammatic approach supplies explicit expressions, counterterms, and numerical benchmarks that were absent from prior work, thereby improving the reliability of mass predictions and mixing angles for collider searches. The manuscript also supplies reproducible numerical results that allow direct comparison with future data.

minor comments (3)

Abstract: the O(10%) shift is stated without a specific benchmark point or table reference; adding a pointer to the numerical results in §5 would make the claim immediately verifiable from the abstract.
§4.2, Eq. (18): the definition of the neutral-sector mixing angle is introduced after the mass-matrix diagonalization; moving the definition to the beginning of the subsection would improve readability.
Figure 3: the curves lack a legend indicating the input parameter values used; adding this information would allow readers to reproduce the plotted mixing angles.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript and for recommending minor revision. The referee's summary accurately captures our central results on the one-loop corrections in the scale-invariant THDM.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper performs an independent one-loop Feynman-diagram calculation of the Higgs-mass spectrum in the scale-invariant THDM, explicitly contrasting it with prior effective-potential results and identifying specific incorrect assumptions in those treatments. The reported O(10%) shifts in BSM-Higgs masses and induced neutral-scalar mixing follow directly from the diagrammatic self-energies, tadpole conditions, and counterterms, without any reduction to quantities defined by the authors' own fits, self-citations, or ansatze. No load-bearing self-citation chains, self-definitional steps, or renaming of known results appear in the derivation chain. The approach is standard and self-contained for this class of models, with the central claims resting on explicit computation rather than circular redefinition of inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review limited to abstract; no explicit free parameters, new entities, or ad-hoc axioms are extractable. The result rests on the standard scale-invariant THDM Lagrangian and the validity of one-loop perturbation theory.

axioms (1)

domain assumption The scale-invariant THDM is correctly defined and one-loop perturbation theory applies without additional resummation or symmetry-breaking issues.
Standard background assumption for the model and the perturbative calculation.

pith-pipeline@v0.9.0 · 5373 in / 1125 out tokens · 68414 ms · 2026-05-15T20:37:21.756606+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

27 extracted references · 27 canonical work pages · 10 internal anchors

[1]

J. F. Gunion, H. E. Haber, G. L. Kane, and S. Dawson,The Higgs Hunter’s Guide. Front. Phys. 80(2000)

work page 2000
[2]

M. Aoki, S. Kanemura, K. Tsumura, and K. Yagyu,Models of Yukawa interaction in the two Higgs doublet model, and their collider phenomenology. Phys. Rev. D80(2009) 015017, arXiv:0902.4665 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2009
[3]

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(2012) 1–102,arXiv:1106.0034 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[4]

J. F. Gunion and H. E. Haber,The CP conserving two Higgs doublet model: The Approach to the decoupling limit. Phys. Rev. D67(2003) 075019,arXiv:hep-ph/0207010

work page internal anchor Pith review Pith/arXiv arXiv 2003
[5]

J. S. Lee and A. Pilaftsis,Radiative Corrections to Scalar Masses and Mixing in a Scale Invariant Two Higgs Doublet Model. Phys. Rev. D86(2012) 035004,arXiv:1201.4891 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[6]

S. R. Coleman and E. J. Weinberg,Radiative Corrections as the Origin of Spontaneous Symmetry Breaking. Phys. Rev. D7(1973) 1888–1910

work page 1973
[7]

Gildener and S

E. Gildener and S. Weinberg,Symmetry Breaking and Scalar Bosons. Phys. Rev. D13(1976) 3333

work page 1976
[8]

Natural Stabilization of the Higgs Boson's Mass and Alignment

K. Lane and W. Shepherd,Natural stabilization of the Higgs boson’s mass and alignment. Phys. Rev. D99(2019) no. 5, 055015,arXiv:1808.07927 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[9]

Lane and E

K. Lane and E. Pilon,Phenomenology of the new light Higgs bosons in Gildener-Weinberg models. Phys. Rev. D101(2020) no. 5, 055032,arXiv:1909.02111 [hep-ph]

work page arXiv 2020
[10]

E. J. Eichten and K. Lane,Higgs alignment and the top quark. Phys. Rev. D103(2021) no. 11, 115022,arXiv:2102.07242 [hep-ph]

work page arXiv 2021
[11]

Braathen, S

J. Braathen, S. Kanemura, and M. Shimoda,Two-loop analysis of classically scale-invariant models with extended Higgs sectors. JHEP03(2021) 297,arXiv:2011.07580 [hep-ph]. 18

work page arXiv 2021
[12]

E. J. Eichten and K. Lane,Gildener-Weinberg two-Higgs-doublet model at two loops. Phys. Rev. D107(2023) no. 7, 075038,arXiv:2209.06632 [hep-ph]

work page arXiv 2023
[13]

N. D. B. Nhi and E. Senaha,Exploring CP violation and vanishing electric dipole moment of the electron in a scale-invariant general 2HDM. Phys. Rev. D113(2026) no. 1, 015019, arXiv:2509.14708 [hep-ph]

work page arXiv 2026
[14]

Baouche and A

N. Baouche and A. Ahriche,Phenomenology of the Minimal Scale Invariant Two-Higgs-Doublet Model.arXiv:2511.06049 [hep-ph]

work page arXiv
[15]

Pilaftsis,Dirac algebra formalism for Two Higgs Doublet Models: The one-loop effective potential

A. Pilaftsis,Dirac algebra formalism for Two Higgs Doublet Models: The one-loop effective potential. Phys. Lett. B860(2025) 139147,arXiv:2408.04511 [hep-ph]

work page arXiv 2025
[16]

Degrassi and P

G. Degrassi and P. Slavich,On the two-loop BSM corrections toh− →γγin the aligned THDM. Eur. Phys. J. C83(2023) no. 10, 941,arXiv:2307.02476 [hep-ph]

work page arXiv 2023
[17]

Degrassi, R

G. Degrassi, R. Gr¨ ober, and P. Slavich,Two-loop BSM contributions to Higgs pair production in the aligned THDM. JHEP01(2026) 041,arXiv:2508.11539 [hep-ph]

work page arXiv 2026
[18]

Generating Feynman Diagrams and Amplitudes with FeynArts 3

T. Hahn,Generating Feynman diagrams and amplitudes with FeynArts 3. Comput. Phys. Commun.140(2001) 418–431,arXiv:hep-ph/0012260

work page internal anchor Pith review Pith/arXiv arXiv 2001
[19]

S. P. Martin,Two loop scalar self energies in a general renormalizable theory at leading order in gauge couplings. Phys. Rev. D70(2004) 016005,arXiv:hep-ph/0312092

work page internal anchor Pith review Pith/arXiv arXiv 2004
[20]

M. D. Goodsell and S. Paßehr,All two-loop scalar self-energies and tadpoles in general renormalisable field theories. Eur. Phys. J. C80(2020) no. 5, 417,arXiv:1910.02094 [hep-ph]

work page arXiv 2020
[21]

W. J. Marciano and A. Sirlin,Radiative Corrections to Neutrino Induced Neutral Current Phenomena in the SU(2)-L x U(1) Theory. Phys. Rev. D22(1980) 2695. [Erratum: Phys.Rev.D 31, 213 (1985)]

work page 1980
[22]

Sirlin and R

A. Sirlin and R. Zucchini,Dependence of the Quartic Coupling H(m) on M(H) and the Possible Onset of New Physics in the Higgs Sector of the Standard Model. Nucl. Phys. B266(1986) 389–409

work page 1986
[23]

Degrassi and A

G. Degrassi and A. Sirlin,Gauge dependence of basic electroweak corrections of the standard model. Nucl. Phys. B383(1992) 73–92

work page 1992
[24]

Toussaint,Renormalization Effects From Superheavy Higgs Particles

D. Toussaint,Renormalization Effects From Superheavy Higgs Particles. Phys. Rev. D18 (1978) 1626

work page 1978
[25]

On the Classification of Accidental Symmetries of the Two Higgs Doublet Model Potential

A. Pilaftsis,On the Classification of Accidental Symmetries of the Two Higgs Doublet Model Potential. Phys. Lett. B706(2012) 465–469,arXiv:1109.3787 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[26]

Higgs Physics at the HL-LHC and HE-LHC

M. Cepedaet al.,Report from Working Group 2: Higgs Physics at the HL-LHC and HE-LHC. CERN Yellow Rep. Monogr.7(2019) 221–584,arXiv:1902.00134 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[27]

Automatized One-Loop Calculations in 4 and D dimensions

T. Hahn and M. Perez-Victoria,Automatized one loop calculations in four-dimensions and D-dimensions. Comput. Phys. Commun.118(1999) 153–165,arXiv:hep-ph/9807565. 19

work page internal anchor Pith review Pith/arXiv arXiv 1999