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In a two-Higgs-doublet extension of the Standard Model, scalar Loryons—particles whose mass comes mostly from electroweak symmetry breaking—can survive only as neutral singlets up to about 700 GeV; any representation containing charged scal

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2026-08-03 09:15 UTC pith:77CE4H6E

load-bearing objection First systematic 2HDM-Loryon study with a plausible qualitative message, but the 700 GeV unitarity ceiling is optimistic because A/H± scattering channels are omitted. the 4 major comments →

arxiv 2601.14389 v3 pith:77CE4H6E submitted 2026-01-20 hep-ph

Constraints on Loryons in a Two Higgs Doublet Model

Can Kilic , Sanjay Mathai , Taewook Youn This is my paper
classification hep-ph
keywords Loryonstwo Higgs doublet modelperturbative unitarityHiggs diphoton ratecustodial symmetrynon-decoupling new physicsHEFTscalar Loryons
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper asks whether Loryons—particles that receive more than half of their mass from electroweak symmetry breaking—can remain viable once the Higgs sector is extended to a two-Higgs-doublet model. The authors calculate constraints from perturbative unitarity, precision electroweak data, and Higgs decay rates for the lowest scalar Loryon representations consistent with custodial symmetry. They find that a neutral singlet Loryon ([1,1]_0) can survive up to about 700 GeV, while any representation containing charged scalars is heavily restricted, with nearly all parameter space excluded when the EWSB mass fraction rises to 0.6. The result matters because it turns a broad class of non-decoupling new-physics models into a concrete, nearly minimal target: essentially only the neutral singlet survives, and future LHC measurements of the Higgs diphoton coupling could close most of what remains.

Core claim

For Loryons coupled to a two-Higgs-doublet sector, the paper establishes that the viable parameter space splits sharply by electric charge content. In the neutral singlet representation [1,1]_0, masses up to roughly 700 GeV are consistent with all constraints studied, at least for an EWSB mass fraction f_phi = 0.5. In representations containing charged scalars—the charged singlet [1,1]_1, the triplets [1,3]_0 and [3,1]_0, and the singlet-plus-triplet [2,2]_0—the same constraints, dominated by the Higgs diphoton rate kappa_gamma and by perturbative unitarity, cut the parameter space dramatically; at f_phi = 0.6 almost the entire region is excluded. The paper further shows that the extended sc

What carries the argument

The central objects are the custodial representations [L,R]_X of the global SU(2)_L × SU(2)_R symmetry, and the EWSB mass fraction f_V = λ_V v^2/2 / (M^2 + λ_V v^2/2) for each SU(2)_V multiplet. The key identity is the mass-squared decomposition m_V^2 = M^2 + λ_V v^2/2, where λ_V = A + B[C_2(L)+C_2(R)-C_2(V)], generalized to a 2HDM through coupling matrices A_ij and B_ij to the two Higgs doublets. This identity determines whether a state qualifies as a Loryon (f > 1/2), sets the strength of the Loryon-Higgs trilinear couplings c_h and c_H, and feeds directly into the enlarged partial-wave scattering matrices whose eigenvalues are bounded by unitarity and into the one-loop diphoton amplitude

Load-bearing premise

The quantitative bounds assume a single favorable 2HDM benchmark—heavy scalars at (m_H, m_H±, m_A) = (380, 450, 450) GeV at or near the alignment limit—chosen to maximize the Loryon parameter space; if the real 2HDM spectrum is heavier or the mixing angles differ, both the unitarity and diphoton constraints tighten and the 700 GeV ceiling shifts.

What would settle it

A future high-precision measurement of the Higgs diphoton rate that keeps kappa_gamma within the SM but with uncertainties below the width of the allowed charged-Loryon windows (roughly the current 2σ band 0.92–1.13, so about ±2%) would falsify the paper's claim that [1,1]_1 and [2,2]_0 Loryons remain viable at f≈0.5, since those windows rely on a delicate cancellation between the Loryon loop and the 2HDM charged-Higgs loop.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Neutral singlet scalar Loryons with mass below about 700 GeV remain a live, experimentally accessible target in a 2HDM.
  • Charged Loryons in the [1,1]_1, [1,3]_0/[3,1]_0, and the triplet of [2,2]_0 representations are confined to small EWSB mass fractions; at f = 0.6 they are almost entirely excluded.
  • Improved measurements of the Higgs diphoton coupling kappa_gamma can rule out all but the [1,1]_0 Loryon, because the allowed charged-Loryon windows are narrow and rely on cancellations with the 2HDM charged-Higgs loop.
  • The HEFT criterion f > 1/2 remains the operative definition of a Loryon in the 2HDM, so the surviving neutral region is precisely the regime where the low-energy description must be HEFT rather than SMEFT.
  • The bounds are benchmark-dependent: adopting heavier 2HDM scalars would tighten unitarity constraints and lower the 700 GeV mass ceiling.

Where Pith is reading between the lines

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

  • The paper's chosen 2HDM benchmark is intentionally favorable (light heavy scalars near the alignment limit), so the true surviving Loryon parameter space is likely smaller than the figures suggest; a full scan over the viable 2HDM region would probably lower the 700 GeV ceiling.
  • The near-total exclusion of charged Loryons implies that any future experimental hint of a charged scalar with a large EWSB mass fraction would point not to a 2HDM-plus-Loryon structure but to a different electroweak symmetry-breaking sector, such as a composite or strongly coupled one.
  • The methods used here—enlarged unitarity scattering bases and kappa_gamma constraints with 2HDM loop interference—could be applied directly to other non-decoupling BSM scalars, such as scalar leptoquarks or additional electroweak multiplets with sizable Higgs couplings.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper analyzes constraints on scalar Loryons—particles obtaining more than half of their mass from electroweak symmetry breaking—in a Two Higgs Doublet Model. It considers the custodial representations [1,1]_0, [1,1]_1, [1,3]_0/[3,1]_0, and [2,2]_0, and derives bounds from perturbative unitarity, the Higgs diphoton rate κγ, the S parameter, and absence of Loryon VEVs. Using a benchmark 2HDM spectrum (m_H,m_H±,m_A)=(380,450,450) GeV at or near the alignment limit, the paper concludes that neutral singlet Loryons remain viable up to about 700 GeV for f_ϕ=0.5, while representations with charged scalars are strongly constrained, especially for f_ϕ=0.6. The main new ingredient is the generalization of the single-Higgs Loryon analysis to the two-doublet scalar sector, including the HEFT condition and the modified unitarity and κγ constraints.

Significance. If the results hold, the paper gives the first systematic Loryon constraints in a 2HDM and identifies a sharp dichotomy: neutral singlet Loryons survive to the TeV-adjacent scale, while charged Loryons are nearly excluded at higher EWSB mass fractions. This is a useful extension of Ref. [1] and provides a concrete target for future Higgs measurements. The paper is transparent in its formalism: the Lagrangians are stated explicitly, the unitarity and κγ calculations follow standard methods, and the benchmark choice is clearly motivated by maximizing the Loryon parameter space. However, the quantitative claims rest on a unitarity truncation that is not fully justified and on two sign errors in the [2,2]_0 section; these need correction before the central conclusions can be considered solid.

major comments (4)
  1. [§3.3.1, Eqs. (3.15)–(3.18)] The statement that omitting the CP-odd and charged Higgs states 'does not introduce a loss of generality' is not justified. Under the diagonal SU(2)_V, h and H are singlets while A and H± form a triplet, and the benchmark (m_H,m_H±,m_A)=(380,450,450) is not custodially symmetric. Moreover, the Loryon Lagrangian in Eqs. (3.8)/(3.9) generates quartic vertices φφAA and φφH+H− through A22 and B22, which contribute to 2→2 amplitudes (e.g. φφ→AA, φA→φA) that are absent from the [a0] matrix in Eq. (3.15). These omitted channels can only increase the largest eigenvalue, so the 700 GeV ceiling for [1,1]_0 and the exclusion contours should be viewed as optimistic. Please include the A/H± block or quantitatively demonstrate its subdominance.
  2. [§3.5.1, Eq. (3.23)] The definition c^i_h = 1/2[C^i_+ sin(β−α) + C^i_− sin(β+α)] is inconsistent with the [1,1] expression in Eq. (3.17), c_h = 1/(2ρ)[C_+ sin(β−α) − C_− sin(α+β)]. Since sin(β+α)=sin(α+β), the relative sign of the C− term differs between the two sections. This sign enters the κγ constraint Eq. (3.27) and the unitarity matrix Eq. (3.26), changing the interference with the H± loop and the eigenvalue structure. Please correct and propagate the corrected sign through the [2,2]_0 results.
  3. [§3.5, Eq. (3.24)] The triplet combination C^1_± has the wrong sign for the B contribution. Using Eq. (3.10) with C2(2)=3/4 and C2(3)=2 gives λ_{V=1}=A+B(3/2−0)=A+3B/2 and λ_{V=3}=A+B(3/2−2)=A−B/2. Equation (3.24) instead writes C^1_±=(A11+1/2 B11)±(A22+1/2 B22), i.e. +B/2 rather than −B/2. This changes the triplet mass m_1^2 and the couplings c^1_h/H, and therefore the [2,2]_0 plots in Figs. 5–8. Please correct and rerun the numerical analysis.
  4. [§3.1 and App. B] Appendix B derives Eq. (B.15) for Loryons heavier than all 2HDM states, but Sec. 3.1 adopts this as 'a working definition of HEFT-relevant Loryons throughout this paper', and the last sentence of App. B concedes that the non-analyticity argument is invalid when the Loryon is lighter than the Higgs. Since the plots include masses below 125 GeV, the paper should explicitly state that for light masses the 'Loryon' designation is a convention rather than a derived EFT criterion, and explain whether any light-mass results depend on this classification.
minor comments (6)
  1. [Abstract] Typo: 'the the [1,1]' should be 'the [1,1]'.
  2. [§2.1 and §2.2] Typos: 'representaion' → 'representation'; 'cannonically' → 'canonically'.
  3. [Fig. 1 caption] Caption reads 'as a function of to the center-of-frame energy'; should be 'center-of-mass energy'.
  4. [§3.4] The claim that [1,3]_0 and [3,1]_0 have unitarity bounds identical to [1,1] would benefit from a short demonstration that the charged-state scattering block is equivalent under SU(2)_V, especially in light of the custodial truncation issue raised in the major comments.
  5. [§2.6, Eq. (2.25)] The κγ formula implicitly assumes no other BSM contributions to Higgs production/decay besides the loop states listed. It would be helpful to state explicitly that SM-like production is assumed and that the 2HDM effects on other Higgs couplings are negligible at the considered benchmark.
  6. [§3.3.1 after Eq. (3.18)] The sentence 'the couplings to H± and A are irrelevant to the constraints on Loryons that we consider' is too strong in the context of unitarity; it is true for the κγ constraint but not for the scattering matrix, as discussed above.

Circularity Check

0 steps flagged

No significant circularity: the central constraints are independent outputs, and the main caveats are benchmark/technical assumptions rather than circular reductions.

full rationale

I found no circular step that reduces the paper's claims to its inputs. The central constraints come from perturbative unitarity applied to explicit scattering matrices and from measured κ_γ values; the Loryon mass fractions f_ϕ are fixed input parameters scanned by hand, not outputs fitted to the constraints they are later tested against. The 700 GeV ceiling for the neutral [1,1]_0 Loryon is a genuine output of combining mass relations, fixed f, unitarity, and mass positivity. The HEFT criterion f > 1/2 is derived in Appendix B from a one-loop effective action in the heavy-Loryon regime, and although it is later adopted as a working definition, this is an extrapolation rather than an equation that presupposes the conclusion. The paper does not rely on self-citation by the current authors; the cited prior work on Loryons is by different authors and is used as background, not to forbid alternatives. I also considered the manuscript's own caveats: the benchmark 2HDM spectrum, the restriction to neutral h/H states in the [a0] matrix, and the assertion that quartic couplings never drive unitarity bounds. These are potential correctness risks or technical limitations, but none makes the derived constraints equivalent to their inputs. In particular, omitting A/H± scattering states may weaken the unitarity analysis, but that is an incompleteness, not a circular reduction; no fitted parameter is renamed as a prediction, and no load-bearing step is defined in terms of the claim it is supposed to establish.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 0 invented entities

The paper introduces no new particles; the scalar Loryons in [1,1]_X, [1,3]_0/[3,1]_0, and [2,2]_0 are adopted from Ref. [1] and recoupled to a 2HDM scalar sector. The central claims depend on hand-chosen inputs (f_phi, the 2HDM benchmark spectrum, mixing angles) and on standard model-building assumptions (custodial symmetry, Z2 symmetries, no Loryon VEVs). The HEFT criterion is extrapolated beyond its derivation, which is the most fragile entry.

free parameters (5)
  • f_phi (EWSB mass fraction) = 0.5 and 0.6; also f_0 = f_1 = 0.5 for [2,2]
    The central scan fixes the fraction of Loryon mass-squared from the Higgs VEVs to 0.5/0.6. This is a hand-chosen input, not an output of the constraints, and it directly sets the coupling/mass relation.
  • 2HDM benchmark masses (m_H, m_H±, m_A) = (380, 450, 450) GeV
    Chosen in Sec. 3 as a favorable benchmark 'maximizing the accessible parameter space for Loryons'. The 700 GeV bound is specific to this choice.
  • tanβ and cos(β−α) benchmark values = tanβ = 1, 1.7, 1.5; cos(β−α) = 0, 0.02, -0.1
    Benchmark points at or near the alignment limit; the shape of the exclusion regions rotates with these angles.
  • A_ij, B_ij (or C±, C_i±) couplings = scanned over the ranges shown in Figs. 3-8
    These are the free Loryon-Higgs couplings of the model. Their allowed regions are the output of the scan, but the parameterization itself is input.
  • Quartic Loryon self-coupling λ4 = positive (unspecified)
    Set positive by hand to ensure m_V^2 > 0 and no Loryon VEV. The paper states quartic self-couplings are not competitively constrained by unitarity.
axioms (6)
  • domain assumption Custodial SU(2)_L × SU(2)_R is a good symmetry of the Loryon sector; Loryons are assigned to complete representations [L,R]_X.
    Used throughout Secs. 2-3 to make the T-parameter vanish at one loop and to organize the multiplets.
  • domain assumption Approximate Z2 symmetry under which Loryons are odd and all SM/2HDM fields are even; it is broken only by higher-dimensional operators to allow decays.
    Used in Sec. 2.2 to forbid tree-level Loryon-Higgs mixing and runaway directions in the potential.
  • domain assumption 2HDM with an additional Z2' symmetry (m_12 = λ_6 = λ_7 = 0) to avoid FCNCs, and the analysis is restricted to the alignment limit region.
    Sec. 3 reduces the 2HDM scalar potential to the five-parameter input set and restricts to a benchmark compatible with collider data.
  • standard math Partial-wave unitarity bound max_{s in P,k} |Re a_k^0| ≤ 1/2, using the pole-avoiding region P from Ref. [28], is the criterion for perturbative unitarity.
    Sec. 2.4; the paper itself notes this is not a definitive proof of unitarity breakdown but a guide for where perturbation theory is valid.
  • ad hoc to paper The HEFT criterion of Eq. (B.15), derived for Loryons heavier than all 2HDM states, is adopted as the working definition of a Loryon for all masses.
    Appendix B explicitly states the non-analyticity condition is invalid when the Loryon is lighter than the Higgs, yet the definition is used throughout the paper.
  • domain assumption The Loryon scalar potential has no VEV, enforced by a positive quartic self-coupling and m_V^2 > 0.
    Secs. 3.4 and 3.5 assume the Loryons do not acquire vacuum expectation values, avoiding additional electroweak symmetry breaking.

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read the original abstract

We consider Loryons, particles beyond the Standard Model that receive a significant fraction of their masses from electroweak symmetry breaking, in the context of a two Higgs doublet model. Using scalar Loryons in the $[1,1]$, $[1,3]$ (as well as the equivalent $[3,1]$) and the $[2,2]$ representations of the custodial $SU(2)_L \times SU(2)_R$ global symmetry as benchmarks, we study the constraints on the Loryon parameter space, focusing on unitarity, Higgs decay observables, and the absence of Loryon vacuum expectation values. We find that while neutral singlet Loryons remain viable for masses up to 700 GeV, representations containing charged scalars are severely constrained by LHC data, particularly as the fraction of mass generated by symmetry breaking increases.

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