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arxiv: 2604.13922 · v1 · submitted 2026-04-15 · ✦ hep-ph

Refining two-loop corrections to trilinear Higgs couplings in the Two-Higgs-Doublet Model

Johannes Braathen , Felix Egle , Alain Verduras Schaeidt This is my paper

Pith reviewed 2026-05-10 13:31 UTC · model grok-4.3

classification ✦ hep-ph
keywords Two-Higgs-Doublet Modeltrilinear Higgs couplingstwo-loop correctionsHiggs pair productionalignment limitrenormalization
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The pith

Leading two-loop corrections to trilinear Higgs couplings are calculated in the Two-Higgs-Doublet Model.

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

The paper computes the leading two-loop corrections to the trilinear Higgs self-couplings in the Two-Higgs-Doublet Model. These couplings control the strength of interactions among Higgs bosons and are essential for predicting how often pairs of Higgs bosons are produced in particle collisions. The authors concentrate on the couplings that involve the lightest Higgs boson, both with itself and with a heavier Higgs boson. They also sort out the renormalization procedure when the model sits in the alignment limit, where its behavior approaches that of the Standard Model. The results are then used to update differential distributions for di-Higgs production at current and future colliders.

Core claim

The authors present new results for the leading two-loop corrections to the trilinear couplings λ_hhh and λ_hhH in the 2HDM. They renormalize the alignment limit in the Higgs basis and examine technical aspects of the calculation. The results show the phenomenological impact on differential distributions in di-Higgs production at colliders.

What carries the argument

Two-loop Feynman diagram evaluation of the trilinear Higgs vertices, together with a consistent renormalization scheme in the alignment limit of the Higgs basis.

If this is right

  • Predictions for the rate of Higgs pair production at the HL-LHC become more precise once the two-loop terms are included.
  • The size of these corrections provides a direct test of whether the perturbative expansion remains reliable in the 2HDM.
  • Differential distributions in di-Higgs events receive measurable shifts that must be accounted for in experimental analyses.
  • The same corrections apply to measurements planned at future linear colliders.

Where Pith is reading between the lines

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

  • Similar two-loop calculations will likely be required for other trilinear couplings or for quartic couplings in the same model.
  • The refined predictions can be used to place tighter constraints on 2HDM parameters when compared with future collider data.
  • The technical methods developed here may be carried over to other extended Higgs sectors that also possess an alignment limit.

Load-bearing premise

The perturbative series remains well-behaved and the two-loop terms constitute the dominant correction in the alignment limit and parameter regions considered.

What would settle it

High-luminosity LHC measurements of the differential distributions in Higgs pair production that agree with one-loop predictions but deviate from the two-loop corrected predictions would indicate that the two-loop terms are not the dominant correction.

Figures

Figures reproduced from arXiv: 2604.13922 by Alain Verduras Schaeidt, Felix Egle, Johannes Braathen.

Figure 1
Figure 1. Figure 1: Results for κλ (left) and λhhH (right) in a 2HDM benchmark scenario with M = mH = 600 GeV, tan β = 2, α = β − π/2 and varying mA = mH± . Black lines indicate results at the leading one￾loop level, while the red solid lines are our new results including leading one- and two-loop corrections to the trilinear scalar couplings. The blue solid line in the left plot for κλ correspond to the result of Refs. [18, … view at source ↗
Figure 2
Figure 2. Figure 2: Results for κλ (left) and λhhH (right) in a 2HDM benchmark scenario with M = 600 GeV, tan β = 2, α = β − π/2 and varying mH = mA = mH± . The colour coding of curves is as in fig. 1. 5 Phenomenological impact on di-Higgs production In this section, we consider the calculation of physical observables involving the trilinear scalar couplings λhhh and λhhH, specifically the total cross-sections and differentia… view at source ↗
Figure 3
Figure 3. Figure 3: Differential cross-sections for Higgs pair production at the (HL-)LHC as a function of the di-Higgs invariant mass mhh. A QCD K-factor of 2 is used to approximate the contribution of NLO QCD corrections, and the PDF factorisation scale is set to µ0 = mhh/2. Left: results for BP1 defined in eq. (26); right: results for BP2 defined in eq. (27). The different lines correspond to the distributions calculated w… view at source ↗
read the original abstract

The precise determination of the Higgs self-couplings is an essential task for understanding electroweak symmetry breaking and probing physics beyond the Standard Model (SM). The calculation of two-loop corrections to scalar couplings is important as it provides a critical test of the perturbative stability of the theoretical predictions, especially in scenarios with extended scalar sectors where large one-loop corrections can occur. Moreover, two-loop corrections need to be taken into account for the future perspective of precisely measuring the trilinear Higgs self-coupling. We present new results for the leading two-loop corrections to trilinear Higgs couplings in the Two-Higgs-Doublet Model (2HDM). We focus in particular on the couplings $\lambda_{hhh}$ and $\lambda_{hhH}$, which are relevant for Higgs pair production at the (HL-)LHC or at future linear colliders. We address the renormalisation of the alignment limit in the Higgs basis and give some insights into technical details of the calculation. Finally, we discuss the phenomenological impact of our results on di-Higgs production differential distributions.

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

0 major / 3 minor

Summary. The manuscript presents new results for the leading two-loop corrections to the trilinear Higgs couplings λ_hhh and λ_hhH in the Two-Higgs-Doublet Model (2HDM). It focuses on the couplings relevant for Higgs pair production, addresses the renormalization of the alignment limit in the Higgs basis, provides insights into technical details of the calculation, and discusses the phenomenological impact on di-Higgs production differential distributions.

Significance. If the results hold, this work is significant for precision Higgs phenomenology in extended scalar sectors. It supplies two-loop corrections that test perturbative stability where one-loop effects can be large, and the discussion of renormalization in the alignment limit plus the impact on di-Higgs distributions directly supports future LHC and linear-collider analyses of Higgs self-couplings.

minor comments (3)
  1. The abstract states that 'leading two-loop corrections' are computed, but the manuscript should explicitly state in §2 or §3 which classes of diagrams (e.g., top-Yukawa or gauge-boson) are retained at two loops and which are neglected, to make the approximation transparent.
  2. In the phenomenological section, the differential distributions for di-Higgs production are shown; adding a direct comparison plot (or table) of the two-loop result versus the one-loop result and versus the SM would make the size of the correction immediately visible to readers.
  3. The notation for the Higgs basis and the alignment limit is introduced, but a short paragraph recalling the relation between the CP-even mixing angle and the alignment condition (e.g., cos(β−α)→0) would help readers who are not 2HDM experts.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript on two-loop corrections to trilinear Higgs couplings in the 2HDM, including the focus on renormalization and di-Higgs phenomenology. The recommendation for minor revision is noted. No specific major comments were provided in the report, so we have no individual points to rebut or revise at this stage. We will incorporate minor improvements for clarity and presentation in the revised version.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper reports a direct perturbative computation of leading two-loop corrections to trilinear Higgs couplings (λ_hhh, λ_hhH) in the 2HDM, using standard QFT techniques for renormalization in the Higgs basis and alignment limit. No equations or steps reduce by construction to fitted parameters, self-definitions, or prior self-citations that would make the central results equivalent to their inputs. The calculation is self-contained against external benchmarks of loop integrals and renormalization conditions, with the perturbative assumption stated explicitly as the natural one for this class of work.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so specific free parameters, axioms, or invented entities cannot be extracted. The 2HDM framework itself contains several input parameters (tan β, mixing angles, quartic couplings) that are typically chosen or constrained by data.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Precision predictions for trilinear scalar couplings and Higgs pair production in models with extended scalar sectors

    hep-ph 2026-04 unverdicted novelty 2.0

    The work reviews precision predictions for trilinear scalar couplings and Higgs pair production at the LHC in models with extended scalar sectors.

Reference graph

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