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arxiv: 2510.17387 · v3 · submitted 2025-10-20 · ✦ hep-ph

One-loop QED and Weak Corrections to γ γ to H^pm H^mp in the Inert Doublet Model

Hamza Abouabid , Abdesslam Arhrib , Jaouad El Falaki , Bin Gong , Qi-Shu Yan This is my paper

Pith reviewed 2026-05-18 06:33 UTC · model grok-4.3

classification ✦ hep-ph
keywords Inert Doublet Modelcharged Higgs pair productionphoton-photon collisionsone-loop correctionsQED effectsweak correctionsSommerfeld resummationdark matter constraints
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0 comments X

The pith

One-loop corrections to charged scalar pair production in photon collisions reach up to 60% at TeV energies in the Inert Doublet Model.

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

This paper carries out a complete one-loop calculation of the process gamma gamma to H+ H- in the Inert Doublet Model, including both weak loop diagrams and QED effects with soft and hard photon radiation. The work uses the on-shell renormalization scheme and adds Sommerfeld resummation to handle the Coulomb singularity that appears near threshold. The size of the corrections is found to be governed by the absolute value of the trilinear scalar coupling lambda between the SM-like Higgs and the charged scalars. After scanning the parameter space under theoretical, collider, and dark matter constraints, the corrections stay moderate and mostly negative at 250 and 500 GeV but can grow as large as +60% at 1 TeV. The results position this process as a useful channel for exploring the charged scalar sector at a future photon collider.

Core claim

We present a complete one-loop analysis of charged scalar boson pair production in photon-photon collisions, γγ → H± H∓, within the Inert Doublet Model. The calculation is carried out in the on-shell renormalization scheme and incorporates both weak corrections and QED effects, including soft and hard photon radiation. Virtual loop contributions and real emission processes are computed using the Feynman diagrammatic method, ensuring the cancellation of ultraviolet and infrared divergences. To properly account for the Coulomb singularity that arises in the QED sector near threshold, we introduce the resummed cross section based on the Sommerfeld factor. The IDM parameter space is explored and

What carries the argument

The resummed cross section that incorporates the Sommerfeld factor to regulate the infrared Coulomb singularity in the QED sector near the production threshold.

If this is right

  • Weak and QED corrections must be included to obtain accurate predictions for the cross section at future photon colliders.
  • The magnitude of the corrections is controlled by the absolute value of the trilinear coupling λ_h0 H+ H- and its correlation with the charged scalar mass.
  • Three representative benchmark points survive all constraints and can be used to guide experimental searches.
  • At higher energies the corrections grow large, showing that higher-order effects play an essential role in this channel.

Where Pith is reading between the lines

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

  • Measuring the size of the correction at a photon collider could provide an indirect handle on the trilinear coupling that is complementary to direct searches for the charged scalars.
  • If the corrections really reach 60 percent, two-loop contributions may become numerically important and should be checked before claiming percent-level precision.
  • The same framework could be applied to related processes such as γγ → H+ H- in other extended Higgs models to compare correction patterns.

Load-bearing premise

The perturbative expansion remains under control even when the reported one-loop corrections reach magnitudes of 60 percent at center-of-mass energies of 1 TeV.

What would settle it

A precision measurement of the γγ → H± H∓ cross section at √s = 1 TeV that lies well outside the interval from -20 percent to +60 percent after Sommerfeld resummation is included.

Figures

Figures reproduced from arXiv: 2510.17387 by Abdesslam Arhrib, Bin Gong, Hamza Abouabid, Jaouad El Falaki, Qi-Shu Yan.

Figure 3.1
Figure 3.1. Figure 3.1: The tree level Feynman diagrams for the process [PITH_FULL_IMAGE:figures/full_fig_p007_3_1.png] view at source ↗
Figure 4.1
Figure 4.1. Figure 4.1: Total cross sections and the percentage of corrections for the process [PITH_FULL_IMAGE:figures/full_fig_p013_4_1.png] view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: Electroweak corrections to γγ → H±H∓ for √ s = 250 GeV, 500 GeV and 1000 GeV as a function of mS and the triple Higgs couplings λh0SS normalized to the SM Higgs vev. Upper panels show the degenerate scenario, middle and lower panels are respectively for the non-degenerate scenario before and after applying dark matter constraint. BP BP1 BP2 BP3 BP4 BP5 BP6 BP7 mH± (GeV) 89.1 116.8 123.4 209.5 243.7 295.4… view at source ↗
read the original abstract

We present a complete one-loop analysis of charged scalar boson pair production in photon-photon collisions, $\gamma\gamma \to H^\pm H^\mp$, within the framework of the Inert Doublet Model (IDM). The calculation is carried out in the on-shell renormalization scheme and incorporates both weak corrections and QED effects, including soft and hard photon radiation. Virtual loop contributions and real emission processes are computed using the Feynman diagrammatic method, ensuring the cancellation of ultraviolet and infrared divergences. To properly account for the Coulomb singularity that arises in the QED sector near threshold, we introduce the resummed cross section based on the Sommerfeld factor. The IDM parameter space is explored under theoretical consistency conditions, collider limits, and dark matter constraints, and three representative scenarios are studied in detail. We find that the magnitude of the quantum corrections is strongly controlled by the absolute value of the trilinear scalar coupling $\lambda_{h^0 H^+ H^-}$, which correlates with the charged scalar mass. When all constraints are applied, the weak corrections are typically in the range of $-12\%$ to $-7\%$ at $\sqrt{s}=250$~GeV, and between $-15\%$ and $6\%$ at $\sqrt{s}=500$~GeV. At higher energies, such as $\sqrt{s}=1$~TeV, the corrections can become very large, ranging from about $-20\%$ up to $+60\%$. Our findings highlight the significant role of higher-order effects in photon-photon collisions and establish $\gamma\gamma \to H^\pm H^\mp$ as a promising process to investigate the charged scalar sector of the IDM at future high-energy photon colliders. Several benchmark points are proposed to facilitate future experimental searches.

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 paper presents a complete one-loop calculation of QED and weak corrections to γγ → H±H∓ in the Inert Doublet Model using the Feynman diagrammatic method in the on-shell renormalization scheme. It includes virtual loops, real soft and hard photon emission with explicit cancellation of UV and IR divergences, and applies Sommerfeld resummation to handle the QED Coulomb singularity near threshold. The IDM parameter space is scanned subject to theoretical consistency, collider limits, and dark matter constraints; three benchmark scenarios are analyzed in detail. The central results are that the magnitude of corrections is controlled by |λ_h0 H+ H−|, with weak corrections typically −12% to −7% at √s=250 GeV, −15% to 6% at √s=500 GeV, and −20% to +60% at √s=1 TeV.

Significance. If the numerical results hold, the work demonstrates that NLO effects can be sizable in photon-photon production of charged scalars and supplies concrete benchmark points for future collider searches. The explicit inclusion of both virtual and real QED contributions together with the Sommerfeld factor is a technical strength that addresses infrared issues cleanly.

major comments (2)
  1. [Abstract] Abstract (final results paragraph): the reported weak corrections reaching +60% at √s=1 TeV are presented as a central finding, yet no estimate of theoretical uncertainty from missing higher-order terms is given. A 60% NLO correction implies that the expansion parameter is not small; the manuscript should either demonstrate that the large logarithms or enhancements are under control or qualify the reliability of the quoted percentages.
  2. [Abstract] Abstract (QED sector paragraph): the Sommerfeld resummation is applied only to the QED Coulomb singularity near threshold. No analogous treatment or two-loop estimate is supplied for the large high-energy weak corrections that dominate away from threshold, leaving open whether the one-loop truncation remains valid in the region where the largest effects are claimed.
minor comments (1)
  1. [Abstract] The abstract states that UV and IR divergences cancel but does not reference a specific numerical check or plot demonstrating the cancellation after combining virtual and real contributions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment point by point below and have revised the manuscript to incorporate qualifications where the concerns are valid.

read point-by-point responses

  1. Referee: [Abstract] Abstract (final results paragraph): the reported weak corrections reaching +60% at √s=1 TeV are presented as a central finding, yet no estimate of theoretical uncertainty from missing higher-order terms is given. A 60% NLO correction implies that the expansion parameter is not small; the manuscript should either demonstrate that the large logarithms or enhancements are under control or qualify the reliability of the quoted percentages.

    Authors: We agree that corrections reaching +60% indicate that higher-order terms could be relevant and that an explicit uncertainty estimate from missing orders is not provided. These enhancements originate from the trilinear coupling λ_h0 H+ H− in parameter regions still allowed by all constraints applied in the scan. Since a two-loop computation lies outside the present one-loop study, we cannot demonstrate control via explicit higher-order results. In the revised version we qualify the abstract and add a short paragraph in the conclusions noting that the quoted NLO percentages are to be understood within the one-loop approximation and serve primarily to highlight the size of radiative effects rather than to provide precision predictions without further study. revision: yes

  2. Referee: [Abstract] Abstract (QED sector paragraph): the Sommerfeld resummation is applied only to the QED Coulomb singularity near threshold. No analogous treatment or two-loop estimate is supplied for the large high-energy weak corrections that dominate away from threshold, leaving open whether the one-loop truncation remains valid in the region where the largest effects are claimed.

    Authors: The Sommerfeld resummation addresses the non-perturbative QED Coulomb singularity that appears only near threshold; it is not applicable to the high-energy weak sector. The weak corrections are computed at fixed one-loop order with all diagrams and on-shell counterterms included. We acknowledge that large high-energy weak corrections raise the question of the truncation’s validity. In the revision we add an explicit statement in the text distinguishing the two cases and noting that the one-loop weak results are presented as such, with the understanding that Sudakov-enhanced higher-order weak contributions may become important at 1 TeV for precision applications. revision: yes

Circularity Check

0 steps flagged

Explicit one-loop integrals yield corrections without reduction to fitted inputs or self-citation chains

full rationale

The derivation consists of a standard on-shell one-loop Feynman diagrammatic computation of virtual weak and QED corrections plus real photon emission for γγ → H±H∓ in the IDM. The quoted percentage corrections are obtained by direct numerical evaluation of the loop integrals over parameter points that satisfy theoretical, collider, and DM constraints. No equation in the paper defines a result in terms of itself, renames a fitted quantity as a prediction, or imports a uniqueness theorem from prior self-work that forces the central numerical outcome. The Sommerfeld factor is a conventional resummation applied only near threshold to the QED Coulomb singularity and does not propagate into the high-energy weak corrections. The calculation is therefore self-contained against external benchmarks and receives only a minimal score for possible incidental self-citations that are not load-bearing.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central numerical claims rest on standard perturbative QFT applied to the IDM parameter space after external constraints are imposed; no new entities are introduced.

free parameters (2)
  • Trilinear scalar coupling λ_h0 H+ H−
    Its absolute value is stated to control the size of the corrections and is scanned under theoretical and experimental bounds.
  • Charged scalar mass m_H±
    Correlates with the trilinear coupling and enters the kinematic and loop integrals.
axioms (2)
  • domain assumption On-shell renormalization scheme
    Invoked to define the counterterms and cancel ultraviolet divergences.
  • domain assumption Cancellation of ultraviolet and infrared divergences between virtual loops and real emission
    Stated to occur after inclusion of soft and hard photon radiation.

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