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Probing standard-model-like di-Higgs production at photon-photon colliders in the $I (1 + 2) HDM$ type-I

Abdesslam Arhrib^1,2,*, Ayoub Hmissou^3,†, Stefano Moretti ^4,5,‡, and Larbi Rahili ^3,§

¹Faculté des Sciences et Techniques, Université Abdelmalek Essaadi, Boîte Postale 416, Tangier, Morocco
²LAPTh, CNRS, Université Savoie Mont-Blanc, 9 Chemin de Bellevue, 74940, Annecy, France
³Laboratory of Theoretical Physics and High Energies (LPTHE), Physics Department, FSA, Ibnou Zohr University, Boîte Postale 8106, Agadir, Morocco
⁴School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ, United Kingdom
⁵Department of Physics and Astronomy, Uppsala University, Box 516, 751 20 Uppsala, Sweden

^*Contact author: aarhrib@uae.ac.ma
^†Contact author: ayoub1hmissou@gmail.com
^‡Contact author: stefano.moretti@cern.ch
^§Contact author: rahililarbi@gmail.com, l.rahili@uiz.ac.ma

Phys. Rev. D 114, 015010 – Published 7 July, 2026

DOI: https://doi.org/10.1103/h3lv-ts6t

Abstract

In this paper, pair production of standard model (SM)-like Higgs bosons, $h h$ , is studied through $γ γ$ scattering at future electron-positron colliders, in the framework of the inert doublet model with two active doublets—i.e., the I( $1 + 2$ )HDM for short. The relevance of the process $γ γ \to h h$ for such a beyond-the-SM (BSM) scenario stems from the fact that it is a one-loop process at lowest order, wherein inert charged states $χ^{\pm}$ contribute alongside $W^{\pm}$ , $H^{\pm}$ , and heavy fermions (primarily, bottom and top quarks), crucially, at the same perturbative order. Given that $χ^{\pm} / H^{\pm}$ masses and $h S^{+} S^{-}$ ( $S^{\pm} = χ^{\pm}, H^{\pm}$ ) couplings are very mildly constrained, there exist regions of the parameter space of the $I (1 + 2) HDM$ where the former can be rather light and the latter rather large. After imposing up-to-date theoretical and experimental constraints on the $I (1 + 2) HDM$ , it is found that the production rates of such processes at future $γ γ$ machines can be enhanced by up to a factor of $\approx 50$ with respect to the SM, significantly exceeding typical yields of conventional two-Higgs-doublet models (2HDMs). Further, thanks to the level of control that one can attain at such facilities on the photon kinematics, leading to excellent invariant mass resolution of the incoming photon pairs, we show how it is possible to extract from this process the value of the $χ^{\pm}$ mass (along with those of the active $H^{\pm}$ states) with high precision, and whichever of the decays of the $h h$ pair, both with and without beam polarization.

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References (95)

G. Aad et al. (ATLAS Collaboration), Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716, 1 (2012).
S. Chatrchyan et al. (CMS Collaboration), Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716, 30 (2012).
G. Aad et al. (ATLAS and CMS Collaboration), Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC $p p$ collision data at $\sqrt{s} = 7$ and 8 TeV, J. High Energy Phys. 08 (2016) 045.
A. M. Sirunyan et al. (CMS Collaboration), Combined measurements of Higgs boson couplings in proton-proton collisions at $\sqrt{s} = 13 Te V$ , Eur. Phys. J. C 79, 421 (2019).
G. Aad et al. (ATLAS Collaboration), Combined measurements of Higgs boson production and decay using up to $80 {fb}^{- 1}$ of proton-proton collision data at $\sqrt{s} = 13 TeV$ collected with the ATLAS experiment, Phys. Rev. D 101, 012002 (2020).
G. Aad et al. (ATLAS Collaboration), A detailed map of Higgs boson interactions by the ATLAS experiment ten years after the discovery, Nature (London) 607, 52 (2022).
A. Tumasyan et al. (CMS Collaboration), A portrait of the Higgs boson by the CMS experiment ten years after the discovery, Nature (London) 607, 60 (2022).
G. Aad et al. (ATLAS Collaboration), Measurement of the properties of Higgs boson production at $\sqrt{s} = 13 TeV$ in the $H \to γ γ$ channel using $139 {fb}^{- 1}$ of $p p$ collision data with the ATLAS experiment, J. High Energy Phys. 07 (2023) 088.
G. Aad et al. (ATLAS Collaboration), Measurements of Higgs boson production by gluon-gluon fusion and vector-boson fusion using $H \to W W^{*} \to e ν μ ν$ decays in $p p$ collisions at $\sqrt{s} = 13 TeV$ with the ATLAS detector, Phys. Rev. D 108, 032005 (2023).
G. Aad et al. (ATLAS and CMS Collaborations), Highlights of the HL-LHC physics projections by ATLAS and CMS, arXiv:2504.00672.
F. Gianotti et al., Physics potential and experimental challenges of the LHC luminosity upgrade, Eur. Phys. J. C 39, 293 (2005).
G. Apollinari, O. Brüning, T. Nakamoto, and L. Rossi, High luminosity large hadron collider HL-LHC, CERN Yellow Rep. 2015, 1 (2015).
P. Bambade et al., The international linear collider: A global project, arXiv:1903.01629.
M. Ahmad et al. in CEPC-SPPC Preliminary Conceptual Design Report. 1. Physics and Detector (Institute of High Energy Physics (IHEP), Chinese Academy of Science, Beijing, China, 2015).
M. Bicer et al. (TLEP Design Study Working Group), First look at the physics case of TLEP, J. High Energy Phys. 01 (2014) 164.
M. Benedikt et al. (FCC Collaboration), Future circular collider feasibility study report: Volume 1, Physics, experiments, detectors, Eur. Phys. J. C 85, 1468 (2025).
H. Abramowicz et al. (Linear Collider Vision Collaboration), A linear collider vision for the future of particle physics, Eur. Phys. J. Special Topics 235, 1641 (2026).
H. Abramowicz et al. (Linear Collider Collaboration), The linear collider facility (LCF) at CERN, arXiv:2503.24049.
E. Accomando et al. (CLIC Physics Working Group), Physics at the CLIC multi-TeV linear collider, arXiv:hep-ph/0412251.
Lucie Linssen, Akiya Miyamoto, Marcel Stanitzki, and Harry Weerts, Physics and detectors at CLIC: CLIC conceptual design report, arXiv:1202.5940.
E. Adli et al., The compact linear $e^{+} e^{-}$ collider (CLIC), arXiv:2503.24168.
K. Fujii et al., Physics case for the international linear collider, arXiv:1506.05992.
S. Khalil and S. Moretti, Standard Model Phenomenology (CRC Press, Boca Raton, FL, 2022).
B. Badelek et al. (ECFA/DESY Photon Collider Working Group), TESLA: The superconducting electron positron linear collider with an integrated x-ray laser laboratory. Technical design report. Part 6. Appendices. Chapter 1. Photon collider at TESLA, Int. J. Mod. Phys. A 19, 5097 (2004).
V. I. Telnov, The Photon collider at ILC: Status, parameters and technical problems, Acta Phys. Pol. B 37, 1049 (2006).
A. De Roeck, Physics at a $γ γ$ , $e γ$ and $e^{-} e^{-}$ option for a linear collider, in 4th ECFA/DESY Workshop on Physics and Detectors for a 90-GeV to 800-GeV Linear e⁺e^- Collider (CERN, Geneva, Switzerland, 2003), pp. 69–78.
I. F. Ginzburg and G. L. Kotkin, Photon collider for energy of 1–2 TeV, Phys. Part. Nucl. 52, 899 (2021).
M. M. Muhlleitner and P. M. Zerwas, Elements of physics with a photon collider, Acta Phys. Pol. B 37, 1021 (2006).
D. Asner, H. Burkhardt, A. De Roeck, J. Ellis, J. Gronberg, S. Heinemeyer, M. Schmitt, D. Schulte, M. Velasco, and F. Zimmermann, Higgs physics with a gamma gamma collider based on CLIC I, Eur. Phys. J. C 28, 27 (2003).
G. V. Jikia and Y. F. Pirogov, Studying triple Higgs vertex in the process $γ γ \to H H$ at TeV energies, Phys. Lett. B 283, 135 (1992).
G. V. Jikia, Higgs boson pair production in high-energy photon-photon collisions, Nucl. Phys. B412, 57 (1994).
D. L. Borden, D. A. Bauer, and D. O. Caldwell, Higgs boson production at a photon linear collider, Phys. Rev. D 48, 4018 (1993).
R. Belusevic and G. Jikia, Higgs selfcoupling in $γ γ$ collisions, Phys. Rev. D 70, 073017 (2004).
M. Berger, J. Braathen, G. Moortgat-Pick, and G. Weiglein, Probing the Higgs potential at a Photon Collider, in 2025 European Physical Society Conference on High Energy Physics (SISSA Medialab, Marseille, France, 2025).
M. M. Muhlleitner, M. Kramer, M. Spira, and P. M. Zerwas, Production of MSSM Higgs bosons in photon-photon collisions, Phys. Lett. B 508, 311 (2001).
D. M. Asner, J. B. Gronberg, and J. F. Gunion, Detecting and studying Higgs bosons at a photon-photon collider, Phys. Rev. D 67, 035009 (2003).
Z. Heng, L. Shang, and P. Wan, Pair production of a 125 GeV Higgs boson in MSSM and NMSSM at the ILC, J. High Energy Phys. 10 (2013) 047.
S.-H. Zhu, C.-S. Li, and C.-S. Gao, Lightest neutral Higgs pair production in photon-photon collisions in the minimal supersymmetric standard model, Phys. Rev. D 58, 015006 (1998).
Y.-J. Zhou, W.-G. Ma, H.-S. Hou, R.-Y. Zhang, P.-J. Zhou, and Y.-B. Sun, Neutral Higgs boson pair production via $γ γ$ collision in the minimal supersymmetric standard model at linear colliders, Phys. Rev. D 68, 093004 (2003).
F. Cornet and W. Hollik, Pair production of two-Higgs-Doublet model light Higgs bosons in $γ γ$ collisions, Phys. Lett. B 669, 58 (2008).
E. Asakawa, D. Harada, S. Kanemura, Y. Okada, and K. Tsumura, Higgs boson pair production at a photon-photon collision in the two Higgs doublet model, Phys. Lett. B 672, 354 (2009).
E. Asakawa, D. Harada, S. Kanemura, Y. Okada, and K. Tsumura, Higgs boson pair production in new physics models at hadron, lepton, and photon colliders, Phys. Rev. D 82, 115002 (2010).
A. Arhrib, R. Benbrik, C.-H. Chen, and R. Santos, Neutral Higgs boson pair production in photon-photon annihilation in the two Higgs doublet model, Phys. Rev. D 80, 015010 (2009).
J. Hernandez-Sanchez, C. G. Honorato, M. A. Perez, and J. J. Toscano, The $γ γ \to ϕ_{i} ϕ_{j}$ processes in the type-III two-Higgs-doublet model, Phys. Rev. D 85, 015020 (2012).
M. Demirci, Pseudoscalar Higgs boson pair production at a photon-photon collision in the two Higgs doublet model, Turk. J. Phys. 43, 442 (2019).
K. H. Phan, D. T. Tran, and T. H. Nguyen, Processes $γ γ \to ϕ_{i} ϕ_{j}$ in inert Higgs doublet models and two Higgs doublet models, arXiv:2409.00662.
B. Grzadkowski, O. M. Ogreid, and P. Osland, Natural multi-Higgs model with dark matter and $C P$ violation, Phys. Rev. D 80, 055013 (2009).
A. Goudelis, B. Herrmann, and O. Stål, Dark matter in the inert doublet model after the discovery of a Higgs-like boson at the LHC, J. High Energy Phys. 09 (2013) 106.
I. Chakraborty and A. Kundu, Two-Higgs doublet models confront the naturalness problem, Phys. Rev. D 90, 115017 (2014).
N. Chakrabarty and I. Chakraborty, On the Higgs mass fine-tuning problem with multi-Higgs doublet models, Int. J. Mod. Phys. A 34, 1950025 (2019).
J. O. aali, B. Manaut, L. Rahili, and S. Semlali, Naturalness implications within the two-real-scalar-singlet beyond the SM, Eur. Phys. J. C 81, 1045 (2021).
A. Hmissou, S. Moretti, and L. Rahili, Investigating the 95 GeV Higgs boson excesses within the $I (1 + 2) HDM$ , Phys. Rev. D 113, 015024 (2026).
A. Hmissou, S. Moretti, and L. Rahili, Could the 650 GeV excess be a pseudoscalar of a 3-Higgs doublet model?, Phys. Rev. D 112, 075049 (2025).
S. Moretti and K. Yagyu, Constraints on parameter space from perturbative unitarity in models with three scalar doublets, Phys. Rev. D 91, 055022 (2015).
V. Keus, S. F. King, and S. Moretti, Three-Higgs-doublet models: Symmetries, potentials and Higgs boson masses, J. High Energy Phys. 01 (2014) 052.
M. Merchand and M. Sher, Constraints on the parameter space in an inert doublet model with two active doublets, J. High Energy Phys. 03 (2020) 108.
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. Rep. 516, 1 (2012).
A. Belyaev, G. Cacciapaglia, I. P. Ivanov, F. Rojas-Abatte, and M. Thomas, Anatomy of the inert two Higgs doublet model in the light of the LHC and non-LHC dark matter searches, Phys. Rev. D 97, 035011 (2018).
P. M. Ferreira, R. Santos, and A. Barroso, Stability of the tree-level vacuum in two Higgs doublet models against charge or $C P$ spontaneous violation, Phys. Lett. B 603, 219 (2004).
M. E. Peskin and T. Takeuchi, Estimation of oblique electroweak corrections, Phys. Rev. D 46, 381 (1992).
W. Grimus, L. Lavoura, O. M. Ogreid, and P. Osland, The Oblique parameters in multi-Higgs-doublet models, Nucl. Phys. B801, 81 (2008).
A. Arhrib, R. Benbrik, and N. Gaur, $H \to γ γ$ in inert Higgs doublet model, Phys. Rev. D 85, 095021 (2012).
H. Abouabid, A. Arhrib, A. Hmissou, and L. Rahili, Revisiting inert doublet model parameters, Eur. Phys. J. C 84, 632 (2024).
P. A. Zyla et al. (Particle Data Group), Review of particle physics, Prog. Theor. Exp. Phys. 2020, 083C01 (2020).
K. Nakamura et al. (Particle Data Group), Review of particle physics, J. Phys. G 37, 075021 (2010).
A. Pierce and J. Thaler, Natural dark matter from an unnatural Higgs boson and new colored particles at the TeV scale, J. High Energy Phys. 08 (2007) 026.
G. Abbiendi et al. (ALEPH, DELPHI, L3, OPAL, LEP Collaborations), Search for charged Higgs bosons: Combined results Using LEP data, Eur. Phys. J. C 73, 2463 (2013).
A. Arbey, F. Mahmoudi, O. Stal, and T. Stefaniak, Status of the charged Higgs boson in two Higgs doublet models, Eur. Phys. J. C 78, 182 (2018).
G. Alguero, G. Belanger, F. Boudjema, S. Chakraborti, A. Goudelis, S. Kraml, A. Mjallal, and A. Pukhov, micromegas 6.0: N-component dark matter, Comput. Phys. Commun. 299, 109133 (2024).
F. Mahmoudi, superiso v2.3: A program for calculating flavor physics observables in Supersymmetry, Comput. Phys. Commun. 180, 1579 (2009).
Y. Amhis et al. (HFLAV Collaboration), Averages of $b$ -hadron, $c$ -hadron, and $τ$ -lepton properties as of summer 2016, Eur. Phys. J. C 77, 895 (2017).
R. Aaij et al. (LHCb Collaboration), Measurement of the $B_{s}^{0} \to μ^{+} μ^{-}$ decay properties and search for the $B^{0} \to μ^{+} μ^{-}$ and $B_{s}^{0} \to μ^{+} μ^{-} γ$ decays, Phys. Rev. D 105, 012010 (2022).
R. Aaij et al. (LHCb Collaboration), Analysis of neutral B-meson decays into two muons, Phys. Rev. Lett. 128, 041801 (2022).
H. Bahl, T. Biekötter, S. Heinemeyer, C. Li, S. Paasch, G. Weiglein, and J. Wittbrodt, higgstools: BSM scalar phenomenology with new versions of higgsbounds and higgssignals, Comput. Phys. Commun. 291, 108803 (2023).
P. Bechtle, S. Heinemeyer, T. Klingl, T. Stefaniak, G. Weiglein, and J. Wittbrodt, higgssignals-2: Probing new physics with precision Higgs measurements in the LHC 13 TeV era, Eur. Phys. J. C 81, 145 (2021).
P. Bechtle, D. Dercks, S. Heinemeyer, T. Klingl, T. Stefaniak, G. Weiglein, and J. Wittbrodt, higgsbounds-5: Testing Higgs sectors in the LHC 13 TeV Era, Eur. Phys. J. C 80, 1211 (2020).
A. Tumasyan et al. (CMS Collaboration), Search for a scalar or pseudoscalar dilepton resonance produced in association with a massive vector boson or top quark-antiquark pair in multilepton events at $\sqrt{s} = 13 TeV$ , Phys. Rev. D 110, 012013 (2024).
A. Djouadi, The Anatomy of electro-weak symmetry breaking: I. The Higgs boson in the standard model, Phys. Rep. 457, 1 (2008).
T. Hahn, Generating Feynman diagrams and amplitudes with feynarts 3, Comput. Phys. Commun. 140, 418 (2001).
T. Hahn and C. Schappacher, The Implementation of the minimal supersymmetric standard model in feynarts and formcalc, Comput. Phys. Commun. 143, 54 (2002).
G. Passarino and M. J. G. Veltman, One loop corrections for $e^{+} e^{-}$ annihilation into $μ^{+} μ^{-}$ in the Weinberg model, Nucl. Phys. B160, 151 (1979).
T. Hahn and M. Perez-Victoria, Automatized one loop calculations in four-dimensions and D-dimensions, Comput. Phys. Commun. 118, 153 (1999).
A. F. Zarnecki, compaz: Parametrization of the photon collider luminosity spectra, Acta Phys. Pol. B 34, 2741 (2003).
I. F. Ginzburg, G. L. Kotkin, V. G. Serbo, and V. I. Telnov, Colliding $γ e$ and $γ γ$ beams based on the single pass accelerators (of Vlepp type), Nucl. Instrum. Methods 205, 47 (1983).
I. F. Ginzburg, G. L. Kotkin, S. L. Panfil, V. G. Serbo, and V. I. Telnov, Colliding $γ e$ and $γ γ$ beams based on the single pass $e^{+} e^{-}$ accelerators 2. Polarization effects. Monochromatization improvement, Nucl. Instrum. Methods Phys. Res., Sect. A 219, 5 (1984).
V. I. Telnov, Problems of obtaining $γ γ$ and $γ e$ colliding beams at linear colliders, Nucl. Instrum. Methods Phys. Res., Sect. A 294, 72 (1990).
I. F. Ginzburg and G. L. Kotkin, Effective photon spectra for the photon colliders, Eur. Phys. J. C 13, 295 (2000).
S. Kanemura, Y. Okada, E. Senaha, and C. P. Yuan, Higgs coupling constants as a probe of new physics, Phys. Rev. D 70, 115002 (2004).
P. Osland, P. N. Pandita, and L. Selbuz, Trilinear Higgs couplings in the two Higgs doublet model with $C P$ violation, Phys. Rev. D 78, 015003 (2008).
J. Braathen and S. Kanemura, On two-loop corrections to the Higgs trilinear coupling in models with extended scalar sectors, Phys. Lett. B 796, 38 (2019).
S. Heinemeyer, M. Mühlleitner, K. Radchenko, and G. Weiglein, Higgs pair production in the 2HDM: Impact of loop corrections to the trilinear Higgs couplings and interference effects on experimental limits, Eur. Phys. J. C 85, 437 (2025).
G. Aad et al. (ATLAS Collaboration), Combination of searches for Higgs boson pair production in $p p$ collisions at $\sqrt{s} = 13 TeV$ with the ATLAS detector, Phys. Rev. Lett. 133, 101801 (2024).
G. Aad et al. (ATLAS Collaboration), Constraints on the Higgs boson self-coupling from single- and double-Higgs production with the ATLAS detector using $p p$ collisions at $\sqrt{s} = 13 TeV$ , Phys. Lett. B 843, 137745 (2023).
A. Hayrapetyan et al. (CMS Collaboration), Constraints on the Higgs boson self-coupling from the combination of single and double Higgs boson production in proton-proton collisions at $\sqrt{s} = 13 TeV$ , Phys. Lett. B 861, 139210 (2025).
L.-Z. Sun and Y.-Y. Liu, Studying the Higgs pair production in the process $γ γ \to H_{0} H_{0}$ in the two Higgs doublet model, Phys. Rev. D 54, 3563 (1996).

Phys. Rev. D 114, 015010– Published 7 July, 2026

Vol. 114, Iss. 1 — 1 July 2026

Received 16 November 2025
Accepted 4 June 2026

DOI: https://doi.org/10.1103/h3lv-ts6t

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Probing standard-model-like di-Higgs production at photon-photon colliders in the $I (1 + 2) HDM$ type-I

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Probing standard-model-like di-Higgs production at photon-photon colliders in the I(1+2)HDM type-I

Abstract

Physics Subject Headings (PhySH)

Article Text

References (95)

Probing standard-model-like di-Higgs production at photon-photon colliders in the $I (1 + 2) HDM$ type-I