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

TL;DR

The paper tackles the challenge of obtaining precise predictions for charged-scalar pair production in photon–photon collisions within the Inert Doublet Model (IDM). It performs a complete one-loop electroweak and QED analysis of $\gamma\gamma \to H^{\pm} H^{\mp}$ in an on-shell renormalization framework, including soft and hard photon emission and Sommerfeld-resummed Coulomb effects near threshold. The study scans IDM parameter space under theoretical, collider, and dark matter constraints, presenting three representative scenarios and multiple benchmarks. The results show that radiative corrections are highly sensitive to the charged-scalar mass and the trilinear coupling $|\lambda_{h^0 H^{+} H^{-}}|$, with corrections reaching very large values at high energies, highlighting the importance of NLO predictions for future high-energy photon colliders probing the IDM and its dark matter implications.

Abstract

We present a complete one-loop analysis of charged scalar boson pair production in photon-photon collisions, $γγ\to H^\pm H^\mp$, 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 $λ_{h^0 H^+ H^-}$, 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 $γγ\to H^\pm H^\mp$ 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.

Figures (8)

• Figure 3.1: The tree level Feynman diagrams for the process $\gamma\gamma \to H^\pm H^\mp$.
• Figure 4.1: Total cross sections and the percentage of corrections for the process $\gamma\gamma \to H^{\pm} H^{\mp}$ with three collision energies $\sqrt{s}=250$ GeV, $500$ GeV, and $1000$ GeV are demonstrated, respectively. As an example, the LO result and the full NLO results of IDM in the scenario I are shown. The full NLO results include the LO, one-loop weak corrections, and the real emission corrections. The x-axis denotes the mass of charged scalar boson mass, and the y-axis denotes the total cross section (upper panel) and the percentage of corrections $\Delta$ (lower panel) given in Eq. (\ref{['split']}).
• Figure 4.2: Electroweak corrections to $\gamma \gamma \to H^\pm H^\mp$ for $\sqrt{s}=250$ GeV, 500 GeV and 1000 GeV as a function of $m_S$ and the triple Higgs couplings $\lambda_{h^0SS}$ 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.
• Figure A.1: Vertex feynman diagrams for $\gamma \gamma \to H^\pm H^\mp$
• Figure A.2: Box contributions to the loop level $\gamma \gamma \to H^\pm H^\mp$