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Impact of one-loop corrections to trilinear scalar couplings on di-Higgs production in the RxSM

Johannes Braathen, Sven Heinemeyer, Andrea Parra Arnay, Alain Verduras Schaeidt

TL;DR

The paper develops a fully on-shell renormalised framework for the RxSM, computes one-loop corrections to the trilinear Higgs couplings $\lambda_{hhh}$ and $\lambda_{hhH}$, and propagates these into di-Higgs production at the HL-LHC and a 1 TeV $e^+e^-$ collider. It demonstrates that radiative corrections can produce large modifications to both total and differential di-Higgs cross-sections, with significant sensitivity to the heavy Higgs resonance through $\lambda_{hhH}$. The analysis identifies parameter regions where the RxSM can be distinguished from the SM—often driven by loop-induced enhancements in $\kappa_\lambda$—and highlights the potential of ILC1000 to outperform the HL-LHC in probing these effects. The work also establishes a complete OS renormalisation for the RxSM, including $\kappa_S$ and $\kappa_{SH}$, and emphasizes the importance of higher-order corrections for robust interpretations of di-Higgs searches in Higgs-portal scenarios.

Abstract

We investigate di-Higgs production at the (HL-)LHC and possible high-energy future $e^+e^-$ colliders within the real Higgs singlet extension of the Standard Model (SM), the RxSM. This model has two CP-even Higgs bosons, $h$ and $H$, for which we assume $m_h\sim 125 \text{ GeV} < m_H$. We analyse the effect of one-loop corrections to the two trilinear scalar couplings relevant for di-Higgs production, $λ_{hhh}$ and $λ_{hhH}$, by performing an extensive parameter scan within the RxSM. We find that the one-loop corrections have a strong impact on the total production cross-sections, as well as on the differential cross-sections with respect to the invariant di-Higgs mass, $m_{hh}$. We evaluate the sensitivity of the HL-LHC and a high-energy $e^+e^-$ collider with $\sqrt{s} = 1 \text{ TeV}$, the ILC1000, to probe BSM physics effects in these processes. We demonstrate that the RxSM can be distinguished from the SM for large parts of the sampled parameter space. The resonant $H$ structure in the $m_{hh}$ distribution, on the other hand, can be observed only if the corresponding couplings, in particular $λ_{hhH}$, are sufficiently large. Here the ILC1000 yields a substantially better sensitivity than the HL-LHC.

Impact of one-loop corrections to trilinear scalar couplings on di-Higgs production in the RxSM

TL;DR

The paper develops a fully on-shell renormalised framework for the RxSM, computes one-loop corrections to the trilinear Higgs couplings and , and propagates these into di-Higgs production at the HL-LHC and a 1 TeV collider. It demonstrates that radiative corrections can produce large modifications to both total and differential di-Higgs cross-sections, with significant sensitivity to the heavy Higgs resonance through . The analysis identifies parameter regions where the RxSM can be distinguished from the SM—often driven by loop-induced enhancements in —and highlights the potential of ILC1000 to outperform the HL-LHC in probing these effects. The work also establishes a complete OS renormalisation for the RxSM, including and , and emphasizes the importance of higher-order corrections for robust interpretations of di-Higgs searches in Higgs-portal scenarios.

Abstract

We investigate di-Higgs production at the (HL-)LHC and possible high-energy future colliders within the real Higgs singlet extension of the Standard Model (SM), the RxSM. This model has two CP-even Higgs bosons, and , for which we assume . We analyse the effect of one-loop corrections to the two trilinear scalar couplings relevant for di-Higgs production, and , by performing an extensive parameter scan within the RxSM. We find that the one-loop corrections have a strong impact on the total production cross-sections, as well as on the differential cross-sections with respect to the invariant di-Higgs mass, . We evaluate the sensitivity of the HL-LHC and a high-energy collider with , the ILC1000, to probe BSM physics effects in these processes. We demonstrate that the RxSM can be distinguished from the SM for large parts of the sampled parameter space. The resonant structure in the distribution, on the other hand, can be observed only if the corresponding couplings, in particular , are sufficiently large. Here the ILC1000 yields a substantially better sensitivity than the HL-LHC.

Paper Structure

This paper contains 26 sections, 54 equations, 17 figures, 4 tables.

Table of Contents

  1. Introduction
  2. General singlet extension of the SM (RxSM)
  3. Model definitions
  4. Theoretical and experimental constraints
  5. Calculational setup and on-shell renormalisation of the RxSM
  6. Tadpole renormalisation
  7. Two-point function renormalisation
  8. Mixing angle renormalisation
  9. Renormalisation of the VEVs
  10. Diagrammatic calculation of trilinear scalar couplings
  11. Renormalisation of the $\mathbb{Z}_2$-breaking couplings
  12. Dependence on the renormalisation scale $Q$
  13. One-loop corrections to $\lambda_{ijk}$
  14. Corrections to $\kappa_\lambda$
  15. Corrections to $\lambda_{hhH}$
  16. ...and 11 more sections

Figures (17)

  • Figure 1: Individual contributions --- see \ref{['one_diagrams']} --- and total one-loop results for $\lambda_{hhh}$ and $\lambda_{hhH}$, using the OS renormalisation scheme defined in \ref{['sec:ren']}. Upper row: results for BP1 from \ref{['points1']}; bottom row: results for BP2 from \ref{['points1']}; left column: results for $\lambda_{hhh}$; right column: results for $\lambda_{hhH}$. The colour coding is as follows: the blue line is the full one-loop result $\hat{\lambda}_{ijk}^{(1)}$, the orange line is the tree-level contribution $\lambda^{(0)}_{ijk}$, the green curve corresponds to the one-loop 1PI contributions $\delta^{(1)}_\text{gen}\lambda_{ijk}$, the red curve represents the external-leg corrections $\delta^{(1)}_\text{wfr}\lambda_{ijk}$, the purple curve is the contribution from the mass renormalisation $\delta^\text{CT}_{m_h^2,m_H^2}\lambda_{ijk}$, the brown curve is the contribution from the renormalisation of $\kappa_S$ and $\kappa_{SH}$$\delta^\text{CT}_{\kappa_S,\kappa_{SH}}\lambda_{ijk}$, the pink curve shows the contribution from the renormalisation of the EW VEV $\delta^\text{CT}_{v}\lambda_{ijk}$, and finally the grey curve is the contribution from the $\alpha$ counterterm $\delta^\text{CT}_\alpha\lambda_{ijk}$.
  • Figure 2: Parameter scan results in the RxSM, using the ranges given in \ref{['eq:paramscan_ranges']}. The colour coding indicates $\kappa_\lambda^{(1)}$. Left: results in the $\{\cos \alpha,v_S\}$ plane; right: results in the $\{\cos \alpha,m_H\}$ plane.
  • Figure 3: Difference between the one-loop and tree-level values of $\kappa_\lambda$, for the same RxSM parameter scan points as in \ref{['hhh']}. Left: results in the $\{\cos \alpha,v_S\}$ plane; right: results in the $\{\cos \alpha,m_H\}$ plane.
  • Figure 4: Results for $\hat{\lambda}_{hhH}^{(1)}$ of our RxSM parameter scan. Left: results in the $\{\cos \alpha,v_S\}$ plane; right: results in the $\{\cos \alpha,m_H\}$ plane.
  • Figure 5: Difference between the one-loop and tree-level values of $\lambda_{hhH}$ for our RxSM parameter scan. Left: results in the $\{\cos \alpha,v_S\}$ plane; right: results in the $\{\cos \alpha,m_H\}$ plane.
  • ...and 12 more figures