An EFT approach to the study of multi-phase criticality scenarios

TL;DR

The paper develops an EFT framework to study multi-phase criticality in a Standard Model extension with two scalar singlets, addressing the hierarchical mass spectrum that arises and its implications for the Higgs-dilaton sector and DM. It constructs a tower of EFTs, performing heavy-scale matching, RG running, and light-scale integration to RG-improve the effective potential, while carefully handling tadpoles and background field shifts. Three representative mass hierarchies are analyzed: approximately degenerate, fully hierarchical, and heavy dilaton, with detailed matching and running procedures for each. The DM phenomenology is integrated via relic density, direct detection, and collider constraints, revealing viable parameter regions with m_s' in the TeV range and showing that EFT running between scales is essential and robust against DM loop corrections. The results demonstrate the MPC scenario remains viable under current experimental bounds and highlight the role of RG-improvement in making precise, testable predictions for Higgs-dilaton couplings and DM signatures.

Abstract

Multi-phase critical scenarios explain the observed Higgs boson mass scale by the almost simultaneous occurrence of two smoothly connected phases of the theory, which differ by the selected vacuum configuration. A generic prediction of the framework is the presence of a further light scalar state, the dilaton, which naturally couples weakly to the Higgs boson. The implementation of the framework usually requires the presence of a third, heavier state, which plays the role of dark matter and ensures the couplings run so that the multi-phase criticality condition is met. In this paper we consider the multi-phase criticality limit of an extension of the Standard Model including two extra scalar singlets, addressing the scenario with effective field theory methods that are particularly suited for treating the hierarchical mass spectrum that this construction yields. The analysis improves on the approximated results available in the Literature and explores the phenomenology of the model at collider and dark matter experiments. We find that the running of scalar couplings in the EFT between the two scales cannot be ignored, but the quantum corrections from the dark matter candidate are not noticeably modified.

Figures (6)

• Figure 1: Parametrisation of the quartic couplings and the mixing angle $\theta$ for fixed dilaton VEV, $w = 6000$ GeV.
• Figure 2: Parametrisation of the quartic couplings and the mixing angle $\theta$ for fixed $\lambda_H = 0.129$.
• Figure 3: Spin independent direct detection limits for $\lambda_H = \lambda_H^{\rm SM}$ (light and dark green) and for $w = 6000$ GeV (dark green).
• Figure 4: Constraint plots for a fixed $w = 6 \text{ TeV}$ (left) and for a fixed $\lambda_h =m_h^2/(2v^2)$ (right).
• Figure 5: The Landau pole scale at which the theory becomes nonperturbative for the case where $\lambda_H$ has been fixed to the SM value at $\mu_L$. $m_s$ has been chosen in such a way that the correct relic density is reproduced within $3 \sigma$ limits.