[Paper Review] Towards a Higgs mass determination in asymptotically safe gravity with a dark portal

Astrid Eichhorn, Martin Pauly+1 more|arXiv (Cornell University)|Jul 16, 2021

Particle physics theoretical and experimental studiesPhysics and Astronomy229 references27 citations

TL;DR

This paper proposes a toy model extending the Standard Model with a dark scalar and fermion coupled via a Higgs portal and asymptotically safe quantum gravity to predict the Higgs mass from first principles. By leveraging asymptotic safety, the dark sector's single free parameter—enabled by spontaneous symmetry breaking—induces significant Higgs mass reduction through tree-level mixing, successfully reconciling the theoretical prediction with the observed 125 GeV Higgs mass.

ABSTRACT

There are indications that an asymptotically safe UV completion of the Standard Model with gravity could constrain the Higgs self-coupling, resulting in a prediction of the Higgs mass close to the vacuum stability bound in the Standard Model. The predicted value depends on the top quark mass and comes out somewhat higher than the experimental value if the current central value for the top quark mass is assumed. Beyond the Standard Model, the predicted value also depends on dark fields coupled through a Higgs portal. Here we study the Higgs self-coupling in a toy model of the Standard Model with quantum gravity that we extend by a dark scalar and fermion. Within the approximations used in arXiv:2005.03661 , there is a single free parameter in the asymptotically safe dark sector, as a function of which the predicted (toy model) Higgs mass can be lowered due to mixing effects if the dark sector undergoes spontaneous symmetry breaking.

Motivation & Objective

• To explore whether asymptotic safety in quantum gravity can predict the Higgs mass within a UV-completed Standard Model extension.
• To investigate how a dark scalar and fermion sector, coupled via a Higgs portal, affects the Higgs mass prediction under asymptotic safety.
• To determine whether spontaneous symmetry breaking in the dark sector can significantly lower the predicted Higgs mass to match the observed 125 GeV value.
• To assess whether the resulting model can simultaneously provide a viable dark matter candidate while satisfying cosmological constraints.
• To evaluate the predictive power of asymptotic safety in reducing the parameter space of BSM models compared to effective field theories.

Proposed method

• Uses the functional renormalization group (FRG) approach to study the RG flow of couplings from the UV fixed point to the IR.
• Introduces a toy model with a real scalar (Higgs), a fermion (top quark analog), a dark scalar, and a dark fermion, all coupled via a Higgs portal and Yukawa interactions.
• Imposes asymptotic safety by requiring all beta functions to vanish at a UV fixed point, reducing the dark sector to a single free parameter.
• Performs a fixed-Yukawa scan to isolate the effect of the dark sector on the Higgs mass while keeping the visible Yukawa coupling constant.
• Analyzes the impact of tree-level mixing between the visible and dark scalars on the physical Higgs mass, particularly when the dark scalar undergoes spontaneous symmetry breaking.
• Evaluates cosmological constraints, including BBN bounds on relativistic degrees of freedom and dark matter relic density, to test viability.

Experimental results

Research questions

• RQ1 Can asymptotic safety in quantum gravity predict the Higgs mass in a UV-completed Standard Model with a dark portal?
• RQ2 How does the inclusion of a dark scalar and fermion sector affect the predicted Higgs mass under asymptotic safety?
• RQ3 What role does spontaneous symmetry breaking in the dark sector play in modifying the Higgs mass prediction?
• RQ4 Can the model simultaneously predict a Higgs mass of 125 GeV and provide a viable dark matter candidate?
• RQ5 To what extent does asymptotic safety reduce the parameter space of BSM models compared to effective field theory approaches?

Key findings

• The predicted Higgs mass in the pure Standard Model with asymptotic safety exceeds the observed 125 GeV when using the central top quark mass value.
• Spontaneous symmetry breaking in the dark scalar sector leads to significant tree-level mixing with the Higgs, which can lower the predicted Higgs mass to match the observed value.
• Without dark sector symmetry breaking, the modification to the Higgs mass is negligible, indicating that SSB is essential for a large effect.
• The single free parameter in the dark sector—arising from asymptotic safety—can be tuned to reproduce the observed Higgs mass of 125 GeV.
• The dark fermion acquires mass after dark scalar SSB and becomes a stable, finite-relic-density dark matter candidate, consistent with BBN constraints.
• The model satisfies cosmological bounds: the dark scalar is unstable (zero relic density), and the dark fermion’s relativistic degrees of freedom do not overclose the universe.