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Stabilizing dark matter with quantum scale symmetry

Abhishek Chikkaballi, Kamila Kowalska, Rafael R. Lino dos Santos, Enrico Maria Sessolo

TL;DR

The paper demonstrates that trans-Planckian quantum scale symmetry, implemented as Gaussian IR-attractive fixed points in the RG flow, can forbid otherwise allowed Yukawa interactions and thereby sequester sectors in a gauge-Yukawa theory. By embedding this mechanism in a concrete SU(6) GUT, it yields a spectrally predictable DM sector whose interactions and masses are largely fixed by the UV completion, with DM phenomenology tied to low-energy observables such as a $Z'$ resonance and relic abundance. The study shows two-component DM possibilities (singlet and/or SU(2)_L doublet) and analyzes how UV-driven Yukawa predictions constrain DM masses, stability, and annihilation channels, while relic-density and collider bounds narrow viable parameter space. Importantly, the results illustrate that UV gravity effects can leave testable imprints on particle phenomenology, linking high-scale quantum gravity to TeV-scale DM physics. The framework is readily extensible to larger SU(N) groups, suggesting a general pathway to UV-complete, predictive DM within AS-inspired GUTs.

Abstract

In the context of gauge-Yukawa theories with trans-Planckian asymptotic safety, quantum scale symmetry can prevent the appearance in the Lagrangian of couplings that would otherwise be allowed by the gauge symmetry. Such couplings correspond to irrelevant Gaussian fixed points of the renormalization group flow. Their absence in the theory implies that different sectors of the gauge-Yukawa theory are secluded from one another, in similar fashion to the effects of a global or a discrete symmetry. As an example, we impose the trans-Planckian scale symmetry on a model of Grand Unification based on the gauge group SU(6), showing that it leads to the emergence of several fermionic WIMP dark matter candidates whose coupling strengths are entirely predicted by the UV completion.

Stabilizing dark matter with quantum scale symmetry

TL;DR

The paper demonstrates that trans-Planckian quantum scale symmetry, implemented as Gaussian IR-attractive fixed points in the RG flow, can forbid otherwise allowed Yukawa interactions and thereby sequester sectors in a gauge-Yukawa theory. By embedding this mechanism in a concrete SU(6) GUT, it yields a spectrally predictable DM sector whose interactions and masses are largely fixed by the UV completion, with DM phenomenology tied to low-energy observables such as a resonance and relic abundance. The study shows two-component DM possibilities (singlet and/or SU(2)_L doublet) and analyzes how UV-driven Yukawa predictions constrain DM masses, stability, and annihilation channels, while relic-density and collider bounds narrow viable parameter space. Importantly, the results illustrate that UV gravity effects can leave testable imprints on particle phenomenology, linking high-scale quantum gravity to TeV-scale DM physics. The framework is readily extensible to larger SU(N) groups, suggesting a general pathway to UV-complete, predictive DM within AS-inspired GUTs.

Abstract

In the context of gauge-Yukawa theories with trans-Planckian asymptotic safety, quantum scale symmetry can prevent the appearance in the Lagrangian of couplings that would otherwise be allowed by the gauge symmetry. Such couplings correspond to irrelevant Gaussian fixed points of the renormalization group flow. Their absence in the theory implies that different sectors of the gauge-Yukawa theory are secluded from one another, in similar fashion to the effects of a global or a discrete symmetry. As an example, we impose the trans-Planckian scale symmetry on a model of Grand Unification based on the gauge group SU(6), showing that it leads to the emergence of several fermionic WIMP dark matter candidates whose coupling strengths are entirely predicted by the UV completion.
Paper Structure (23 sections, 62 equations, 6 figures, 4 tables)

This paper contains 23 sections, 62 equations, 6 figures, 4 tables.

Table of Contents

  1. Introduction
  2. General notions of asymptotic safety
  3. Vanishing couplings from quantum scale symmetry
  4. SU(6) GUT
  5. General introduction
  6. The model
  7. Trans-Planckian fixed points
  8. Naturally small Yukawa couplings
  9. Scalar potential
  10. Predictions for dark matter
  11. Two-component dark matter
  12. Singlet fermion DM ($v_{s_{21}} < v_{s_6}$)
  13. Doublet DM ($v_{s_{6}}\ll v_{s_{21}}$)
  14. Summary and conclusions
  15. SU(6) scalar potential
  16. ...and 8 more sections

Figures (6)

  • Figure 1: The three diagrams of the upper row contribute to the beta function of Yukawa coupling $y_{11}$. The three diagrams of the lower row contribute to the beta function of Yukawa coupling $y_{12}$.
  • Figure 2: (a) The RG flow of the SU(6) Yukawa (solid) and gauge (dotted) couplings from the deep trans-Planckian UV to the EWSB scale for $f_g=0.05$ and $f_y=0.016$. We have selected $\tan\beta=1$ at the EWSB scale. (b) The flow of the SU(6) Yukawa (solid) and gauge (dotted) couplings from the deep trans-Planckian UV to the EWSB scale for $f_g=0.01$ and $f_y=0.016$. (c) The flow of the top-quark Yukawa coupling from the deep trans-Planckian UV to the EWSB scale for $f_g=0$ and different choices of the fixed point, corresponding to different $f_y$.
  • Figure 3: Trans-Planckian RG flow of the Yukawa couplings from the deep UV fixed point of Table \ref{['tab:fixpointUV']}. Solid lines show the couplings that are predictions of the theory, while dashed and dot-dashed are the couplings that can be freely adjusted.
  • Figure 4: Decay chains of the heavy Majorana fermions $N_1$, $N_2$, $N_3$, and $N_4$ in the presence of non-zero (yet arbitrarily small) Yukawa couplings $\tilde{y}_{11}$ and $\tilde{y}_{22}$.
  • Figure 5: The region of under-abundant relic density (in blue) in the SM-singlet DM case.
  • ...and 1 more figures