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$\mathbb Z_2$-Stable Dark Matter via Broken $\text{SU}(5)$ Gauge Bosons

E. J. Thompson

TL;DR

The paper embeds a stable dark matter candidate in SU(5) by exploiting the broken directions associated with the leptoquark vectors $X$ and $Y$ through a gauge-covariant projector formalism. A $Z_2$ symmetry guarantees DM stability and sequestering from SM gauge fields, while two UV realizations (Model A with a dimension-8 portal and Model B with a dimension-6 portal) govern how the dark sector communicates with the SM. Integrating out the heavy XY states yields ultra-feeble portals and a loop-induced gluon coupling that is negligibly small at GUT-scale masses, making direct detection ineffective. Cosmology proceeds via UV freeze-in, with Model B naturally reproducing the observed relic density for reasonable reheating temperatures and $M_X$, whereas Model A requires higher $T_R$ or additional Higgs portals. Proton-decay bounds fix the heavy scale $M_X$ in the canonical GUT window, tying the DM origin directly to GUT dynamics and preserving standard $\Lambda$CDM structure on cosmological scales.

Abstract

I construct and analyze a dark matter sector that is neutral under the unbroken Standard Model gauge group and couples only to the broken $\text{SU}(5)$ gauge directions, the leptoquark vectors $X,Y$. An exact $\mathbb Z_2$ renders the dark matter stable. I give a gauge-covariant definition of projectors onto the unbroken Standard Model and broken ($X,Y$) subspaces, demonstrate that the covariant derivative of dark matter selects only $X,Y$, and integrate out $X,Y$ at tree level to obtain the leading effective operators. I also derive the loop-induced $χ^2\,G^a_{μν}G^{aμν}$ coupling to gluons, prove color neutrality, and show consistency with cold dark matter phenomenology. Cosmological production proceeds via UV freeze-in or even more suppressed channels in.

$\mathbb Z_2$-Stable Dark Matter via Broken $\text{SU}(5)$ Gauge Bosons

TL;DR

The paper embeds a stable dark matter candidate in SU(5) by exploiting the broken directions associated with the leptoquark vectors and through a gauge-covariant projector formalism. A symmetry guarantees DM stability and sequestering from SM gauge fields, while two UV realizations (Model A with a dimension-8 portal and Model B with a dimension-6 portal) govern how the dark sector communicates with the SM. Integrating out the heavy XY states yields ultra-feeble portals and a loop-induced gluon coupling that is negligibly small at GUT-scale masses, making direct detection ineffective. Cosmology proceeds via UV freeze-in, with Model B naturally reproducing the observed relic density for reasonable reheating temperatures and , whereas Model A requires higher or additional Higgs portals. Proton-decay bounds fix the heavy scale in the canonical GUT window, tying the DM origin directly to GUT dynamics and preserving standard CDM structure on cosmological scales.

Abstract

I construct and analyze a dark matter sector that is neutral under the unbroken Standard Model gauge group and couples only to the broken gauge directions, the leptoquark vectors . An exact renders the dark matter stable. I give a gauge-covariant definition of projectors onto the unbroken Standard Model and broken () subspaces, demonstrate that the covariant derivative of dark matter selects only , and integrate out at tree level to obtain the leading effective operators. I also derive the loop-induced coupling to gluons, prove color neutrality, and show consistency with cold dark matter phenomenology. Cosmological production proceeds via UV freeze-in or even more suppressed channels in.

Paper Structure

This paper contains 8 sections, 31 equations, 1 figure.

Table of Contents

  1. Introduction
  2. $\text{SU}(5)$ Decomposition and Lie--algebra projectors
  3. Dark sector and $\mathbb Z_2$ stability
  4. Integrating out $X,Y$
  5. Loop-induced $\chi^2 G^a_{\mu\nu}G^{a\mu\nu}$ and direct detection
  6. Cosmological production and CDM properties
  7. Low-energy SM limit and proton-decay bounds
  8. Conclusions and outlook

Figures (1)

  • Figure 1: Toy galaxy rotation curve illustrating the separate contributions of the bulge, stellar disk, and a spherical dark–matter halo to the circular velocity $v_c(R)$. The solid blue, orange, and green curves show $v_{\rm bulge}(R)$, $v_{\rm disk}(R)$, and $v_{\rm DM}(R)$, respectively. The red dashed curve is the total baryonic contribution $v_{\rm bar} = (v_{\rm bulge}^2 + v_{\rm disk}^2)^{1/2}$, which decreases at large radii, while the purple dash–dotted curve includes the dark–matter halo and yields an approximately flat rotation curve. Brown points with error bars represent cartoon "observed" data for a Milky–Way–like galaxy.