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Comparable Dark Matter and Baryon energy densities from Dark Grand Unification

Yi Chung

Abstract

We investigate a theory of $SU(9)$ dark grand unification, where dark matter consists of asymmetric dark baryons from the $Sp(4)_D$ dark QCD sector. By unifying the dark color gauge group with the Standard Model gauge group, the asymmetry generation in both sectors originates from a common process that preserves a $U(1)_{D-(B-L)}$ symmetry, resulting in comparable number densities. Furthermore, thanks to dark grand unification, the $Sp(4)_D$ dark QCD sector shares a similar matter content with the QCD sector, leading to comparable running of the gauge couplings from the scale as high as $10^{15}$ GeV. This predicts a dark color confinement scale and thus dark baryon masses around the GeV scale, comparable to visible baryon masses. Together with the similar number densities, the model provides an explanation for the observed similarity between the energy densities of dark matter and baryons, $ρ_D \approx 5\,ρ_B$. The model also features some novel phenomenology, including a GeV-scale flavored dark QCD sector with diquark dark baryons and light dark mesons. The interaction between the dark sector and the visible sector occurs via a new $Z'$ boson with a mass of $\mathcal{O}(10)$ TeV, which could be searched for at future hadron colliders. We also briefly discuss an $SU(8)$ dark grand unified theory featuring an $SU(3)_D$ dark QCD sector.

Comparable Dark Matter and Baryon energy densities from Dark Grand Unification

Abstract

We investigate a theory of dark grand unification, where dark matter consists of asymmetric dark baryons from the dark QCD sector. By unifying the dark color gauge group with the Standard Model gauge group, the asymmetry generation in both sectors originates from a common process that preserves a symmetry, resulting in comparable number densities. Furthermore, thanks to dark grand unification, the dark QCD sector shares a similar matter content with the QCD sector, leading to comparable running of the gauge couplings from the scale as high as GeV. This predicts a dark color confinement scale and thus dark baryon masses around the GeV scale, comparable to visible baryon masses. Together with the similar number densities, the model provides an explanation for the observed similarity between the energy densities of dark matter and baryons, . The model also features some novel phenomenology, including a GeV-scale flavored dark QCD sector with diquark dark baryons and light dark mesons. The interaction between the dark sector and the visible sector occurs via a new boson with a mass of TeV, which could be searched for at future hadron colliders. We also briefly discuss an dark grand unified theory featuring an dark QCD sector.

Paper Structure

This paper contains 24 sections, 59 equations, 5 figures, 4 tables.

Table of Contents

  1. Motivation
  2. The Model
  3. The choice of dark color gauge group
  4. Fermion content and $SU(9)$ Dark Grand Unification
  5. Scalar content and symmetry breaking pattern
  6. Yukawa interaction terms and fermion masses
  7. Mass spectrum, running couplings, and confinement scales
  8. Conserved $U(1)$ symmetries
  9. The Dark Sector
  10. Dark hadron spectrum in the massless limit
  11. A realistic spectrum with massive dark quarks
  12. Cosmology
  13. Generation of the dark matter and baryon asymmetries
  14. Stability of dark baryon dark matter
  15. Annihilation of the symmetric abundances
  16. ...and 9 more sections

Figures (5)

  • Figure 1: One-loop running of the coupling constants originated from the $SU(9)$ gauge group, including $\alpha_s$, $\alpha_w$, $\alpha_Y$ for the three SM gauge groups and $\alpha_D$ for the dark color group. The running coupling constants of unified group $SU(7)_{\rm DU}\times U(1)_X$ above the $\Lambda_{\rm DU}$ scale are also shown, which ultimately unify at the $\Lambda_{\rm GUT}$ scale. In this figure, the $Sp(4)'$ and $U(1)'_5$ couplings are not included since they are not part of $SU(9)$ gauge group. Furthermore, we assume the $Sp(4)'$ coupling to be infinite in this calculation. The impact of this coupling, especially on dark color confinement scale, will be discussed in the end of the subsection \ref{['sec:Spectrum']}.
  • Figure 2: One-loop running of ${\alpha_s}$ and ${\alpha_D}$ according to different ${\alpha'_4}$.
  • Figure 3: The low energy spectrum of the $Sp(4)$ dark QCD secter in the massless limit. From left to right are the spectrums of mesons (fundamental/antisymmetric quarks), chimera baryons, and glueballs. The PS, V, T, AV, AT, S denote the pseudoscalar, vector, tensor, axial-vector, axial-tensor and scalar mesons of fundamental dark quarks, while letters in lowercase represents mesons of antisymmetric dark quarks. The chimera baryons are denoted following analogy with QCD baryons. The glueball states are labeled by their $J^P$ properties. The left-hand axis shows the masses in units of the gradient-flow scale and the right-hand axis shows the masses in units of decay constant of the fundamental pseudoscalar meson. This summary plot is taken from Ref. Bennett:2023mhh.
  • Figure 4: Feynman diagrams of the relevant decay processes for the generation of the dark matter and baryon asymmetries. From left to right: (1) the tree-level diagram of $\psi_a$ decay, (2) the loop-level diagram of $\psi_a$ decay, and (3) $\psi_c$ decay into SM fermions and dark quarks.
  • Figure 5: Relevant processes among dark hadrons and SM fermions, including (1) dark $\rho$ baryons annihilation (2) dark $\eta$ meson decays (3) interactions between dark $\rho$ baryons and SM fermions.