Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Heavy Long-lived Dark Vector Via a Gluonic Portal

Xiaoyong Chu, Qiyuan Gao, Hongkai Liu, Teng Ma, Chengjie Yang

TL;DR

We study a dark vector $Z'$ that couples exclusively to SM gluons through higher-dimensional portals, yielding leading dim-8 operators $Z'GGG$ and $Z'Z'GG$ generated by heavy UV states charged under both QCD and the dark gauge group. CP/C invariance restricts the operator basis to six forms, with $O_5$–$O_6$ enabling $Z'\to ggg$ decays and potentially destabilizing $Z'$, while a residual ${\mathcal Z}_2$ symmetry can forbid those decays and allow $Z'$ to serve as dark matter. The paper maps collider ( monojet+MET, displaced vertices, and multi-jet resonances) and cosmological (BBN, CMB, late-Universe) constraints for unstable $Z'$ and analyzes $Z'$ as DM under freeze-in or freeze-out, including direct and indirect detection. It finds complementary bounds: LHC data constrain $\,\Lambda\lesssim \mathcal{O}(10^4)~$GeV in the unstable case, while cosmology probes up to UV scales $\Lambda \sim 10^9$ GeV; for DM, freeze-in can accommodate a wide mass range with very small couplings, whereas thermal freeze-out is viable only for heavier $Z'$ and is strongly restricted by direct/indirect searches. Overall, the gluonic portal offers a robust, testable long-lived DM framework with clear UV-scale implications and distinctive collider/cosmology signatures.

Abstract

We study a dark gauge boson $ Z' $ that exclusively couples to the QCD gluons through higher dimensional operators. These operators are generated from integrating out of heavy ultraviolet resonances carrying both QCD and dark gauge charges. With $ SU(3)_C $ gauge invariance, charge and parity symmetries preserved, we find that the leading effective operators are restricted to have the form of $ Z'GGG $ and $ Z'Z'GG $ at dimension-eight, which can naturally render the $Z^\prime$ particle long-lived, and serve as a viable dark matter candidate. We investigate the phenomenology of these operators with both collider experiments and cosmological observation, without and with the assumption that this dark gauge boson plays the role of the dominant dark matter component. For an unstable $Z'$, we show that depending on its lifetime, it can be probed by various observables up to ultraviolet physics scale around $10^9$ GeV. For $Z'$ being dark matter, we find that $m_{Z^\prime} \gtrsim 1 $ TeV is consistent with the thermal freeze-out scenario. In contrast, in the freeze-in scenario, the extremely small couplings leave the relevant parameter space largely unconstrained by current experiments.

Heavy Long-lived Dark Vector Via a Gluonic Portal

TL;DR

We study a dark vector that couples exclusively to SM gluons through higher-dimensional portals, yielding leading dim-8 operators and generated by heavy UV states charged under both QCD and the dark gauge group. CP/C invariance restricts the operator basis to six forms, with – enabling decays and potentially destabilizing , while a residual symmetry can forbid those decays and allow to serve as dark matter. The paper maps collider ( monojet+MET, displaced vertices, and multi-jet resonances) and cosmological (BBN, CMB, late-Universe) constraints for unstable and analyzes as DM under freeze-in or freeze-out, including direct and indirect detection. It finds complementary bounds: LHC data constrain GeV in the unstable case, while cosmology probes up to UV scales GeV; for DM, freeze-in can accommodate a wide mass range with very small couplings, whereas thermal freeze-out is viable only for heavier and is strongly restricted by direct/indirect searches. Overall, the gluonic portal offers a robust, testable long-lived DM framework with clear UV-scale implications and distinctive collider/cosmology signatures.

Abstract

We study a dark gauge boson that exclusively couples to the QCD gluons through higher dimensional operators. These operators are generated from integrating out of heavy ultraviolet resonances carrying both QCD and dark gauge charges. With gauge invariance, charge and parity symmetries preserved, we find that the leading effective operators are restricted to have the form of and at dimension-eight, which can naturally render the particle long-lived, and serve as a viable dark matter candidate. We investigate the phenomenology of these operators with both collider experiments and cosmological observation, without and with the assumption that this dark gauge boson plays the role of the dominant dark matter component. For an unstable , we show that depending on its lifetime, it can be probed by various observables up to ultraviolet physics scale around GeV. For being dark matter, we find that TeV is consistent with the thermal freeze-out scenario. In contrast, in the freeze-in scenario, the extremely small couplings leave the relevant parameter space largely unconstrained by current experiments.

Paper Structure

This paper contains 23 sections, 72 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Leading Operators between Dark Gauge Bosons and Gluons
  3. General Phenomenology of the Gluonic $Z^\prime$
  4. The decay of the gluonic $Z^\prime$
  5. Collider Constraints
  6. Missing Energy and Displaced Vertex
  7. Other Constraints at Colliders
  8. Constraints from cosmological observations
  9. Gluonic $Z'$ as a Dark Matter Candidate
  10. Freeze-in Production
  11. Freeze-out Production
  12. Direct detection
  13. Indirect detection
  14. Collider search and other probes
  15. Conclusions
  16. ...and 8 more sections

Figures (8)

  • Figure 1: Dependence of the $Z'$ proper lifetime on the model parameters and its impact on experimental signatures, shown for $Y_1 = 1$ ( left panel) and $Y_2 = 1$ ( right panel). Diagonal lines indicate iso-lifetime contours (e.g., $\tau_{Z'} = 10^{-7}\,\mathrm{sec},\, 10^{-2}\,\mathrm{sec},\, 10^{12}\,\mathrm{sec},\, 10^{27}\,\mathrm{sec}$), representing typical lifetimes that are sensitive to different experiments: purple for collider probes and blue for cosmological probes. These contours partition the plane into several search regimes: prompt decays for $\tau_{Z'}<10^{-7}\,\mathrm{sec}$; displaced vertices for $10^{-7}\,\mathrm{sec}\lesssim\tau_{Z'}\lesssim10^{-2}\,\mathrm{sec}$; and missing-energy channels for $\tau_{Z'}\gtrsim10^{-7}\,\mathrm{sec}$. Cosmological bounds apply to $10^{-2}\,\mathrm{sec}\lesssim\tau_{Z'}\lesssim10^{12}\,\mathrm{sec}$ (BBN) and $10^{12}\,\mathrm{sec}\lesssim\tau_{Z'}\lesssim10^{27}\,\mathrm{sec}$ (CMB/CR). The gray solid line indicates the age of the Universe, serving as a reference for whether the $Z'$ is effectively stable as a DM candidate. The shaded gray region with $\Lambda<m_{Z'}$ marks the breakdown of the EFT approach.
  • Figure 2: The representative leading-order Feynman diagrams contributing to the $Z'$ production at LHC, induced by the operators $\mathcal{O}_{1-6}$. The operators $\mathcal{O}_5$ and $\mathcal{O}_6$ generate a $gggZ^\prime$ vertex corresponding to the leftmost diagram. The four operators $\mathcal{O}_1$ to $\mathcal{O}_4$ generate a $ggZ^\prime Z^\prime$ vertex contributing to the three rightmost diagrams.
  • Figure 3: The quantities $\sigma_{\mathrm{prod}} \times \mathcal{A} \times \epsilon$ for the missing energy ( left panel) and displaced vertex ( right panel) signatures at the ATLAS detector with $\sqrt{s} = 13~\mathrm{TeV}$, evaluated at a fixed cutoff scale $\Lambda = 10~\mathrm{TeV}$. For the missing energy signature, we impose the selection criteria $E_T^{\text{miss}} > 1200~\mathrm{GeV}$, $|\eta_j| < 2.4$, and $\epsilon = 1$. For the displaced vertex signature, we require at least one displaced vertex within $|\eta| < 2.4$ and $\epsilon = 1$. Each line corresponds to the case where a single Wilson coefficient is set to unity while all others are set to zero, with the color coding indicating the associated operator as labeled.
  • Figure 4: Abundance of $\Omega_{Z^{\prime}}$ evaluated at $T = m_{Z^{\prime}}/100$ in the $(m_{Z^{\prime}}, 1/\Lambda)$ plane for $T_{\mathrm{RH}} = 10^{5}\,\mathrm{GeV}$ ( left panel) and $10^{7}\,\mathrm{GeV}$ ( right panel), with $X_{1} = Y_{1} = 1$. The green solid line indicates the thermalization threshold, separating the freeze–in regime (below) from the thermalized regime (above). Three black dashed lines correspond to $\Omega_{Z'} = [1,10^{-10},10^{-20}]\,\Omega_{\mathrm{DM}}$, respectively. The dark gray region denotes $\tau_{Z'} < 10^{-2}\,\mathrm{sec}$ (only appearing in left panel due to the different selected parameter range on the y-axis), which is irrelevant for the cosmological probes.
  • Figure 5: Constraints on an unstable gluonic $Z'$ with $X_1 = Y_1 = 1$ with other coefficients set to zero, for reheating temperature $T_{\mathrm{RH}} = 10^5$ GeV ( left panel) and $10^7$ GeV ( right panel). In both panels, collider bounds from missing-energy searches ATLAS:2021kxv are indicated by the light-gray regions, while displaced-vertex searches ATLAS:2025pakATLAS:2022gbw exclude the red regions. Cosmological limits from BBN Kawasaki:2004quAngel:2025dkw, CMB Acharya:2019uba, and late-Universe observations Planck:2018vygPaopiamsap:2023uuoFermi-LAT:2012pls are shown as distinct blue shaded regions. Orange dashed lines indicates $\Omega_{Z'} = \Omega_{\rm DM}$ generated via the freeze-in mechanism. The dark-gray area marks the EFT-invalid region, where $\Lambda \le m_{Z'}$, while the EFT approach may already become invalid for collider constraints at $1/\Lambda \gtrsim 10^{-3}\,\text{GeV}^{-1}$; same for Fig. \ref{['fig:Zp1-constraints']} below.
  • ...and 3 more figures