Dark matter trio in classically conformal theories: WIMP, supercooling, and monopole

Abstract

Beyond solving the hierarchy problem, classically conformal (CC) theories naturally accommodate dark matter (DM). In this work, we explore the CC $SU(2)_X$ gauge theory with a triplet dark scalar, uncovering three distinct DM scenarios: WIMP, supercooled DM, and monopole. The production mechanisms are strongly influenced by the CC model's unique first-order phase transition evolution history, which differs significantly from those in non-conformal models. We obtain the viable parameter space for each scenario and investigate the current constraints and future sensitivities at terrestrial experiments and gravitational wave observatories.

Figures (5)

• Figure 1: Contours of FOPT characteristic parameters $\alpha$ (purple), $\beta /H$ (blue), $T_*$ (green), and $T_{\text{rh}}$ (red) for $m_s<m_h$ (left) and $m_s>m_h$ (right). The black and gray shaded areas denote the unphysical and $w < 1 \text{ TeV}$ regions, respectively, while the gray dashed line separates FOPT from non-FOPT areas. In the right panel, the black dashed line is the boundary of different thermal history patterns.
• Figure 2: Valid DM scenarios in the $(m_X, m_s)$ plane for $m_s < m_h$ (left) and $m_s > m_h$ (right). Bold colored curves indicate parameter space with the correct DM relic abundance: WIMP (green), supercooled DM (blue), and monopole DM (red, left panel only). Contours of $g_X$ and $\theta$ are shown as orange and magenta contours, respectively. All other conventions follow Fig. \ref{['fig:foptparam']}.
• Figure 3: Experimental constraints and projected sensitivities in the $(m_X, m_s)$ plane for $m_s < m_h$ (left) and $m_s > m_h$ (right). Medium gray: collider and beam-dump experiment exclusions; light gray: astrophysical bound from SN1987A; hatched gray: direct detection limits. Colored dashed contours (left) show the projected reach of LLP searches. Blue and light-blue shaded regions (right) indicate the sensitivity of LISA and BBO to the stochastic GW background from the FOPT. Colored regions near $m_X\sim\text{TeV}$ (right) depict collider constraints and projections (see Fig. \ref{['fig:zoom']} for details). Other conventions follow Figs. \ref{['fig:foptparam']} and \ref{['fig:DM']}.
• Figure 4: Zoomed-in view of the right panel of Fig. \ref{['fig:DM_ex']}. Shaded regions show collider constraints and projections: LHC Run 2 (semi-transparent black), HL-LHC extrapolation (purple), and a 10 TeV muon collider ($\mu$C) with $s$ produced via VBF and decaying to $b\bar{b}$ (light green), $VV$ (orange), and $hh$ (red). Conventions follow Fig. \ref{['fig:DM_ex']}.
• Figure A1: Scaling of $(S_3/T)g_X^3$ with $(1 - T_{\text{roll}}/T)$. At fixed $w = 10^6$ GeV, numerical results for $g_X = 10^{-1}$, $10^{-2}$, and $10^{-3}$ collapse onto a universal line, confirming the analytical scaling of Eq. \ref{['eq:S3_approx']} (dashed line).