Accidental Dark Matter: Case in the Scale Invariant Local $B-L$ Models

TL;DR

This work analyzes accidental dark matter (aDM) within a classically scale-invariant local $U(1)_{B-L}$ framework, where hidden-sector Coleman–Weinberg dynamics generate the electroweak scale and SUSY-like stabilization arises without imposed discrete symmetries. The authors classify aDM candidates into a real singlet with accidental $Z_2$ and a $U(1)_{B-L}$-charged complex scalar with accidental $Z_3$, examining their relic densities via Higgs portal and dark Higgs portal, and assessing collider and direct-detection constraints. The $Z_3$ scenario benefits from semi-annihilation, allowing lighter DM and enabling a GeV-scale gamma-ray excess explanation from the galactic center, while the $Z_2$ case often requires heavier DM due to LHC $Z'$ bounds. The results illustrate how DM dynamics can trigger CSI spontaneous breaking and provide distinct experimental signatures, with potential generalization to other local gauge groups.

Abstract

We explore the idea of accidental dark matter (aDM) stability in the scale invariant local $U(1)_{B-L}$ model, which is a theory for neutrino and at the same time radiatively breaks scale invariance via quantum mechanical dynamics in the $U(1)_{B-L}$ sector. A real singlet scalar can be accidental DM with an accidental $Z_2$, by virtue of both extended symmetries. A $U(1)_{B-L}$ charged complex scalar can also be a viable accidental DM due to an accidental (or remanent) $Z_3$. They can reproduce correct relic density via the annihilations through the conventional Higgs portal or dark Higgs portal. The dark Higgs portal scenario is in tension with the LHC bound on $Z_{B-L}$, and only heavy DM of a few TeVs can have correct relic density. In particular, DM may trigger spontaneous breaking of scale Invariance (SISB). The situation is relaxed significantly in the $Z_3$ case due to the effective semi-annihilation mode and then light DM can be accommodated easily. In addition, the $Z_3$ model can accommodate the GeV scale $γ-$ray excess from the galactic center (GC) via semi-annihilation into pseudo Goldstone boson (PGSB). The best fit is achieved at a DM about 52 GeV, with annihilation cross section consistent with the thermal relic density. The invisible Higgs branching ratio is negligible because the Higgs portal quartic coupling is very small $λ_{hφ} \lesssim 10^{-3}$.

Figures (7)

• Figure 1: Plots of the LHC and LEP constraints on the parameter space of $Z'$ in the MSIBL. Upper: exclusion on the $( m_{Z'} , g_{B-L} )$ plane; Lower: exclusion on the $( v_\phi , g_{B-L} )$ plane. In these plots, the two dashed lines show the upper bounds on $g_{B-L}$, 0.5 and 0.7, respectively. The curves labeled with 50 GeV, etc., stand for the masses of the PGSB $\phi$ without considering the dark matter contribution to CW potential.
• Figure 2: Surviving spectrum. All the points satisfy $0.09<\Omega h^2<0.12$ and are allowed by LUX. Top (bottom) left: $Z'$ ($\phi$) in the Higgs portal scenario; Top (bottom) right: $Z'$ ($\phi$) in the dark Higgs portal scenario. The perturbativity bounds on $g_{B-L}$ is schematically presented in two cases, i.e., the line $g_{B-L}=0.5$ and 0.7.
• Figure 3: RGE flows of four couplings with a large $\lambda_{s\phi}(v_\phi)$, left: $\Lambda=10^3v_\phi$; right: $\Lambda=10^{10}v_\phi$. The perturbativity upper bound at $\Lambda$ for the quartic couplings and $g_{B-L}$ are $4\pi$ and $\sqrt{4\pi}$, respectively.
• Figure 4: Status of dark matter under the currently most stringent bound from DM direct search, LUX LUX. In this plot all the points have good relic density, namely have $0.09<\Omega h^2<0.12$. The points in the Higgs portal scenario are around the blue band. While the red points are samples from the mixing effect with $m_\phi$ near $2m_S$, see details in the text.
• Figure 5: Dark Higgs portal scenario on the $v_\phi-g_{B-L}$ plane. The LEP II excludes the region with $v_\phi<3$ TeV. The green and red points belong to the scenarios where DM and $Z'$ dominantly trigger CSI spontaneously breaking, respectively. We have imposed a perturbativity upper bound $\lambda_{s\phi}\leq6.0$ in numerical scanning.