[Paper Review] Candidates for dark matter in the ${SU}(3)_C {SU}(3)_L {U}(1)_N$ models

H. N. Long, N. Q. Lan+2 more|ArXiv.org|Nov 21, 2006

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper identifies scalar and fermionic dark matter candidates in the SU(3)C×SU(3)L×U(1)N (3-3-1) model, where the lightest Higgs bosons—specifically a CP-even scalar and a CP-odd pseudoscalar—serve as self-interacting dark matter (SIDM) due to their singlet nature under SM gauge groups. The model naturally stabilizes these states without requiring an additional symmetry, and the Spergel-Steinhardt bound yields a mass range of 4.7–23 MeV for scalar candidates, consistent with the 511 keV INTEGRAL line.

ABSTRACT

It has recently been pointed out that the 511 keV emission line detected by INTEGRAL/SPI from the bulge of our galaxy could be explained by annihilations of light dark matter particles into $e^+ e^-$. We present the possibility that dark matter could be made of scalar candidates, namely, of the Higgs bosons in the models based on ${SU}(3)_C\otimes {SU}(3)_L \otimes {U}(1)_N$ (3-3-1) gauge group. These particles are singlet of the ${SU}(2)_L \otimes {U}(1)_Y$ group, so they do not interact with the ordinary particles, exept the Higgs boson in the standard model. The Spergel-Steinhardt condition for self-interacting dark matter gives a bound on the mass of the candidates to be a few MeVs. Besides the scalar candidates, which exist in both non-SUSY and SUSY 3-3-1 models with right-handed neutrinos, the spin $\fr 1 2$ candidate exists in a variant 3-3-1 version with exotic neutral lepton. In contrast to the singlet models, where an extra symmetry must be imposed to account the stability of the dark matter, here the decay of the candidates is automatically forbidden in all orders of perturbative expansion. This is because of the following feature: these scalars are singlets, i.e., in bottom of the Higgs triplet. Therefore, the standard model fermions and the standard gauge bosons cannot couple with them.

Motivation & Objective

• To identify viable dark matter candidates in the 3-3-1 model that satisfy self-interacting dark matter (SIDM) criteria.
• To explain the 511 keV gamma-ray line from the Galactic bulge via light dark matter annihilation into e⁺e⁻.
• To demonstrate that dark matter stability arises naturally from gauge quantum numbers, avoiding the need for ad hoc global symmetries.
• To explore both scalar and fermionic dark matter candidates in variants of the 3-3-1 model with right-handed neutrinos or exotic neutral leptons.

Proposed method

• Construct a 3-3-1 model with SU(3)C×SU(3)L×U(1)N gauge symmetry, including Higgs triplets transforming under the SU(3)L group.
• Identify scalar and pseudoscalar Higgs states that are singlets under the SM’s SU(2)L×U(1)Y, ensuring minimal coupling to standard model particles.
• Use the Spergel-Steinhardt condition for self-interacting dark matter to constrain the mass of the lightest Higgs state.
• Compute the scalar and pseudoscalar mass spectra via a Higgs potential including trilinear and quartic couplings, with parameters tuned to yield light dark matter candidates.
• Apply the condition that the lightest neutral Higgs must be stable due to its singlet nature, forbidding decay in all perturbative orders.
• Analyze the model’s consistency with anomaly cancellation, asymptotic freedom, and the emergence of natural supersymmetry at ~4 TeV.

Experimental results

Research questions

• RQ1 Can the 511 keV gamma-ray line from the Galactic bulge be explained by light dark matter annihilation into e⁺e⁻ in the 3-3-1 model?
• RQ2 Do scalar Higgs bosons in the 3-3-1 model with right-handed neutrinos qualify as self-interacting dark matter candidates without requiring an additional symmetry?
• RQ3 What is the mass range of the lightest Higgs state that satisfies the Spergel-Steinhardt bound for SIDM in this model?
• RQ4 How does the inclusion of exotic neutral leptons in a variant 3-3-1 model affect the existence and properties of fermionic dark matter candidates?
• RQ5 Can the natural stability of the dark matter candidate be attributed to its gauge quantum numbers rather than an imposed global symmetry?

Key findings

• The lightest neutral scalar Higgs boson in the 3-3-1 model with right-handed neutrinos has a mass in the range 4.7–23 MeV, satisfying the Spergel-Steinhardt condition for self-interacting dark matter.
• The lightest pseudoscalar Higgs state is nearly massless (M₄ ≈ 5 GeV, M₅ = M₆ = 0), indicating the presence of two Goldstone bosons from spontaneous symmetry breaking.
• The scalar dark matter candidate is naturally stable because it is a singlet under the SM’s SU(2)L×U(1)Y group, preventing coupling to standard model gauge bosons and fermions.
• The model predicts a light pseudoscalar Higgs with mass ≈5 GeV, which may contribute to the 511 keV line if it annihilates into e⁺e⁻ via loop-induced processes.
• A spin-1/2 dark matter candidate exists in a variant 3-3-1 model with exotic neutral leptons, offering an alternative to scalar candidates.
• The model realizes natural supersymmetry at ~4 TeV due to the Landau pole at sin²θW = 1/4, consistent with perturbative unification.