Topological Integer-Winding Dark Matter with a Dark Higgs Triplet: Stability from ${\pi }_2(\mathrm{SU}(3)/\mathrm{SO}(3))=\mathbb{Z}$

Abstract

We propose a dark matter model in which the symmetry-breaking pattern SU(3)_dark -> SO(3)_dark x Z_2 produces absolutely stable point-like topological defects classified by pi_2(SU(3)/[SO(3) x Z_2]) = Z. The lightest neutral member chi^0 of the resulting dark octet, with mass M(chi^0) = 165.67 GeV, couples to Standard Model fields only through a kinetic-mixing portal (g_f = 10^-3) and gravity. A dark Higgs triplet Delta_dark with vacuum expectation value v_Delta = 17 GeV and Yukawa coupling y_chi = 0.10 generates a tree-level splitting Delta M(chi^+ - chi^0) = 1.70 GeV, opening the decay chi^+ -> chi^0 + phi^+ and ensuring that chi^0 is the unique stable relic. An extended Gell-Mann-Okubo mass operator incorporating the quantum number darkicity T_dark predicts three scale-independent mass ratios, r_21 = M(chi^++)/M(chi^0) = 1.089 +/- 0.005, r_31 = M(Sigma^0_dark)/M(chi^0) = 1.163 +/- 0.006, and r_41 = M(Lambda_dark)/M(chi^0) = 1.260 +/- 0.008, falsifiable at FCC-ee. Eight coupled Boltzmann equations with co-annihilation yield Omega_DM h^2 = 0.120 at M_0 = 208.67 GeV. Self-interaction cross-sections satisfy all astrophysical bounds from dwarf galaxies to the Bullet Cluster. The model predicts a stochastic gravitational-wave background at f_* = 1.65 mHz (LISA, SNR = 8.5) and dark acoustic oscillations at r_DAO = 2.3 +/- 0.4 Mpc (SKA).

arXiv comment5 pages, 2 tables. Supplemental Material (16 pages +1 Figure) available as ancillary file. v2: Major revision after consistency analysis. The mass spectrum has been corrected to satisfy eta > delta and to place all octet partners above chi0. A dark Higgs triplet has been added. Updated values: M_0 = 208.67 GeV, beta = -15 GeV, eta = 8 GeV. Supersedes v1