拓扑整数绕数暗物质：由 $\pi_2(\mathrm{SU}(3)/\mathrm{SO}(3)) = \mathbb{Z}$ 保证的稳定性
Topological Integer-Winding Dark Matter with a Dark Higgs Triplet: Stability from $π_2(\mathrm{SU}(3)/\mathrm{SO}(3)) = \mathbb{Z}$
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中文总结 AI 辅助
提出基于 SU(3)_dark→SO(3)_dark×Z_2 破缺产生拓扑稳定暗物质的模型，预言质量比与引力波信号，可被 FCC-ee 和 LISA 检验。
中文摘要 AI 辅助
我们提出一个暗物质模型，其中对称性破缺模式 SU(3)_dark → SO(3)_dark × Z_2 产生绝对稳定的点状拓扑缺陷，由 $\pi_2(\mathrm{SU}(3)/[\mathrm{SO}(3) \times \mathrm{Z}_2]) = \mathbb{Z}$ 分类。所得暗八重态中最轻的中性成员 $\chi^0$ 仅通过动力学混合门户（$g_f = 10^{-3}$）和引力与标准模型场耦合。一个包含量子数暗性 $T_{\mathrm{dark}}$ 的扩展 Gell-Mann-Okubo 质量算符预言了两个与尺度无关的质量比：$r_{21} = M(\chi^{++})/M(\chi^0) = 1.042 \pm 0.003$ 和 $r_{31} = M(\Sigma^0_{\mathrm{dark}})/M(\chi^0) = 0.809 \pm 0.004$，可在 FCC-ee 上被证伪。包含共湮灭的八个耦合玻尔兹曼方程在 $M_0 = 150$ GeV 时给出 $\Omega_{\mathrm{DM}} h^2 = 0.120$。自相互作用截面满足从矮星系到子弹星系团的所有天体物理约束。该模型预言了在 $f_* = 1.65$ mHz 处的随机引力波背景（LISA，信噪比 SNR = 8.5）以及在 $r_{\mathrm{DAO}} = 2.3 \pm 0.4$ Mpc 处的暗声学振荡（SKA）。
英文摘要
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).
发表机构
- Max-Planck-Institut für Physik（马克斯·普朗克物理研究所）
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