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arXiv 2104.02870hep-ph
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$SO(5) \times U(1) \times SU(3)$规范-Higgs统一中的电弱和左右相变

Electroweak and Left-Right Phase Transitions in $SO(5) \times U(1) \times SU(3)$ Gauge-Higgs Unification

Shuichiro Funatsu, Hisaki Hatanaka, Yutaka Hosotani, Yuta Orikasa, Naoki Yamatsu

备注：
43 pages, 6 figures, typos corrected
发表信息：
Phys. Rev. D 104, 115018 (2021)
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摘要：

GUT激发的$SO(5)\times U(1) \times SU(3)$规范-Higgs统一中的电弱相变被证明是弱的一级相变，并且发生在$T = T_c^{\rm EW} \sim 163\,$ GeV，这与微扰理论中标准模型中的行为非常相似。在较高温度下出现新相。$SU(2)_L \times U(1)_Y$（$θ_H=0$）和$SU(2)_R \times U(1)_{Y'}$（$θ_H=π$）相在$T \sim m_{\rm KK}$以上变得几乎简并，其中$m_{\rm KK}$是通常在13 $\,$ TeV左右的卡鲁扎-克莱因质量标度，而$θ_H$是沿第五维的阿哈罗诺夫-玻姆相。两相在$T = T_c^{\rm LR} \sim m_{\rm KK}$处退化。随着早期宇宙演化过程中温度的下降，$SU(2)_R \times U(1)_{Y'}$相变得不稳定。从$SU(2)_R \times U(1)_{Y'}$相到$SU(2)_L \times U(1)_Y$相的隧穿速率变得相当大，并且在$T=2.5 \sim 2.6\,$ TeV处发生一级相变。在这种左右相变中产生的引力波数量很小，远低于激光干涉仪空间天线（LISA）的灵敏度。还给出了对$SU(2)_R \times U(1)_{Y'}$阶段的详细分析。结果表明，$W$玻色子，$Z$玻色子和光子，$θ_H$从0到$π$变化，在$SU(2)_R \times U(1)_{Y'}$相位转化为规范玻色子。确定了$SU(2)_R \times U(1)_{Y'}$相中夸克、轻子和暗费米子的规范耦合和波函数。

英文摘要：

The electroweak phase transition in GUT inspired $SO(5)\times U(1) \times SU(3)$ gauge-Higgs unification is shown to be weakly first order and occurs at $T = T_c^{\rm EW} \sim 163\,$GeV, which is very similar to the behavior in the standard model in perturbation theory. A new phase appears at higher temperatures. $SU(2)_L \times U(1)_Y$ ($θ_H=0$) and $SU(2)_R \times U(1)_{Y'}$ ($θ_H=π$) phases become almost degenerate above $T \sim m_{\rm KK}$ where $m_{\rm KK}$ is the Kaluza-Klein mass scale typically around 13$\,$TeV and $θ_H$ is the Aharonov-Bohm phase along the fifth dimension. The two phases become degenerate at $T = T_c^{\rm LR} \sim m_{\rm KK}$. As the temperature drops in the evolution of the early Universe the $SU(2)_R \times U(1)_{Y'}$ phase becomes unstable. The tunneling rate from the $SU(2)_R \times U(1)_{Y'}$ phase to the $SU(2)_L \times U(1)_Y$ phase becomes sizable and a first-order phase transition takes place at $T=2.5 \sim 2.6\,$TeV. The amount of gravitational waves produced in this left-right phase transition is small, far below the reach of the sensitivity of Laser Interferometer Space Antenna (LISA). A detailed analysis of the $SU(2)_R \times U(1)_{Y'}$ phase is also given. It is shown that the $W$ boson, $Z$ boson and photon, with $θ_H$ varying from 0 to $π$, are transformed to gauge bosons in the $SU(2)_R \times U(1)_{Y'}$ phase. Gauge couplings and wave functions of quarks, leptons and dark fermions in the $SU(2)_R \times U(1)_{Y'}$ phase are determined.

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