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

Abstract

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 $T=T_c^{\mathrm{EW}}\sim 163$GeV, which is very similar to the behavior in the standard model in perturbation theory. A new phase appears at higher temperatures. $SU(2{)}_L\times U(1{)}_Y$ ($\hat{I}{¸}_H=0$) and $SU(2{)}_R\times U(1{)}_{Y^{\prime }}$ ($\hat{I}{¸}_H=\ddot{I}€$) phases become almost degenerate above $T\sim m_{\mathrm{KK}}$ where $m_{\mathrm{KK}}$ is the Kaluza-Klein mass scale typically around 13TeV and $\hat{I}{¸}_H$ is the Aharonov-Bohm phase along the fifth dimension. The two phases become degenerate at $T=T_c^{\mathrm{LR}}\sim m_{\mathrm{KK}}$. As the temperature drops in the evolution of the early Universe the $SU(2{)}_R\times U(1{)}_{Y^{\prime }}$ phase becomes unstable. The tunneling rate from the $SU(2{)}_R\times U(1{)}_{Y^{\prime }}$ 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 $SU(2{)}_R\times U(1{)}_{Y^{\prime }}$ phase is also given. It is shown that the $W$ boson, $Z$ boson and photon, with $\hat{I}{¸}_H$ varying from 0 to $\ddot{I}€$, are transformed to gauge bosons in the $SU(2{)}_R\times U(1{)}_{Y^{\prime }}$ phase. Gauge couplings and wave functions of quarks, leptons and dark fermions in the $SU(2{)}_R\times U(1{)}_{Y^{\prime }}$ phase are determined.

43 pages, 6 figures, typos corrected