QCD-induced Electroweak Phase Transition

Abstract

Phase transitions associated with nearly conformal dynamics are known to lead to significant supercooling. A notorious example is the phase transition in Randall-Sundrum models or their CFT duals. In fact, it was found that the phase transition in this case is first-order and the tunneling probability for the radion/dilaton is so small that the system typically remains trapped in the false vacuum and the phase transition never completes. The universe then keeps expanding and cooling. Eventually the temperature drops below the QCD scale. We show that the QCD condensates which subsequently form give an additional contribution to the radion/dilaton potential, an effect which had been ignored so far. This significantly reduces the barrier in the potential and allows the phase transition to complete in a substantially larger region of parameter space. Due to the supercooling, electroweak symmetry is then broken simultaneously. This class of models therefore naturally leads to an electroweak phase transition taking place at or below QCD temperatures, with interesting cosmological implications and signatures.

Figures (5)

• Figure 1: Schematic plot of the QCD confinement scale $\Lambda_{\rm QCD}$ as a function of the IR scale $\mu$ for $\mu_{\rm min}=2.5 \,$TeV, $n_c=3$ and $n=0.1,0.2,0.3,0.4,0.5$ (in blue, yellow, green, red, purple).
• Figure 2: The radion potential plotted around the Goldberger-Wise barrier without (left) and with (right) the contribution from the gluon condensate for $\mu_{\rm min}=2.5\,$TeV, $n = 0.15$, $n_c=3$, $\epsilon = 1/20$, $v_{\rm IR}=1$ and $\delta=-1/2$. The combined potential is negative near the origin because the gluon condensate contributes with a negative sign, while the Goldberger-Wise potential vanishes there. For better comparison, we have shifted the combined potential to make it vanish at the origin too. Notice that the barrier does not completely disappear even with the contribution from the gluon condensate.
• Figure 3: Schematic plot of the combined potential for the AdS-Schwarzschild and Randall-Sundrum spaces, glued together at the origin and evaluated at the critical temperature.
• Figure 4: Results for $\mu_{\rm min}=2.5\,$TeV and $N=4.5$ without the QCD effect. For the left panel, we have fixed $\tilde{\delta}=-0.5$, and for the right panel, $v_{_{\rm IR}} =0.5$. Regions where the phase transition can complete via the nucleation of $O(4)$-symmetric bubbles are shown in green, while regions where the nucleation rate is too low are colored in red. Regions above the purple dashed and dotted lines are allowed according to the analytical estimate of the bubble action for $O(4)$- and $O(3)$-symmetric bubbles, respectively. In the hashed region (above the black, dashed line in the left panel and to right of the black, dashed line in the right panel), the backreaction constraint is not fulfilled. The blue, orange, green, red dashed-dotted lines (from bottom to top in the left panel and in the reversed order in the right panel) correspond to the radion mass being $m_{\rm radion} = 200\, \text{GeV}, 600\, \text{GeV}, 1\, \text{TeV}, 1.4\, \text{TeV}$, respectively.
• Figure 5: Results for $\mu_{\rm min }=2.5 \, \text{TeV}$, $N=4.5$ and $n=0.1$ and $n=0.3$ when the QCD effect is included. For the left panel, we have fixed $\tilde{\delta}=-0.5$, and for the right panel, $v_{_{\rm IR}} =0.5$. Regions where the phase transition can complete via the nucleation of $O(4)$-symmetric bubbles for both $n=0.1$ and $n=0.3$ are shown in green. This to be compared with the allowed regions in fig. \ref{['fig:Resultsna0']} without the QCD effect. Regions where the nucleation rate is too low are colored in pale (dark) red for $n=0.3$ ($n=0.1$). The corresponding green dashed lines delimit the region satisfying eq. \ref{['CondensateEffectRegion']}, where we expect the QCD effect to be important. In the hashed region (above the black, dashed line in the left panel and to right of the black, dashed line in the right panel), the backreaction constraint is not fulfilled. The radion masses are as in fig. \ref{['fig:Resultsna0']}.