Endpoint of the hot electroweak phase transition

Abstract

We give the nonperturbative phase diagram of the four-dimensional hot electroweak phase transition. The Monte-Carlo analysis is done on lattices with different lattice spacings ($a$). A systematic extrapolation $a \to 0$ is done. Our results show that the finite temperature SU(2)-Higgs phase transition is of first order for Higgs-boson masses $m_H<66.5 \pm 1.4$ GeV. At this endpoint the phase transition is of second order, whereas above it only a rapid cross-over can be seen. The full four-dimensional result agrees completely with that of the dimensional reduction approximation. This fact is of particular importance, because it indicates that the fermionic sector of the Standard Model can be included perturbatively. We obtain that the Higgs-boson endpoint mass in the Standard Model is $72.4 \pm 1.7$ GeV. Taking into account the LEP Higgs-boson mass lower bound excludes any electroweak phase transition in the Standard Model.

Figures (4)

• Figure 1: Schematic view of the phase diagram. The solid line represents the LCP defined by the endpoint condition. The numbers on the line correspond to the temporal extension for which the endpoint is realized (the dashed lines show their projection to the $\kappa$ - $\lambda$ plane). The dotted lines running into these numbered points correspond to first order phase transitions for $g_R^2$ = const. but different $R_{HW}$-s. A LCP defined by a constant $R_{HW}$ value is shown by the long dashed line.
• Figure 2: Dependence of $c_2$ on $\lambda$ for $L_t=3$.
• Figure 3: Dependence of $R_{HW,c}$, i.e. $R_{HW}$ corresponding to the endpoint of first order phase transitions on $1/L_t^2$ and extrapolation to the infinite volume limit.
• Figure 4: Phase diagram of the SU(2)-Higgs model in the ($T_c /m_H - R_{HW}$) plane. The continuous line -- representing the phase-boundary -- is a quadratic fit to the data points.