End Point of the Hot Electroweak Phase Transition

We study the hot electroweak phase transition by four-dimensional lattice simulations and give the phase diagram. A continuum extrapolation is done. We find that the phase transition is first order for Higgs-boson masses $m_H<66.5\mathrm{}\pm 1.4\mathrm{GeV}$. Above this end point a rapid crossover occurs. Our result agrees with that of the dimensional reduction approach. It also indicates that the fermionic sector of the standard model (SM) may be included perturbatively. We obtain that the end point in the SM is $72.4\pm 1.7\mathrm{GeV}$. Thus, the LEP Higgs-boson mass lower bound excludes any electroweak phase transition in the SM.