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 6 1.4 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 6 1.7 GeV. Thus, the LEP Higgs-boson mass lower bound excludes any electroweak phase transition in the SM. [S0031-9007(98)08047-8] The observed baryon asymmetry is finally determined at the electroweak phase transition (EWPT) [1]. The understanding of this asymmetry needs a quantitative description of the phase transition. Unfortunately, the perturbative approach breaks down for the physically allowed Higgs-boson masses (e.g., m H . 70 GeV) [2]. In order to understand this nonperturbative phenomenon a systematically controllable technique is used, namely, lattice Monte Carlo (MC) simulations. Since merely the bosonic sector is responsible for the bad perturbative features (due to infrared problems) the simulations are done without the inclusion of fermions. The first results dedicated to these questions were obtained on four-dimensional (4D) lattices [3]. Soon after, simulations of the reduced model in three dimensions were initiated as another approach [4]. This technique contains two steps. The first is a perturbative reduction of the original 4D model to a three-dimensional (3D) one by integrating out the heavy degrees of freedom. The second step is the nonperturbative analysis of the 3D model on the lattice, which is less CPU-time consuming than the MC simulation in the 4D model. The comparison of the results obtained by the two techniques is not only a useful cross-check on the perturbative reduction procedure for heavy bosonic modes, but also could give an indication that the fermions, which behave similarly to the heavy bosonic nodes, might be included perturbatively.In the recent years exhaustive studies have been carried out both in the 4D [5] and in the 3D [6] sectors of the problem. These works determined several cosmologically important quantities such as the critical temperature (T c ), interface tension (s), and latent heat (De).Previous works show that the strength of the first order EWPT gets weaker as the mass of the Higgs-boson increases. Actually the line of the first order phase transitions separating the symmetric and Higgs phases on the m H -T c plane has an end point, m H,c . There are several direct and indirect evidences for that. In four dimensions at m H ഠ 80 GeV the EWPT turned out to be extremely weak, even consistent with the no phase transition scenario on the 1.5s level [7]. 3D results show that for m H . 95 GeV no first order phase transition exists [8] and more specifically that the end point is m H,c ഠ 67 GeV [9,10]. In this Letter we present the analysis of the end point on 4D ...

No abstract

We present a non-perturbative computation of the running of the coupling α s in QCD with two flavours of dynamical fermions in the Schrödinger functional scheme. We improve our previous results by a reliable continuum extrapolation. The Λ-parameter characterizing the high-energy running is related to the value of the coupling at low energy in the continuum limit. An estimate of Λr 0 is given using large-volume data with lattice spacings a from 0.07 fm to 0.1 fm. It translates into Λ (2) MS = 245(16)(16) MeV [assuming r 0 = 0.5 fm]. The last step still has to be improved to reduce the uncertainty.

We determine the renormalization group invariant quark mass corresponding to the sum of the strange and the average light quark mass in the quenched approximation of QCD, using as essential input the mass of the K-mesons. In the continuum limit we find $(M_s + M_{light})/F_K=0.874(29)$, which includes systematic errors. Translating this non-perturbative result into the running quark masses in the $\msbar$-scheme at $\mu=2 GeV$ and using the quark mass ratios from chiral perturbation theory, we obtain $\mbar_s(2 GeV)=97(4) MeV$. With the help of recent results by the CP-PACS Collaboration, we estimate that a 10% higher value would be obtained if one replaced $F_K$ by the nucleon mass to set the scale. This is a typical ambiguity in the quenched approximation.Comment: 23 pages, late

No abstract