We provide nonperturbative evidence for the fact that there is no hot first or second order electroweak phase transition at large Higgs masses, m H 95, 120, and 180 GeV. This means that the line of first order phase transitions separating the symmetric and broken phases at small m H has an end point m H,c . In the minimal standard electroweak theory 70 , m H,c , 95 GeV and most likely m H,c ഠ 80 GeV. If the electroweak theory is weakly coupled and the Higgs boson is found to be heavier than the critical value (which depends on the theory in question), cosmological remnants from the electroweak epoch are improbable.[S0031-9007(96)01335-X]PACS numbers: 11.30. Qc, 11.10.Wx, 11.15.Ha, 98.80.Cq The transition between the high temperature symmetric (or confinement) phase and the low T broken (or Higgs) phase in the standard electroweak theory (MSM) or its extensions is known to be of first order for small values of the Higgs mass m H . This follows from perturbative studies of the effective potential [1] and nonperturbative lattice Monte Carlo simulations [2][3][4]. In the region of applicability of the perturbative expansion the strength of the electroweak phase transition decreases when m H increases. However, the nature of the electroweak phase transition at "large" Higgs masses m H * m W remains unclear, since the perturbative expansion for the description of the phase transition is useless there. This Letter contains the results of the first nonperturbative lattice analysis of the problem for "large" Higgs masses, m H 95, 120, 180 GeV. We shall show that the system behaves very regularly there, much like water above the critical point. As there is no distinction between liquid water and vapor, there is no distinction between the symmetric and broken phases; there is no long-range order.In Ref.[3] it has been shown that in a weakly coupled electroweak theory and in many of its extensions (supersymmetric or not) the hot electroweak (EW) phase transition can be described by an SU͑2͒ 3 U͑1͒ 1 Higgs model in three Euclidean dimensions. Dimensional reduction has its own limitations, described in detail in [3]. For example, for the MSM the 3D approximation is accurate to within a few percent for 30 & m H & 250 GeV. At the lower end of this inequality the high temperature expansion breaks down because the phase transition is very strongly first order and particle masses in the broken phase are ϳT [5]. The upper end is the usual condition for the applicability of perturbation theory in the scalar sector of the MSM. In the minimal sypersymmetric standard model (MSSM) the latter condition is satisfied automatically. Hence, the 3D description is valid for a wide range of the phenomenologically interesting part of the parameter space of the MSM and MSSM.Since the effects of the U(1) subgroup are perturbative deep in the Higgs phase and high in the symmetric phase, the presence of the U(1) factor cannot change the qualitative features of the phase diagram. Thus we shall take sin u W 0. The effective Lagrangian iswhere G a i...

The free energy density, or pressure, of QCD has at high temperatures an expansion in the coupling constant g, known so far up to order g 5 . We compute here the last contribution which can be determined perturbatively, g 6 ln(1/g), by summing together results for the 4-loop vacuum energy densities of two different three-dimensional effective field theories. We also demonstrate that the inclusion of the new perturbative g 6 ln(1/g) terms, once they are summed together with the so far unknown perturbative and non-perturbative g 6 terms, could potentially extend the applicability of the coupling constant series down to surprisingly low temperatures.

We study on the lattice the 3d SU(2)+Higgs model, which is an effective theory of a large class of 4d high temperature gauge theories. Using the exact constant physics curve, continuum (V → ∞, a → 0) results for the properties of the phase transition (critical temperature, latent heat, interface tension) are given. The 3-loop correction to the effective potential of the scalar field is determined. The masses of scalar and vector excitations are determined and found to be larger in the symmetric than in the broken phase. The vector mass is considerably larger than the scalar one, which suggests a further simplification to a scalar effective theory at large m H . The use of consistent 1-loop relations between 3d parameters and 4d physics permits one to convert the 3d simulation results to quantitatively accurate numbers for different physical theories, such as the Standard Model -excluding possible nonperturbative effects of the U(1) subgroup -for Higgs masses up to about 70 GeV. The applications of our results to cosmology are discussed.

We formulate the rules for dimensional reduction of a generic finite temperature gauge theory to a simpler three-dimensional effective bosonic theory in terms of a matching of Green's functions in the full and the effective theory, and present a computation of a generic set of 1-and 2-loop graphs needed for the application of these rules. As a concrete application we determine the explicit mapping of the physical parameters of the standard electroweak theory to a three-dimensional SU(2)×U(1) gauge-Higgs theory. We argue that this three-dimensional theory has a universal character and appears as an effective theory for many extensions of the Standard Model.

We compute how the initial energy density and produced gluon, quark and antiquark numbers scale with atomic number and beam energy in ultrarelativistic heavy ion collisions. The computation is based on the argument that the effect of all momentum scales can be estimated by performing the computation at one transverse momentum scale, the saturation momentum. The initial numbers are converted to final ones by assuming kinetic thermalisation and adiabatic expansion. The main emphasis of the study is at LHC and RHIC energies but it is observed that even at SPS energies this approach leads to results which are not unreasonable: what is usually described as a completely soft nonperturbative process can also be described in terms of gluons and quarks. The key element is the use of the saturation scale.

We develop a method for the construction of the effective potential at high temperatures based on the effective field theory approach and renormalization group. It allows one to sum up the leading logarithms in all orders of perturbation theory. The method reproduces the known one-loop and two-loop results in a very simple and economic way and clarifies the issue of the convergence of the perturbation theory. We also discuss the assumptions being made for the determination of the critical temperature of the electroweak phase transition, and analyse different perturbative uncertainties in its determination. These results are then used for the non-perturbative lattice Monte Carlo simulations of the EW phase transition in forthcoming paper.

We study how bubbles grow after the initial nucleation event in generic first-order cosmological phase transitions characterized by the values of the latent heat L, interface tension a, and correlation length 6, and driven by a scalar order parameter d. Equations coupling b(t,x) and the fluid variables vit,x), T(t,x) and depending on a dissipative constant l-are derived and solved numerically in the ( 1 + 1)-dimensional case starting from a slightly deformed critical bubble configuration #(O,x). The parameters L, u , & corresponding to QCD and electroweak phase transitions are chosen and the whole history of the bubble with the formation of combustion and shock fronts is computed as a function of I?.Both deflagrations and detonations can appear depending on the values of the parameters. Reheating due to collisions of bubbles is also computed. PACS number(s1: 98.80.Cq,

We study to what extent the three-dimensional SU(N) + adjoint Higgs theory can be used as an effective theory for finite temperature SU(N) gauge theory, with N = 2, 3. The parameters of the 3d theory are computed in 2-loop perturbation theory in terms of T /Λ MS , N, N f . The perturbative effective potential of the 3d theory is computed to two loops for N = 2. While the Z(N) symmetry probably driving the 4d confinementdeconfinement phase transition (for N f = 0) is not explicit in the effective Lagrangian, it is partly reinstated by radiative effects in the 3d theory. Lattice simulations in the 3d theory are carried out for N = 2, and the static screening masses relevant for the high-temperature phase of the 4d theory are measured. In particular, we measure non-perturbatively the O(g 2 T ) correction to the Debye screening mass. We find that non-perturbative effects are much larger in the SU(2) + adjoint Higgs theory than in the SU(2) + fundamental Higgs theory.