Mikko Laine

The Pressure of hot QCD up to g6 ln(1/g)

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.

Generic rules for high temperature dimensional reduction and their application to the standard model

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 Greens 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)xU(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 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.

THE ELECTROWEAK PHASE TRANSITION: A NON-PERTURBATIVE ANALYSIS

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 (

Quark mass thresholds in QCD thermodynamics

V\to\infty, a\to 0

Is There a Hot Electroweak Phase Transition at mH > ∼ mW?

) 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 Higgs masses. 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 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 mH. 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.

Lightest sterile neutrino abundance within the nuMSM

We discuss radiative corrections to how quark mass thresholds are crossed, as a function of the temperature, in basic thermodynamic observables such as the pressure, the energy and entropy densities, and the heat capacity of high temperature QCD. The indication from leading order that the charm quark plays a visible role at surprisingly low temperatures, is confirmed. We also sketch a way to obtain phenomenological estimates relevant for generic expansion rate computations at temperatures between the QCD and electroweak scales, pointing out where improvements over the current knowledge are particularly welcome.

3D SU(N) + ADJOINT HIGGS THEORY AND FINITE TEMPERATURE QCD

We provide non-perturbative evidence for the fact that there is no hot electroweak phase transition at large Higgs masses,

The universality class of the electroweak theory

m_H = 95

Two-loop QCD gauge coupling at high temperatures

, 120 and 180 GeV. This means that the line of first order phase transitions separating the symmetric and broken phases at small

Static correlation lengths in QCD at high temperatures and finite densities

m_H