K. Farakos

3D physics and the electroweak phase transition: Perturbation theory

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.

3D physics and the electroweak phase transition: A framework for lattice Monte Carlo analysis

Abstract We discuss a framework relying on both perturbative and non-perturbative lattice computations which will be able to reliably determine the parameters of the EW phase transition. A motivation for the use of 3d effective theory in the lattice simulations, rather than the complete 4d one, is provided. We introduce and compute on the 2-loop level a number of gauge-invariant order parameters - condensates, which can be measured with high accuracy in MC simulations. The relation between MS and lattice condensates is found, together with the relation between lattice couplings and continuum parameters (the constant physics curves). These relations are exact in the continuum limit.

The electroweak phase transition at mH ⋍ mW

Abstract We study the finite temperature electroweak transition with non-perturbative lattice Monte Carlo simulations. We find that it is of first order, at least for Higgs masses up to 80 GeV. The critical temperature of the phase transition is found to be smaller than that determined by a 2-loop renormalization group improved effective potential. The jump of the order parameter at the critical temperature is considerably larger than the perturbative value. By comparing lattice data and perturbation theory, we demonstrate that the latter, for the computation of the vacuum expectation value of the Higgs field ν ( T ) in the broken phase at given temperature, converges quite well, provided ν ( T )/ T > 1. An upper bound on the Higgs mass necessary for electroweak baryogenesis in the light of the lattice data is briefly discussed.

Schwinger-Dyson approach for a Lifshitz-type Yukawa model

We consider a

Lattice evidence for gauge field localization on a brane

3+1

U(1)L ⊗ U(1)R symmetric yukawa model in the symmetric phase

dimensional field theory at a Lifshitz point for a dynamical critical exponent

Dimensional reduction and the Higgs potential

z=3

Geometrical hierarchy and spontaneous symmetry breaking

, with a scalar and a fermion field coupled via a Yukawa interaction. Using the nonperturbative Schwinger-Dyson approach we calculate quantum corrections to the effective action. We demonstrate that a first order derivative kinetic term as well as a mass term for the fermion arise dynamically. This signals the restoration of Lorentz symmetry in the IR regime of the single fermion model, although for theories with more than one fermionic species such a conclusion will require fine-tuning of couplings. The limitations of the model and our approach are discussed.

Topography of the hot sphaleron transitions

We examine the problem of gauge-field localization in higher-dimensional gauge theories. In particular, we study a five-dimensional U(1) by lattice techniques and we find that gauge fields can indeed be localized. Two models are considered. The first one has anisotropic couplings independent of each other and of the coordinates. It can be realized on a homogeneous but anisotropic flat Euclidean space. The second model has couplings depending on the extra transverse fifth direction. This model can be realized by a U(1) gauge theory on the Randall-Sundrum background. We find that in both models a new phase exists, the layer phase, in which a massless photon is localized on the fourdimensional layers. We find that this phase is separated from the strong coupling phase by a second order phase transition.

Liouville-Lifshitz theory in 3 + 1 dimensions

The lattice regularizedSU(2)l ⊗SU(2)r symmetric scalar fermion model with explicit mirror fermions is investigated in the phase with unbroken symmetry. In the present work numerical Monte Carlo calculations with dynamical fermions are performed on 43·8 and 43·16 lattices near the expected perturbative Gaussian fixed point. The bare Yukawa coupling of the mirror fermion is fixed at zero. Global symmetries of the model are discussed, and the numerical results are supported by lattice perturbation theory.