Gauge boson masses in the 3D, SU(2) gauge-Higgs model

Abstract

We study gauge boson propagators in the symmetric and symmetry broken phases of the 3-d, SU(2) gauge-Higgs model. Correlation functions for the gauge fields are calculated in Landau gauge. They are found to decay exponentially at large distances leading to a non-vanishing mass for the gauge bosons. We find that the W-boson screening mass drops in the symmetry broken phase when approaching the critical temperature. In the symmetric phase the screening mass stays small and is independent of the scalar-gauge coupling (the hopping parameter). Numerical results coincide with corresponding calculations performed for the pure gauge theory. We find m w = 0.35(1)g 2 T in this phase which is consistent with analytic calculations based on gap equations. This is, however, significantly smaller than masses extracted from gauge invariant vector boson correlation functions. As internal consistency check we also have calculated correlation functions for gauge invariant operators leading to scalar and vector boson masses. Finite lattice size effects have been systematically analyzed on lattices of size L 2 × L z with L = 4 − 24 and L z = 16 − 128.

Non-perturbative renormalization flow in quantum field theory and statistical physics

“…This is possible even for h close to 1, so that the system is far from the spinodal line. This case corresponds to weak first-order phase transitions, as can be verified by observing that the saddle-point action (6.17), the location of the true vacuum 20) and the difference in free-energy density between the minima ∆U m 3 6.21) go to zero in the limit m k f /λ k f → 0 for fixed h. This is in agreement with the discussion of fig. 25 in the previous subsection.…”

“…This concerns, in particular, the Lorentz symmetry or its Euclidean counterpart of four-dimensional rotations and Osterwalder-Schrader positivity [18]. In this line of thought the recent high precision numerical simulations of the high temperature electroweak interactions [19,20] can be considered as a fine example of a quantitative (theoretical) transition from microphysics to macrophysics, despite the presence of strong effective interactions and a large correlation length. They have confirmed that the high temperature first-order phase transition which would be present in the standard model with modified masses turns into a crossover for realistic masses, as has been suggested earlier by analytical methods [11,12,21,22].…”

“…(2.19) by means of a Legendre transform, a suitable field redefinition and the association Λ = k [92,96,97]. Although the formal relation is simple, the practical calculation of S W k from Γ k (and vice versa) can be quite involved 20 . In the presence of massless particles the Legendre transform of Γ k does not remain local and S W k is a comparatively complicated object.…”

Conjecture on the infrared structure of the vacuum Schrödinger wave functional of QCD

“…Moreover, by appealing to known d = 3 gauge dynamics, we can estimate the d = 4 coupling strength in terms of the renormalization constant Z. In d = 3 the coupling g 2 3 has dimensions of mass, and there is a unique [for given SU (N )] dynamically-determined ratio M/g 2 3 , which has been estimated by a number of authors [27,28,29,30,31,32,33,34,35,36,37]. Knowing only this ratio we can estimate the d = 4 QCD coupling α s (M 2 ), getting a value around 0.4Z.…”

The Ising model universality of the electroweak theory

“…The transition is of the first order at small Higgs masses, but it has been found to turn into a regular cross-over when m H > ∼ 75 GeV [1][2][3][4]. A second order transition appears at the endpoint of the first order transition line, and the macroscopic behaviour of the system is determined by the universal properties of the endpoint.…”