Method for comparing finite temperature field theory results with lattice data

The values of the presently available truncated perturbative expressions for the pressure of the quark-gluon plasma at finite temperatures and finite chemical potential are trustworthy only at very large energies. When used down to temperatures close to the critical one Tc, they suffer from large uncertainties due to the renormalization scale freedom. In order to reduce these uncertainties, we perform resummations of the pressure by applying Pade-related approximants to the available perturbation series for the short-distance and for the long-distance contributions. In the two contributions, we use two different renormalization scales which reflect different energy regions contributing to the different parts. Application of the obtained expressions at low temperatures is made possible by replacing the usual four-loop barMS beta function for alpha_s by its Borel-Pade resummation, eliminating thus the unphysical Landau singularities of alpha_s. The obtained results are remarkably insensitive to the chosen renormalization scale and can be compared with lattice results -- for the pressure (p), the chemical potential contribution (delta p) to the pressure, and various susceptibilities. A good qualitative agreement with the lattice results is revealed down to temperatures close to Tc.Comment: 24 pages, 17 figures, revtex4; Ref.[25] is new; the ordering of the references and grammatic and stylistic errors are corrected - version as it appears in PR

Gauge Coupling Beta Functions in the Standard Model to Three Loops

In this paper we compute the three-loop corrections to the beta functions of the three gauge couplings in the Standard Model of particle physics using the minimal subtraction scheme and taking into account Yukawa and Higgs self couplings.Comment: 4 pages, 1 figure, v2: minor changes, references adde

Renormalization constants and beta functions for the gauge couplings of the Standard Model to three-loop order

We compute the beta functions for the three gauge couplings of the Standard Model in the minimal subtraction scheme to three loops. We take into account contributions from all sectors of the Standard Model. The calculation is performed using both Lorenz gauge in the unbroken phase of the Standard Model and background field gauge in the spontaneously broken phase. Furthermore, we describe in detail the treatment of $\gamma_5$ and present the automated setup which we use for the calculation of the Feynman diagrams. It starts with the generation of the Feynman rules and leads to the bare result for the Green's function of a given process.Comment: 44 pages, 9 figures; v2: sign in eq.(29) corrected; final result unchange

Off-shell two loop QCD vertices

We calculate the triple gluon, ghost-gluon and quark-gluon vertex functions at two loops in the MSbar scheme in the chiral limit for an arbitrary linear covariant gauge when the external legs are all off-shell.Comment: 29 latex pages, 32 figures, anc directory contains txt file with electronic version of vertex functions for each of the three 3-point cases in the MSbar scheme and includes the projection matrice

Duality between constraints and gauge conditions

It is shown that in the first order gauge theories under some general assumptions gauge conditions can play the role of new local symmetry generators, while the original constraints become gauge fixing terms. It is possible to associate with this new symmetry a second BRST charge and its anticommutator with the original BRST charge is the Hodge operator of the corresponding cohomology complex.Comment: 7 pages, LaTeX, some changes in the BRST sectio

Two loop QCD vertices at the symmetric point

We compute the triple gluon, quark-gluon and ghost-gluon vertices of QCD at the symmetric subtraction point at two loops in the MSbar scheme. In addition we renormalize each of the three vertices in their respective momentum subtraction schemes, MOMggg, MOMq and MOMh. The conversion functions of all the wave functions, coupling constant and gauge parameter renormalization constants of each of the schemes relative to MSbar are determined analytically. These are then used to derive the three loop anomalous dimensions of the gluon, quark, Faddeev-Popov ghost and gauge parameter as well as the beta-function in an arbitrary linear covariant gauge for each MOM scheme. There is good agreement of the latter with earlier Landau gauge numerical estimates of Chetyrkin and Seidensticker.Comment: 36 latex pages, anc directory contains txt file with anomalous dimensions, beta-functions, coupling constant mappings, conversion functions and amplitudes in analytic for

Quantum properties of a non-Abelian gauge invariant action with a mass parameter

We continue the study of a local, gauge invariant Yang-Mills action containing a mass parameter, which we constructed in a previous paper starting from the nonlocal gauge invariant mass dimension two operator F_{\mu\nu} (D^2)^{-1} F_{\mu\nu}. We return briefly to the renormalizability of the model, which can be proven to all orders of perturbation theory by embedding it in a more general model with a larger symmetry content. We point out the existence of a nilpotent BRST symmetry. Although our action contains extra (anti)commuting tensor fields and coupling constants, we prove that our model in the limit of vanishing mass is equivalent with ordinary massless Yang-Mills theories. The full theory is renormalized explicitly at two loops in the MSbar scheme and all the renormalization group functions are presented. We end with some comments on the potential relevance of this gauge model for the issue of a dynamical gluon mass generation.Comment: 17 pages. v2: version accepted for publication in Phys.Rev.

A nonperturbative model for the strong running coupling within potential approach

A nonperturbative model for the QCD invariant charge, which contains no low-energy unphysical singularities and possesses an elevated higher loop corrections stability, is developed in the framework of potential approach. The static quark-antiquark potential is constructed by making use of the proposed model for the strong running coupling. The obtained result coincides with the perturbative potential at small distances and agrees with relevant lattice simulation data in the nonperturbative physically-relevant region. The developed model yields a reasonable value of the QCD scale parameter, which is consistent with its previous estimations obtained within potential approach.Comment: 14 pages, 4 figure

Banks-Zaks fixed point analysis in momentum subtraction schemes

We analyse the critical exponents relating to the quark mass anomalous dimension and beta-function at the Banks-Zaks fixed point in Quantum Chromodynamics (QCD) in a variety of representations for the quark in the momentum subtraction (MOM) schemes of Celmaster and Gonsalves. For a specific range of values of the number of quark flavours, estimates of the exponents appear to be scheme independent. Using the recent five loop modified minimal subtraction (MSbar) scheme quark mass anomalous dimension and estimates of the fixed point location we estimate the associated exponent as 0.263-0.268 for the SU(3) colour group and 12 flavours when the quarks are in the fundamental representation.Comment: 33 latex pages, 25 tables, anc directory contains txt file with electronic version of renormalization group function

Low momentum propagators at two loops in gluon mass model

We compute the two loop corrections to the gluon propagator for low momentum in a gluon mass model. This model has recently been proposed as an alternative to the Gribov construction in the way it handles Gribov copies in the gauge fixing. The corrections provide improvements for estimating the point where the gluon propagator freezes in relation to lattice data.Comment: 16 latex pages, 1 figur