SU(2) x U(1) Yang-Mills theories in 3d with Higgs field and Gribov ambiguity

We study the structure of the gauge propagators of a 3d version of the electroweak interaction in terms of the Higgs vacuum expectation value., of the non-Abelian gauge coupling g, and of the Abelian gauge coupling g', when nonperturbative effects related to the non-Abelian gauge fixing are introduced by means of an adapted path integral measure. In the perturbative regime of small nonAbelian coupling g and sufficiently large, nu the well-known standard Z and W propagators are recovered, together with a massless photon. In general, depending on the relative magnitudes of g, g' and., we uncover a quite different propagator structure. In a later stage of research, the results here derived can be used to study the associated phase diagram in more depth

Spontaneous breaking of the BRST symmetry in the presence of the Gribov horizon : renormalizability

An all orders algebraic proof of the multiplicative renormalizability of the novel formulation of the Gribov-Zwanziger action proposed in Phys. Rev. D 86, 045005 (2012) [arXiv:1205.3934], and allowing for an exact but spontaneously broken BRST symmetry, is provided.Comment: 15 page

Nonperturbative aspects of Euclidean Yang-Mills theories in linear covariant gauges : Nielsen identities and a BRST-invariant two-point correlation function

In order to construct a gauge-invariant two-point function in a Yang-Mills theory, we propose the use of the all-order gauge-invariant transverse configurations A(h). Such configurations can be obtained through the minimization of the functional A(min)(2) along the gauge orbit within the BRST-invariant formulation of the Gribov-Zwanziger framework recently put forward in [1,2] for the class of the linear covariant gauges. This correlator turns out to provide a characterization of nonperturbative aspects of the theory in a BRST-invariant and gauge-parameter-independent way. In particular, it turns out that the poles of are the same as those of the transverse part of the gluon propagator, which are also formally shown to be independent of the gauge parameter alpha entering the gauge condition through the Nielsen identities. The latter follow from the new exact BRST-invariant formulation introduced before. Moreover, the correlator enables us to attach a BRST-invariant meaning to the possible positivity violation of the corresponding temporal Schwinger correlator, giving thus for the first time a consistent, gauge parameter independent, setup to adopt the positivity violation of as a signature for gluon confinement. Finally, in the context of gauge theories supplemented with a fundamental Higgs field, we use to probe the pole structure of the massive gauge boson in a gauge-invariant fashion

Semiclassical analysis of the phases of 4d SU(2) Higgs gauge systems with cutoff at the Gribov horizon

We present an analytical study of continuum 4d SU(2) gauge-Higgs models with a single Higgs field with fixed length in either the fundamental or adjoint representation. We aim at analytically probing the renowned predictions of Fradkin and Shenker on the phase diagram in terms of confinement versus Higgs behavior, obtained for the lattice version of the model. We work in the Landau version of the ' t Hooft R xi gauges in which case we can access potential nonperturbative physics related to the existence of the Gribov copies. In the fundamental case, we clearly show that in the perturbative regime of small gauge coupling constant g and large Higgs vacuum expectation value (vev) nu, there is a Higgs phase with Yukawa gauge boson propagators without Gribov effects. For a small value of the Higgs vev nu and/or large g, we enter a region with Gribov-type propagators that have no physical particle interpretation: the gauge bosons are as such confined. The transition between both behaviors is found to be continuous. In the adjoint case, we find evidence of a more drastic transition between the different behaviors for the propagator of the off- diagonal gauge bosons, whereas the "photon,'' i.e. the diagonal component of the gauge field, displays a propagator of the Gribov-type. In the limit of infinite Higgs condensate, we show that a massless photon is recovered. We compare our findings with those of Fradkin and Shenker as well as with more recent numerical lattice simulations of the fundamental Higgs model. We also carefully discuss in which region of the parameter space (nu, g) our approximations are trustworthy

Wilson Expansion of QCD Propagators at Three Loops: Operators of Dimension Two and Three

In this paper we construct the Wilson short distance operator product expansion for the gluon, quark and ghost propagators in QCD, including operators of dimension two and three, namely, A^2, m^2, m A^2, \ovl{\psi} \psi and m^3. We compute analytically the coefficient functions of these operators at three loops for all three propagators in the general covariant gauge. Our results, taken in the Landau gauge, should help to improve the accuracy of extracting the vacuum expectation values of these operators from lattice simulation of the QCD propagators.Comment: 20 pages, no figure

Is soft breaking of BRST symmetry consistent?

A definition of soft breaking of BRST symmetry in the field-antifield formalism is proposed, valid for general gauge theories and arbitrary gauge fixing. The Ward identities for the generating functionals of Green's functions are derived, and their gauge dependence is investigated. We discuss the Gribov-Zwanziger action for the one-parameter family of R_xi gauges. It is argued that gauge theories with a soft breaking of BRST symmetry are inconsistent.Comment: 1+16 pages; v2: example of section 5 changed to R_xi gauges; v3: small corrections to section 5, one reference added, published versio