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

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

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

On bounds and boundary conditions in the continuum Landau gauge

© 2015, The Author(s). In this note, we consider the Landau gauge in the continuum formulation. Our purposes are twofold. Firstly, we try to work out the consequences of the recently derived Cucchieri–Mendes bounds on the inverse Faddeev operator at the level of the path integral quantization. Secondly, we give an explicit (renormalizable) prescription to implement the so-called Landau B-gauges as introduced by Maas.17 pages; 2 .pdf figures. v2: version accepted for publication in Eur. Phys. J. Cstatus: publishe

Effect of the Gribov horizon on the Polyakov loop and vice versa

© 2015, The Author(s). We consider finite-temperature SU(2) gauge theory in the continuum formulation, which necessitates the choice of a gauge fixing. Choosing the Landau gauge, the existing gauge copies are taken into account by means of the Gribov–Zwanziger quantization scheme, which entails the introduction of a dynamical mass scale (Gribov mass) directly influencing the Green functions of the theory. Here, we determine simultaneously the Polyakov loop (vacuum expectation value) and Gribov mass in terms of temperature, by minimizing the vacuum energy w.r.t. the Polyakov-loop parameter and solving the Gribov gap equation. Inspired by the Casimir energy-style of computation, we illustrate the usage of Zeta function regularization in finite-temperature calculations. Our main result is that the Gribov mass directly feels the deconfinement transition, visible from a cusp occurring at the same temperature where the Polyakov loop becomes nonzero. In this exploratory work we mainly restrict ourselves to the original Gribov–Zwanziger quantization procedure in order to illustrate the approach and the potential direct link between the vacuum structure of the theory (dynamical mass scales) and (de)confinement. We also present a first look at the critical temperature obtained from the refined Gribov–Zwanziger approach. Finally, a particular problem for the pressure at low temperatures is reported.19 pages, 8 .pdf figures. v2: extended section 3 + extra references; version accepted for publication in EPJCstatus: publishe

Double nonperturbative gluon exchange: An update on the soft-Pomeron contribution to pp scattering

© 2017 American Physical Society. We employ a set of recent, theoretically motivated fits to nonperturbative unquenched gluon propagators to check on how far double gluon exchange can be used to describe the soft sector of pp scattering data (total and differential cross section). In particular, we use the refined Gribov-Zwanziger gluon propagator (as arising from dealing with the Gribov gauge fixing ambiguity) and the massive Cornwall-type gluon propagator (as motivated from Dyson-Schwinger equations) in conjunction with a perturbative quark-gluon vertex, next to a model based on the nonperturbative quark-gluon Maris-Tandy vertex, popular from Bethe-Salpeter descriptions of hadronic bound states. We compare the cross sections arising from these models with older ISR and more recent TOTEM and ATLAS data. The lower the value of total energy s, the better the results appear to be.14 pages, 8 .pdf figures. To appear in Phys.Rev.Cstatus: publishe

Exact nilpotent nonperturbative BRST symmetry for the Gribov-Zwanziger action in the linear covariant gauge

© 2015 American Physical Society. We point out the existence of a nonperturbative exact nilpotent BRST symmetry for the Gribov-Zwanziger action in the Landau gauge. We then put forward a manifestly BRST invariant resolution of the Gribov gauge fixing ambiguity in the linear covariant gauge.8 pages. v2: version accepted for publication in PhysRevDstatus: publishe

More on the nonperturbative Gribov-Zwanziger quantization of linear covariant gauges

© 2016 American Physical Society. In this paper, we discuss the gluon propagator in the linear covariant gauges in D = 2, 3, 4 Euclidean dimensions. Nonperturbative effects are taken into account via the so-called refined Gribov-Zwanziger framework. We point out that, as in the Landau and maximal Abelian gauges, for D = 3, 4, the gluon propagator displays a massive (decoupling) behavior, while for D = 2, a scaling one emerges. All results are discussed in a setup that respects the Becchi-Rouet-Stora-Tyutin (BRST) symmetry, through a recently introduced nonperturbative BRST transformation. We also propose a minimizing functional that could be used to construct a lattice version of our nonperturbative definition of the linear covariant gauge.15 pages, 1 figure; V2 typos fixed and inclusion of section on the ghost propagator. To appear in PhysRev Dstatus: publishe