arXiv subjects

Axel Maas

Publications and source records attributed to Axel Maas.

At least 109 records · Page 6Linked to original sources

arXiv2012

The gluon propagator close to criticality

The deconfinement phase transition of pure Yang-Mills theory at finite temperature is reflected in the behavior of gauge-fixed gluonic correlation functions. This is one of many examples of how physical information can be extracted from gauge-dependent correlations which is not always obvious. Here, we study the behavior of the Landau-gauge gluon propagator of pure SU(2) across the phase transition in 2+1 and 3+1 dimensions in order to assess to what extend the corresponding critical behavior is reflected in these correlations. We discuss why it should emerge from a continuum perspective and test our expectations in lattice simulations. A comparison with SU(3) furthermore reveals quite clear indications for a sensitivity of the gluon propagator to the order of the transition.

hep-lat↗

arXiv2011

On the structure of the residual gauge orbit

Gauge-fixed correlation functions are a valuable tool in intermediate steps when determining gauge-invariant physics. However, when obtaining them in different calculations, it is necessary to use exactly the same definition of the gauge to ensure comparability. Beyond perturbation theory, this is complicated by the Gribov-Singer ambiguity. In principle, lattice gauge theory can manipulate individual Gribov copies, thus making it an excellent method to deal with the ambiguity. However, to compare to continuum methods this requires to replicate the same treatment outside the lattice, usually in a path integral formulation. Here, the properties of the gauge orbit will be investigated with respect to this question. Especially, the possibility of employing averages over Gribov copies in non-perturbative generalizations of the Landau gauge will be discussed.

hep-th↗

arXiv2011

Employing the perturbative definition of the Higgs mass in a non-perturbative calculation

In perturbative calculations the masses of the Higgs, the Ws and the Z are usually determined from the pole position of the corresponding gauge-dependent propagators. In full non-perturbative lattice calculations it is much more direct to instead investigate the bound state spectrum with its gauge-independent meaning, which then contains bound states of Higgses and/or Ws and Zs. It is possible to extend the perturbative definition of the Higgs mass also to such a full non-perturbative setting by determining the respective full non-perturbative propagators of the Higgs, the Ws, and the Z, and analyze their analytic structure. This helps connecting the Higgs properties indirectly with gauge-invariant physics. This is here studied, using lattice gauge theory, for the case of a W-Z-Higgs system.

hep-lat↗

arXiv2011

Yang-Mills Theory in lambda-Gauges

The gauge-independent phenomenon of color confinement in Yang-Mills theory manifests itself differently in different gauges. Therefore, the gauge dependence of quantities related to the infrared structure of the theory becomes important for understanding the confinement mechanism. Particularly useful are classes of gauges that are controlled by a single gauge parameter. We present results on propagators and the color-Coulomb potential for the so-called lambda-gauges, which interpolate between the (minimal) Landau gauge and the (minimal complete) Coulomb gauge. Results are reported for the SU(2) lattice gauge theory in three and four space-time dimensions. We investigate especially intermediate and low momenta. We find a continuous evolution of all quantities with the gauge parameter, except at zero four-momentum.

hep-lat↗

arXiv2011

A study of the influence of the gauge group on the Dyson-Schwinger equations for scalar-Yang-Mills systems

The particular choice of the gauge group for Yang-Mills theory plays an important role when it comes to the influence of matter fields. In particular, both the chosen gauge group and the representation of the matter fields yield structural differences in the quenched case. Especially, the qualitative behavior of the Wilson potential is strongly dependent on this selection. Though the algebraic reasons for this observation is clear, it is far from obvious how this behavior can be described besides using numerical simulations. Herein, it is investigated how the group structure appears in the Dyson-Schwinger equations, which as a hierarchy of equations for the correlation functions have to be satisfied. It is found that there are differences depending on both the gauge group and the representation of the matter fields. This provides insight into possible truncation schemes for practical calculations using these equations.

hep-ph↗

arXiv2011

On the gauge boson's properties in a candidate technicolor theory

The technicolor scenario replaces the Higgs sector of the standard model with a strongly interacting sector. One candidate for a realization of such a sector is two-technicolor Yang-Mills theory coupled to two degenerate flavors of adjoint, massless techniquarks. Using lattice gauge theory the properties of the technigluons in this scenario are investigated as a function of the techniquark mass towards the massless limit. For that purpose the minimal Landau gauge two-point and three-point correlation functions are determined, including a detailed systematic error analysis. The results are, within the relatively large systematic uncertainties, compatible with a behavior very similar to QCD at finite techniquark mass. However, the limit of massless techniquarks exhibits features which could be compatible with a (quasi-)conformal behavior.

hep-lat↗

arXiv2011

On the gauge-algebra dependence of Landau-gauge Yang-Mills propagators

Yang-Mills theory can be formulated for any semi-simple Lie algebra, and thus any semi-simple Lie group. In principle, the dynamics could be different for each one. However, functional studies predict that the propagators in Landau gauge depend only quantitatively on the gauge algebra. In particular, genuine non-perturbative effects should be present even in the large N-limit for su(N) gauge algebras. Lattice gauge theory is used to investigate this in detail. The propagators are determined for the gauge groups SU(2), SU(3), SU(4), SU(5), SU(6) and G2, in two and three dimensions. In accordance with the prediction no qualitative dependence on the gauge group is found. In particular, no diminishing of non-perturbative contributions is found for N becoming large in the SU(N) case. Quantitative effects are found, and analyzed in detail.

hep-lat↗

arXiv2011

Rho-meson, Bethe-Salpeter equation, and the far infrared

The Bethe-Salpeter equation in QCD connects the gauge-dependent gluon and quark degrees of freedom with the gauge-invariant properties of mesons. We study the rho meson mass and decay constant for various versions of the gauge-dependent input functions discussed in the literature, which start to differ generically below the hadronic scale, and show qualitative different infrared behavior. We find that, once the gauge-dependent quark-gluon vertex is permitted to vary as well, the rho mass and decay constant is reproduced equally well for all forms investigated. A possible conclusion from this is that these $ρ$-meson properties are only sensitive to changes in the input at scales above a few hundred MeV.

hep-ph↗

arXiv2011

Scalar-matter-gluon interaction

A full non-perturbative treatment of gauge theories requires to include matter fields on equal footing with the gauge fields. Scalar matter can act as a role model for generic matter, as many questions, e.g. confinement, can be posed without referring to a particular Lorentz structure. Due to their rather simple structure they are also useful to develop methods. One possible way to describe gauge theories beyond perturbation theory is based on correlation functions. After a short discussion of the setup, lattice gauge theory is used to analyze the interaction of gluons with quenched fundamental and adjoint scalars. Both the two-point and three-point correlation functions for massive and massless adjoint and fundamental scalars will be determined, in minimal Landau gauge. The findings are in agreement with the possibility that scalars are only slightly affected by the interaction with gluons. The results are compared briefly with dynamical, massive scalars, showing no significant changes in the confinement region compared to the quenched case.

hep-lat↗

arXiv2011

Accessing directly the properties of fundamental scalars in the confinement and Higgs phase

The properties of elementary particles are encoded in their respective propagators and interaction vertices. For a SU(2) gauge theory coupled to a doublet of fundamental complex scalars these propagators are determined in both the Higgs phase and the confinement phase and compared to the Yang-Mills case, using lattice gauge theory. Since the propagators are gauge-dependent, this is done in the Landau limit of 't Hooft gauge, permitting to also determine the ghost propagator. It is found that neither the gauge boson nor the scalar differ qualitatively in the different cases. In particular, the gauge boson acquires a screening mass, and the scalar's screening mass is larger than the renormalized mass. Only the ghost propagator shows a significant change. Furthermore, indications are found that the consequences of the residual non-perturbative gauge freedom due to Gribov copies could be different in the confinement and the Higgs phase.

hep-lat↗

arXiv2010

On the Infrared Behaviour of Landau Gauge Yang-Mills Theory with Differently Charged Scalar Fields

Recently it has been argued that infrared singularities of the quark-gluon vertex of Landau gauge QCD can confine static quarks via a linear potential. It is demonstrated that the same mechanism also may confine fundamental scalar fields. This opens the possibility that within functional approaches static confinement is an universal property of the gauge sector even though it is formally represented in the functional equations of the matter sector. The colour structure of Dyson-Schwinger equations for fundamental and adjoint scalar fields is determined for the gauge groups SU(N) and G(2) exhibiting interesting cancelations purely due to colour algebra.

hep-ph↗

arXiv2010

Gauges, propagators, and physics

When a theory shall be described at all scales, it is necessary to start from its elementary degrees of freedom. Herein, one possible chain of steps for this purpose will be briefly outlined for the example of a gauge theory, like QCD. Starting with the elementary constituents, gluons and quarks, step by step the final observables, physical states, will be built up. This process is based on the elementary correlation functions, and uses a combination of both numerical lattice calculations and functional continuum methods. While the process uses a fixed gauge at each intermediate step, the final observables are gauge-invariant.

hep-ph↗

arXiv2010

On gauge fixing

Gauge fixing is a useful tool to simplify calculations. It is also valuable to combine different methods, in particular lattice and continuum methods. However, beyond perturbation theory the Gribov-Singer ambiguity requires further gauge conditions for a well-defined gauge-fixing prescription. Different additional conditions can, in principle, lead to different results for gauge-dependent correlation functions, as will be discussed for the example of Landau gauge. Also the relation of lattice and continuum gauge fixing beyond perturbation theory will be briefly outlined.

hep-lat↗

arXiv2010

Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3)

We study a gauge invariant order parameter for deconfinement and the chiral condensate in SU(2) and SU(3) Yang-Mills theory in the vicinity of the deconfinement phase transition using the Landau gauge quark and gluon propagators. We determine the gluon propagator from lattice calculations and the quark propagator from its Dyson-Schwinger equation, using the gluon propagator as input. The critical temperature and a deconfinement order parameter are extracted from the gluon propagator and from the dependency of the quark propagator on the temporal boundary conditions. The chiral transition is determined using the quark condensate as order parameter. We investigate whether and how a difference in the chiral and deconfinement transition between SU(2) and SU(3) is manifest.

hep-ph↗

arXiv2010

Strong-coupling study of the Gribov ambiguity in lattice Landau gauge

We study the strong-coupling limit beta=0 of lattice SU(2) Landau gauge Yang-Mills theory. In this limit the lattice spacing is infinite, and thus all momenta in physical units are infinitesimally small. Hence, the infrared behavior can be assessed at sufficiently large lattice momenta. Our results show that at the lattice volumes used here, the Gribov ambiguity has an enormous effect on the ghost propagator in all dimensions. This underlines the severity of the Gribov problem and calls for refined studies also at finite beta. In turn, the gluon propagator only mildly depends on the Gribov ambiguity.

hep-lat↗

arXiv2010

Constructing non-perturbative gauges using correlation functions

Gauge fixing in the non-perturbative domain of non-Abelian gauge theories is obstructed by the Gribov-Singer ambiguity. To compare results from different methods it is necessary to resolve this ambiguity explicitly. Such a resolution is proposed using conditions on correlation functions for a family of non-perturbative Landau gauges. As a consequence, the various results available for correlation functions could possibly correspond to different non-perturbative Landau gauges, discriminated by an additional non-perturbative gauge parameter. The proposal, the necessary assumptions, and evidence from lattice gauge theory calculations, are presented in detail.

hep-lat↗

arXiv2009

Adjoint quarks and fermionic boundary conditions

We study quenched SU(2) lattice gauge theory with adjoint fermions in a wide range of temperatures. We focus on spectral quantities of the Dirac operator and use the temporal fermionic boundary conditions as a tool to probe the system. We determine the deconfinement temperature through the Polyakov loop, and the chiral symmetry restoration temperature for adjoint fermions through the gap in the Dirac spectrum. This chiral transition temperature is about four times larger than the deconfinement temperature. In between the two transitions we find that the system is characterized by a non-vanishing chiral condensate which differs for periodic and anti-periodic fermion boundary conditions. Only for the latter (physical) boundary conditions, the condensate vanishes at the chiral transition. The behavior between the two transitions suggests that deconfinement manifests itself as the onset of a dependence of spectral quantities of the Dirac operator on boundary conditions. This picture is supported further by our results for the dual chiral condensate.

hep-lat↗

arXiv2009

Describing gluons at zero and finite temperature

Any description of gluons requires a well-defined gauge. This is complicated non-perturbatively by Gribov copies. A possible method-independent gauge definition to resolve this problem is presented and afterwards used to study the properties of gluons at any temperature. It is found that only chromo-electric properties reflect the phase transition. From these the gauge-invariant phase transition temperature is determined for SU(2) and SU(3) Yang-Mills theory independently.

hep-lat↗