arXiv subjects

Christian S. Fischer

Publications and source records attributed to Christian S. Fischer.

161 records · Page 9Linked to original sources

arXiv2007

Lower dimensional Yang-Mills theory as a laboratory to study the infrared regime

Lattice studies of the infrared regime of gauge theories are complicated by the required extensive limits, the performed gauge fixing and the demand for high statistics. Using a general power counting scheme for the infrared limit of Landau gauge SU(N) Yang-Mills theory in arbitrary dimensions we show that the infrared behavior of Greens functions is both qualitatively and quantitatively similar in two, three and four spacetime dimensions. Therefore, lower dimensional lattice simulations can serve as a simplified laboratory to analyze the presently applied approximations and to obtain first results for higher correlation functions.

hep-ph↗

arXiv2007

Large volume behavior of Yang-Mills propagators

We summarize results on finite-volume effects in the propagators of Landau gauge Yang-Mills theory using Dyson-Schwinger equations on a 4-dimensional torus. We demonstrate explicitly how the solutions for the gluon and the ghost propagator tend towards their respective infinite volume forms in the corresponding limit. We discuss the relation of our solutions with results from lattice Monte-Carlo simulations.

hep-lat↗

arXiv2007

Large volume behaviour of Yang-Mills propagators

We investigate finite volume effects in the propagators of Landau gauge Yang-Mills theory using Dyson-Schwinger equations on a 4-dimensional torus. In particular, we demonstrate explicitly how the solutions for the gluon and the ghost propagator tend towards their respective infinite volume forms in the corresponding limit. This solves an important open problem of previous studies where the infinite volume limit led to an apparent mismatch, especially of the infrared behaviour, between torus extrapolations and the existing infinite volume solutions obtained in 4-dimensional Euclidean space-time. However, the correct infinite volume limit is approached rather slowly. The typical scales necessary to see the onset of the leading infrared behaviour emerging already imply volumes of at least 10 to 15 fm in lengths. To reliably extract the infrared exponents of the infinite volume solutions requires even much larger ones. While the volumes in the Monte-Carlo simulations available at present are far too small to facilitate that, we obtain a good qualitative agreement of our torus solutions with recent lattice data in comparable volumes.

hep-ph↗

arXiv2006

Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory

We uniquely determine the infrared asymptotics of Green functions in Landau gauge Yang-Mills theory. They have to satisfy both, Dyson-Schwinger equations and functional renormalisation group equations. Then, consistency fixes the relation between the infrared power laws of these Green functions. We discuss consequences for the interpretation of recent results from lattice QCD.

hep-th↗

arXiv2006

Infrared Properties of QCD from Dyson-Schwinger equations

I review recent results on the infrared properties of QCD from Dyson-Schwinger equations. The topics include infrared exponents of one-particle irreducible Green's functions, the fixed point behaviour of the running coupling at zero momentum, the pattern of dynamical quark mass generation and properties of light mesons.

hep-ph↗

arXiv2006

Soft gluons are heavy and rowdy

We study dynamical mass generation in pure Yang-Mills theory and report on a recently developed ansatz that exactly solves the tower of Dyson-Schwinger equations in Landau gauge at low Euclidean momentum, featuring enhanced gluon-gluon vertices, a finite ghost-gluon vertex in agreement with an old argument of Taylor, and an IR suppressed gluon propagator. This ansatz reinforces arguments in favor of the concept of a gluon mass gap at low momentum (although the minimum of the gluon's dispersion relation is not at zero momentum). As an application, we have computed the spectrum of oddballs, three-gluon glueballs with negative parity and C-parity. The three body problem is variationally solved employing the color density-density interaction of Coulomb gauge QCD with a static Cornell potential. Like their even glueball counterparts, oddballs fall on Regge trajectories with similar slope to the pomeron. However their intercept at t=0 is smaller than the omega Regge trajectory and therefore the odderon may only be visible in experimental searches (for example at BNL) with higher -t than conducted to date at DESY.

nucl-th↗

arXiv2005

Studying unquenching effects in QCD with Dyson-Schwinger equations

We summarise recent results on the properties of gluons, quarks and light mesons from the Green's functions approach to QCD. We discuss a self-consistent, infrared power law solution for the Schwinger-Dyson equations of the 1PI-Greens functions of Yang-Mills theory. The corresponding running coupling has a universal fixed point at zero momentum. Based on these analytical results a truncation scheme for the coupled system of Schwinger-Dyson equations for the propagators of QCD and the Bethe-Salpeter equation for light mesons has been formulated. We compare numerical results for charge eigenstate vector and pseudoscalar meson observables with corresponding lattice data. The effects of unquenching the system are found to be small but not negligible.

hep-ph↗

arXiv2005

Infrared exponents of Yang-Mills theory

In this talk I summarise recent results on the infrared exponents of SU($N_c$)-Yang-Mills theory. I discuss a self-consistent power law solution for the Dyson-Schwinger equations for general 1PI-Greens functions in the infrared. The corresponding running coupling has a fixed point at zero momentum, which turns out to be universal and gauge invariant within a class of transverse gauges. When calculated on a torus the infrared exponents of the ghost and gluon propagators differ from the corresponding continuum solutions. They agree, however, well with results from lattice calculations.

hep-lat↗

arXiv2005

Infrared Behaviour and Running Couplings in Interpolating Gauges in QCD

We consider the class of gauges that interpolates between Landau- and Coulomb-gauge QCD, and show the non-renormalisation of the two independent ghost-gluon vertices. This implies the existence of two RG-invariant running couplings, one of which is interpreted as an RG-invariant gauge parameter. We also present the asymptotic infrared limit of solutions of the Dyson-Schwinger equations in interpolating gauges. The infrared critical exponents of these solutions as well as the resulting infrared fixed point of one of the couplings are independent of the gauge parameter. This coupling also has a fixed point in the Coulomb gauge limit and constitutes a second invariant charge besides the well known colour-Coulomb potential.

hep-ph↗

arXiv2005

Vertex functions and infrared fixed point in Landau gauge SU(N) Yang-Mills theory

The infrared behaviour of vertex functions in an SU(N) Yang-Mills theory in Landau gauge is investigated employing a skeleton expansion of the Dyson-Schwinger equations. The three- and four-gluon vertices become singular if and only if all external momenta vanish while the dressing of the ghost-gluon vertex remains finite in this limit. The running coupling as extracted from either of these vertex functions possesses an infrared fixed point. In general, diagrams including ghost-loops dominate in the infrared over purely gluonic ones.

hep-th↗

arXiv2004

Renormalization flow of Yang-Mills propagators

We study Landau-gauge Yang-Mills theory by means of a nonperturbative vertex expansion of the quantum effective action. Using an exact renormalization group equation, we compute the fully dressed gluon and ghost propagators to lowest nontrivial order in the vertex expansion. In the mid-momentum regime, $p^2\sim\mathcal{O}(1)\text{GeV}^2$, we probe the propagator flow with various {\em ansätze} for the three- and four-point correlations. We analyze the potential of these truncation schemes to generate a nonperturbative scale. We find universal infrared behavior of the propagators, if the gluon dressing function has developed a mass-like structure at mid-momentum. The resulting power laws in the infrared support the Kugo-Ojima confinement scenario.

hep-ph↗

arXiv2004

Semiperturbative construction for the quark-gluon vertex

We construct a model for the quark-gluon vertex of Landau gauge QCD. This is of twofold interest: on the one hand the quark-gluon interaction is at the heart of quark confinement, on the other hand it is a central element in hadron phenomenology based on QCD Greens functions. We employ the non-Abelian one-loop diagram in perturbation theory, which is of order Nc. As a novelty we replace the tree-level quark and gluon propagators in this diagram by their dressed counterparts solving the Dyson-Schwinger equations. The Nc-suppressed Abelian diagram is an order of magnitude smaller in various kinematics. We also study the effect of ghost dressing factors on the vertex obtaining a construction in good agreement with recent low-momentum lattice calculations.

hep-ph↗

arXiv2003

Non-perturbative Propagators, Running Coupling and Dynamical Mass Generation in Ghost-Antighost Symmetric Gauges in QCD

We present approximate non-perturbative solutions for the propagators as well as the running coupling of QCD from a coupled system of renormalised, truncated Dyson--Schwinger equations. We employ ansaetze for the dressed vertices such that the running coupling and the quark mass function are independent of the renormalisation point. Our solutions are in good agreement with the results of recent lattice calculations. We find a weakly vanishing gluon propagator at small momenta and an infrared singular ghost propagator in agreement with Zwanziger's horizon condition and the Kugo-Ojima confinement criterion. The running coupling possesses an infrared fixed point at alpha(0) = 8.92/N_c. To investigate the influence of boundary conditions on the propagators we solved the ghost and gluon DSEs also on a four-torus. Our results show typical finite volume effects but are still close to the continuum solutions for sufficiently large volumes. For the quark propagator we find dynamically generated quark masses that agree well with phenomenological values. The effects of unquenching the system are found to be small. In particular the infrared behaviour of the ghost and gluon dressing functions found in pure Yang-Mills theory is almost unchanged as long as the number of light flavors is smaller than four.

hep-ph↗

arXiv2003

Non-perturbative Propagators, Running Coupling and Dynamical Quark Mass of Landau gauge QCD

The coupled system of renormalized Dyson-Schwinger equations for the quark, gluon and ghost propagators of Landau gauge QCD is solved within truncation schemes. These employ bare as well as non-perturbative ansaetze for the vertices such that the running coupling as well as the quark mass function are independent of the renormalization point. The one-loop anomalous dimensions of all propagators are reproduced. Dynamical chiral symmetry breaking is found, the dynamically generated quark mass agrees well with phenomenological values and corresponding results from lattice calculations. The effects of unquenching the system are small. In particular the infrared behavior of the ghost and gluon dressing functions found in previous studies is almost unchanged as long as the number of light flavors is smaller than four.

hep-ph↗

arXiv2003

Kugo-Ojima confinement and QCD Green's functions in covariant gauges

In Landau gauge QCD the Kugo-Ojima confinement criterion and its relation to the infrared behaviour of the gluon and ghost propagators are reviewed. It is demonstrated that the realization of this confinement criterion (which is closely related to the Gribov-Zwanziger horizon condition) results from quite general properties of the ghost Dyson-Schwinger equation. The numerical solutions for the gluon and ghost propagators obtained from a truncated set of Dyson--Schwinger equations provide an explicit example for the anticipated infrared behaviour. The results are in good agreement, also quantitatively, with corresponding lattice data obtained recently. The resulting running coupling approaches a fixed point in the infrared, $α(0) = 8.915/N_c$. Solutions for the coupled system of Dyson--Schwinger equations for the quark, gluon and ghost propagators are presented. Dynamical generation of quark masses and thus spontaneous breaking of chiral symmetry takes place. In the quenched approximation the quark propagator functions agree well with those of corresponding lattice calculations. For a small number of light flavours the quark, gluon and ghost propagators deviate only slightly from the ones in quenched approximation. While the positivity violation of the gluon spectral function is manifest in the gluon propagator, there are no clear indications of analogous positivity violations for quarks so far.

nucl-th↗

arXiv2003

Kugo-Ojima confinement criterion, Zwanziger-Gribov horizon condition, and infrared critical exponents in Landau gauge QCD

The Kugo-Ojima confinement criterion and its relation to the infrared behaviour of the gluon and ghost propagators in Landau gauge QCD are reviewed. The realization of this confinement criterion (which in Landau gauge relates to Zwanziger's horizon condition) results from quite general properties of the ghost Dyson-Schwinger equation. The numerical solutions for the gluon and ghost propagators obtained from a truncated set of Dyson-Schwinger equations provide an explicit example for the anticipated infrared behaviour. These results are in good agreement, also quantitatively, with corresponding lattice data obtained recently. The resulting running coupling approaches a fixed point in the infrared, $α(0) = 8.9/N_c$. Solutions for the coupled system of Dyson-Schwinger equations for the quark, gluon and ghost propagators are presented. Dynamical generation of quark masses and thus spontaneous breaking of chiral symmetry is found. In the quenched approximation the quark propagator functions agree well with those of corresponding lattice calculations. For a small number of light flavours the quark, gluon and ghost propagators deviate only slightly from the quenched ones. While the positivity violation of the gluon spectral function is apparent in the gluon propagator, there are no clear indications of positivity violations in the Landau gauge quark propagator.

hep-ph↗

arXiv2002

Infrared Exponents and the Running Coupling of Landau gauge QCD and their Relation to Confinement

The infrared behaviour of the gluon and ghost propagators in Landau gauge QCD is reviewed. The Kugo-Ojima confinement criterion and the Gribov-Zwanziger horizon condition result from quite general properties of the ghost Dyson-Schwinger equation. The numerical solutions for the gluon and ghost propagators obtained from a truncated set of Dyson-Schwinger equations provide an explicit example for the anticipated infrared behaviour. The results are in good agreement with corresponding lattice data obtained recently. The resulting running coupling approaches a fix point in the infrared, $α(0) = 8.92/N_c$. Two different fits for the scale dependence of the running coupling are given and discussed.

hep-ph↗