Features of ghost-gluon and ghost-quark bound states related to BRST quartets

The BRST quartet mechanism in infrared Landau gauge QCD is investigated. Based on the observed positivity violation for transverse gluons $A_{\mathrm {tr}}$ the field content of the non-perturbative BRST quartet generated by $A_{\mathrm {tr}}$ is derived. To identify the gluon's BRST-daughter state as well as the Faddeev-Popov--charge conjugated second parent state, a truncated Bethe-Salpeter equation for the gluon-ghost bound state in the adjoint colour representation is derived and studied. This equation is found to be compatible with the so-called scaling solutions of functional approaches. Repeating the same construction for quarks instead of $A_{\mathrm {tr}}$ leads in a similar way to a truncated Bethe-Salpeter equation for the quark-ghost bound state in the fundamental representation. Within the scaling solution the infrared divergence of the quark-gluon vertex is exactly the right one to make this Bethe-Salpeter equation infrared consistent.Comment: 7 pages, 2 figures; version accepted for publication in Physics Letters

QCD Green Functions and their Application to Hadron Physics

In a functional approach to QCD the infrared behaviour of Landau gauge Green functions is investigated. It can be proven that the ghost Dyson-Schwinger equation implies the Gribov-Zwanziger horizon condition. Its relation to the Kugo-Ojima confinement scenario is elucidated. Positivity violation for gluons is demonstrated, and the analytic structure of the gluon propagator is studied. Quark confinement is related to an infrared divergence of the quark-gluon vertex. It is shown that in the latter various components are non-vanishing due to the dynamical breaking of chiral symmetry. As a result an infrared finite running coupling in the Yang-Mills sector is derived whereas the running coupling related to the quark-gluon vertex is infrared divergent. In Coulomb gauge QCD already the one-gluon-exchange (over-)confines. This leads to a vanishing quark propagator, and thus quarks are confined. Nevertheless colour singlet quantities derived from the quark propagator are well-defined. Especially the expression for the quark condensate proves that chiral symmetry is dynamically broken. As expected the properties of mesons can be directly calculated whereas the mass of coloured diquarks diverges, and thus diquarks are confined. The latter nevertheless possess a well-defined size. In the third part the results obtained so far will be used to formulate a covariant Faddeev approach to nucleons. The resulting amplitudes describe the quark core of the nucleon. Besides the mass of this state also the electromagnetic form factors are calculated. The results for charge radii and magnetic moments as a function of the quark current mass provide some indication what the missing pion cloud may contribute to the nucleons' properties.Comment: 21 pages, 32 figures; lectures presented at the conference ``Infrared QCD in Rio: Propagators, Condensates and Topological Effects (IRQCD 2006)'', Rio de Janeiro, Brazil, 5-9 Jun 2006; a few typos corrected (no other changes

On Confinement, Chiral Symmetry Breaking, and the UA(1) anomaly in Functional Approaches

The so-called decoupling and scaling solutions of functional equations of Landau gauge Yang-Mills theory are briefly reviewed. In both types of solutions the positivity violation seen in the gluon propagator is taken as an indication of gluon confinement. In the scaling solution the resulting infrared singularities of the quark-gluon vertex are responsible for the linear potential between static quarks and are therefore signaling quark confinement. A corresponding description of the UA(1) anomaly in functional approaches is only known for the scaling solution. Nevertheless, it seems puzzling at first sight that quark confinement is related to the dynamical and anomalous breaking of chiral symmetry in a self-consistent manner: One obtains either all these phenomena or none. For the scaling solution also fundamental scalar fields are confined. This provides evidence 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.Comment: 10 pages, 2 figures; talk given at the workshop "The many faces of QCD", 1-5 Nov 2010, Ghent, Belgiu

Asymptotically Safe f(R)f(R)-Gravity Coupled to Matter II: Global Solutions

Ultraviolet fixed point functions of the functional renormalisation group equation for $f(R)$-gravity coupled to matter fields are discussed. The metric is split via the exponential parameterisation into a background and a fluctuating metric, the former is chosen to be the one of a four-sphere. Also when scalar, fermion and vector fields are included global quadratic solutions exist as in the pure gravity case for discrete sets of values for some endomorphism parameters defining the coarse-graining scheme. The asymptotic, large-curvature behaviour of the fixed point functions is analysed for generic values of these parameters. Examples for global numerical solutions are provided. A special focus is given to the question whether matter fields might destabilise the ultraviolet fixed point function. Similar to a previous analysis of a polynomial, small-curvature approximation to the fixed point functions different classes for such functions are found.Comment: 12 pages, 2 figure

Algorithmic derivation of Dyson-Schwinger Equations

We present an algorithm for the derivation of Dyson-Schwinger equations of general theories that is suitable for an implementation within a symbolic programming language. Moreover, we introduce the Mathematica package DoDSE which provides such an implementation. It derives the Dyson-Schwinger equations graphically once the interactions of the theory are specified. A few examples for the application of both the algorithm and the DoDSE package are provided. The package can be obtained from physik.uni-graz.at/~mah/DoDSE.html.Comment: 17 pages, 11 figures, downloadable Mathematica package v2: adapted to version 1.2 of DoDSE package with simplified handling and improved plotting of graphs; references adde

The non-perturbative BRST quartet mechanism in Landau gauge QCD: Ghost-gluon and ghost-quark bound states

The non-perturbative BRST quartet mechanism in infrared Landau gauge QCD is presented. It is demonstrated that positivity violation for transverse gluons allows to identify the gluon's non-perturbative BRST quartet. To describe the respective BRST-daughter state a truncated Bethe-Salpeter equation for the gluon-ghost bound state is investigated. An analogous construction for quarks yields a truncated Bethe-Salpeter equation for the quark-ghost bound state. The gluon-ghost bound state equation in two space-time dimensions has been numerically solved.Comment: 3 pages, 1 figure; Poster presented at the Xth Quark Confinement and the Hadron Spectrum, Munich, Germany, 201

Extraction of Spectral Functions from Dyson-Schwinger Studies via the Maximum Entropy Method

It is shown how to apply the Maximum Entropy Method (MEM) to numerical Dyson-Schwinger studies for the extraction of spectral functions of correlators from their corresponding Euclidean propagators. Differences to the application in lattice QCD are emphasized and, as an example, the spectral functions of massless quarks in cold and dense matter are presented.Comment: 16 pages, 7 figure

Asymptotically safe f(R)-gravity coupled to matter I: the polynomial case

We use the functional renormalization group equation for the effective average action to study the non-Gaussian renormalization group fixed points (NGFPs) arising within the framework of f(R)-gravity minimally coupled to an arbitrary number of scalar, Dirac, and vector fields. Based on this setting we provide comprehensible estimates which gravity-matter systems give rise to NGFPs suitable for rendering the theory asymptotically safe. The analysis employs an exponential split of the metric fluctuations and retains a 7-parameter family of coarse-graining operators allowing the inclusion of non-trivial endomorphisms in the regularization procedure. For vanishing endomorphisms, it is established that gravity coupled to the matter content of the standard model of particle physics and many beyond the standard model extensions exhibit NGFPs whose properties are strikingly similar to the case of pure gravity: there are two UV-relevant directions and the position and critical exponents converge rapidly when higher powers of the scalar curvature are included. Conversely, none of the phenomenologically interesting gravity-matter systems exhibits a stable NGFP when a Type II coarse graining operator is employed. Our analysis resolves this tension by demonstrating that the NGFPs seen in the two settings belong to different universality classes.Comment: 49 pages, 5 figure