Axel Maas

On the infrared behavior of Landau gauge Yang-Mills theory

Abstract We discuss the properties of ghost and gluon propagators in the deep infrared momentum region of Landau gauge Yang–Mills theory. Within the framework of Dyson–Schwinger equations and the functional renormalization group we demonstrate that it is only a matter of infrared boundary conditions whether infrared scaling or decoupling occurs. We argue that the second possibility is at odds with global BRST symmetry in the confining phase. For this purpose we improve upon existing truncation schemes in particular with respect to transversality and renormalization.

Enhanced Production of Low-Mass Electron-Positron Pairs in 40-AGeV Pb-Au Collisions at the CERN SPS

We report on first measurements of low-mass electron-positron pairs in Pb-Au collisions at the CERN SPS beam energy of 40 AGeV. The observed pair yield integrated over the range of invariant masses 0.2<m</=1 GeV/c(2) is enhanced over the expectation from neutral meson decays by a factor of 5.9+/-1.5(stat)+/-1.2(syst data)+/-1.8(syst meson decays), somewhat larger than previously observed at the higher energy of 158 AGeV. The results are discussed with reference to model calculations based on pi(+)pi(-)-->e(+)e(-) annihilation with a modified rho propagator. They may be linked to chiral symmetry restoration and support the notion that the in-medium modifications of the rho are more driven by baryon density than by temperature.

The HERMES dual-radiator ring imaging Cherenkov detector

Abstract The construction and use of a dual radiator Ring Imaging Cherenkov (RICH) detector is described. This instrument was developed for the HERMES experiment at DESY which emphasises measurements of semi-inclusive deep-inelastic scattering. It provides particle identification for pions, kaons, and protons in the momentum range from 2 to 15 GeV , which is essential to these studies. The instrument uses two radiators, C 4 F 10 , a heavy fluorocarbon gas, and a wall of silica aerogel tiles. The use of aerogel in a RICH detector has only recently become possible with the development of clear, large, homogeneous and hydrophobic aerogel. A lightweight mirror was constructed using a newly perfected technique to make resin-coated carbon-fiber surfaces of optical quality. The photon detector consists of 1934 photomultiplier tubes (PMT) for each detector half, held in a soft steel matrix to provide shielding against the residual field of the main spectrometer magnet.

Gauge bosons at zero and finite temperature

Abstract Gauge theories of the Yang–Mills type are the single most important building block of the standard model of particle physics and beyond. They are an integral part of the strong and weak interactions, and in their Abelian version of electromagnetism. Since Yang–Mills theories are gauge theories their elementary particles, the gauge bosons, cannot be described without fixing a gauge. Therefore, to obtain their properties a quantized and gauge-fixed setting is necessary. Beyond perturbation theory, gauge-fixing in non-Abelian gauge theories is obstructed by the Gribov–Singer ambiguity, which requires the introduction of non-local constraints. The construction and implementation of a method-independent gauge-fixing prescription to resolve this ambiguity is the single most important first step to describe gauge bosons beyond perturbation theory. Proposals for such a procedure, generalizing the perturbative Landau gauge, are described here. Their implementation are discussed for two example methods, lattice gauge theory and the quantum equations of motion. After gauge-fixing, it is possible to study gauge bosons in detail. The most direct access is provided by their correlation functions. The corresponding two- and three-point correlation functions are presented at all energy scales. These give access to the properties of the gauge bosons, like their absence from the asymptotic physical state space, particle-like properties at high energies, and the running coupling. Furthermore, auxiliary degrees of freedom are introduced during gauge-fixing, and their properties are discussed as well. These results are presented for two, three, and four dimensions, and for various gauge algebras. Finally, the modifications of the properties of gauge bosons at finite temperature are presented. Evidence is provided that these reflect the phase structure of Yang–Mills theory. However, it is found that the phase transition is not deconfining the gauge bosons, although the bulk thermodynamical behavior is of a Stefan–Boltzmann type. The resolution of this apparent contradiction is also presented. In addition, this resolution provides an explicit and constructive solution to the Linde problem. Thus, the technical and conceptual framework presented here can be taken as a basis how to determine correlation functions in Yang–Mills theory, therefore opening up the avenue to investigate theories of direct practical relevance. The status of this effort will be briefly described, alongside with connections to other approaches to Yang–Mills theory beyond perturbation theory.

Infrared behavior of the ghost-gluon vertex in Landau gauge Yang-Mills theory

A semiperturbative calculation of the ghost-gluon vertex in Landau-gauge Yang-Mills theory in four and three Euclidean space-time dimensions is presented. Nonperturbative gluon and ghost propagators are employed, which have previously been calculated from a truncated set of Dyson-Schwinger equations and which are in qualitative and quantitative agreement with corresponding lattice results. Our results for the ghost-gluon vertex show only relatively small deviations from the tree-level one in agreement with recent lattice data. In particular, we do not see any sign for a singular behavior of the ghost-gluon vertex in the infrared.

Modification of the rho meson detected by low-mass electron-positron pairs in central Pb-Au collisions at 158A GeV/c

Abstract We present a measurement of e + e − pair production in central Pb Au collisions at 158 A GeV / c . As reported earlier, a significant excess of the e + e − pair yield over the expectation from hadron decays is observed. The improved mass resolution of the present data set, recorded with the upgraded CERES experiment at the CERN-SPS, allows for a comparison of the data with different theoretical approaches. The data clearly favor a substantial in-medium broadening of the ρ spectral function over a density-dependent shift of the ρ pole mass. The in-medium broadening model implies that baryon induced interactions are the key mechanism to the observed modifications of the ρ meson at SPS energy.

More on Gribov copies and propagators in Landau-gauge Yang-Mills theory

Fixing a gauge in the nonperturbative domain of Yang-Mills theory is a nontrivial problem due to the presence of Gribov copies. In particular, there are different gauges in the nonperturbative regime which all correspond to the same definition of a gauge in the perturbative domain. Gauge-dependent correlation functions may differ in these gauges. Two such gauges are the minimal Landau gauge and the absolute Landau gauge, both corresponding to the perturbative Landau gauge. These, and their numerical implementation, are described and presented in detail. Other choices will also be discussed. This investigation is performed, using numerical lattice gauge theory calculations, by comparing the propagators of gluons and ghosts for the minimal Landau gauge and the absolute Landau gauge in SU(2) Yang-Mills theory. It is found that the propagators are different in the far infrared and even at energy scales of the order of half a GeV. In particular, the finite-volume effects are also modified. This is observed in two and three dimensions. Some remarks on the four-dimensional case are provided as well.

Two and three-point Green's functions in two-dimensional Landau-gauge Yang-Mills theory

The ghost and gluon propagator and the ghost-gluon and three-gluon vertex of two-dimensional SU(2) Yang-Mills theory in (minimal) Landau gauge are studied using lattice gauge theory. It is found that the results are qualitatively similar to the ones in three and four dimensions. The propagators and the Faddeev-Popov operator behave as expected from the Gribov-Zwanziger scenario. In addition, finite-volume effects affecting these Greens functions are investigated systematically. The critical infrared exponents of the propagators, as proposed in calculations using stochastic quantization and Dyson-Schwinger equations, are confirmed quantitatively. For this purpose lattices of volume up to (42.7 fm){sup 2} have been used.

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.

High-temperature limit of Landau-gauge Yang-Mills theory

Abstract.The infrared properties of the high-temperature limit of Landau-gauge Yang-Mills theory are investigated. In a first step the high-temperature limit of the Dyson-Schwinger equations is taken. The resulting equations are identical to the Dyson-Schwinger equations of the dimensionally reduced theory, a three-dimensional Yang-Mills theory coupled to an effective adjoint Higgs field. These equations are solved analytically in the infrared and ultraviolet, and numerically for all Euclidean momenta. We find infrared enhancement for the Faddeev-Popov ghosts, infrared suppression for transverse gluons and a mass for the Higgs. These results imply long-range interactions and over-screening in the chromomagnetic sector of high-temperature Yang-Mills theory while in the chromoelectric sector only screening is observed.