Confinement and Green functions in Landau-gauge QCD
Institut fur Physik, Karl-Franzens-Universitat, Universitatsplatz 5, A-8010 Graz, AustriaIn a functionalapproachto QCD the infraredbehaviourof LandaugaugeGreenfunctionsis inves-tigated. Positivity violation for, and thus conﬁnement of, gluons is demonstrated, and the analyticstructure of the gluon propagator is studied. Quark conﬁnem ent is related to an infrared diver-gence of the quark-gluon vertex. In the latter various components are dynamically induced dueto the spontaneous breaking of chiral symmetry. As a result an infrared ﬁnite running coupling inthe Yang-Mills sector is derived whereas the running coupling related to the quark-gluonvertex isinfrared divergent. Based on a truncation for the quark-gluon vertex Dyson-Schwinger equation,which respects the analytically determined infrared behavior, numerical results for the coupledsystem of the quark propagator and vertex Dyson-Schwinger equations are presented. The result-ing quark mass function as well as the vertex function show only a very weak dependence on thecurrent quark mass in the deep infrared. From this we infer by an analysis of the quark-quarkscattering kernel a linearly rising quark potential with an almost mass independent string tensionin the case of broken chiral symmetry.8th Conference Quark Conﬁnement and the Hadron SpectrumSeptember 1-6, 2008Mainz, Germany

title: Going beyond the propagators of Landau gauge Yang-Mills theory
abstract: We present results for the propagators and the ghost-gluon vertex of Landau gauge Yang-Mills theory obtained from Dyson-Schwinger equations. Solving these three quantities simultaneously constitutes a new step in truncating these equations. We also introduce a new model for the three-gluon vertex that is motivated by lattice results. It features a zero crossing which is confirmed a posteriori by a Dyson-Schwinger calculation. Within our setup we can reproduce lattice data very well. We establish that also for the ghost-gluon vertex a difference between decoupling and scaling solutions is present. For the scaling solution we discuss the possibility of modifying the infrared exponents via an angle dependence of the ghost-gluon vertex. However, no such dependence is found in our calculations. Finally, we calculate the Schwinger function for the gluon propagator.

title: Spurious divergences in Dyson-Schwinger equations
abstract: A bstractWe revisit the treatment of spurious ultraviolet divergences in the equation of motion of the gluon propagator caused by a momentum cutoff and the resulting violation of gauge invariance. With present continuum studies of the gluon propagator from its Dyson-Schwinger equation reaching the level of quantitatively accurate descriptions, it becomes increasingly important to understand how to subtract these spurious divergences in an unambiguous way. Here we propose such a method. It is based entirely on the asymptotic perturbative behavior of the QCD Green’s functions without affecting non-perturbative aspects such as mass terms or the asymptotic infrared behavior. As a particular example, this allows us to assess the possible influence of the tadpole diagram beyond perturbation theory. Finally, we test this method numerically by solving the system of Dyson-Schwinger equations of the gluon and ghost propagators.

title: On the influence of three-point functions on the propagators of Landau gauge Yang-Mills theory
abstract: A bstractWe solve the Dyson-Schwinger equations of the ghost and gluon propagators of Landau gauge Yang-Mills theory together with that of the ghost-gluon vertex. The latter plays a central role in many truncation schemes for functional equations. By including it dynamically we can determine its influence on the propagators. We also suggest a new model for the three-gluon vertex motivated by lattice data which plays a crucial role to obtain stable solutions when the ghost-gluon vertex is included. We find that both vertices have a sizable quantitative impact on the mid-momentum regime and contribute to the reduction of the gap between lattice and Dyson-Schwinger equation results. Furthermore, we establish that the three-gluon vertex dressing turns negative at low momenta as suggested by lattice results in three dimensions.

title: Infrared analysis of Dyson-Schwinger equations taking into account the Gribov horizon in Landau gauge
abstract: The low momentum behavior of the Landau gauge Gribov-Zwanziger action is investigated using the respective Dyson-Schwinger equations. Because of the mixing of the gluon and the auxiliary fields four scenarios can be distinguished for the infrared behavior. Two of them lead to inconsistencies and can be discarded. Another one corresponds to the case where the auxiliary fields behave exactly like the Faddeev-Popov ghosts and the same scaling relation as in standard Landau gauge, {kappa}{sub A}+2{kappa}{sub c}=0, is valid. Even the parameter {kappa} is found to be the same, 0.595. The mixed propagators, which appear, are suppressed in all loops, and their anomalous infrared exponent can also be determined. A fourth case provides an even stricter scaling relation that includes also the mixed propagators, but possesses the same qualitative feature, i.e. the propagators of the Faddeev-Popov ghost and the auxiliary fields are infrared enhanced and the mixed and the gluon propagators are infrared suppressed. In this case the system of equations to obtain the parameter {kappa} is nonlinear in all variables.

title: The infrared behavior of Landau gauge Yang–Mills theory in d=2, 3 and 4 dimensions
abstract: We develop a general power counting scheme for the infrared limit of Landau gauge SU ( N ) Yang–Mills theory in arbitrary dimensions. Employing a skeleton expansion, we find that the infrared behavior is qualitatively independent of the spacetime dimension d . In the cases d = 2 , 3 and 4 even the quantitative results for the infrared exponents of the vertices differ only slightly. Therefore, corresponding lattice simulations provide interesting qualitative information for the physical case. We furthermore find that the loop integrals depend only weakly on the numerical values of the IR exponents.

title: Photon and pion scattering on the basis of quark models
abstract: Within the framework of constituent quark models of simple and complex hadrons it is possible to investigate the interrelations of scattering observables and dynamical assumptions about the underlying quark structure of the participating hadrons. In the case of simple hadrons, here baryons, the inclusion of the coupling of bound q3-states to meson-baryon decay channels, accounts for the full complexity of the fact that all excited baryonic states are in fact resonances. We present here such a description of the baryonic excitation spectrum within the non-relativistic quarkmodel with all terms of the Fermi-Breit interaction. In this case the very hadronic vertices that are responsible for the dressing of hadrons also provide a semi realistic description of various scattering observables for pion scattering and photo-production of pions. The treatment of more complex hadronic systems within the framework of a quark shell model of nuclei is then used to investigate the role of the quark Pauli principle in intermediate energy excitations of nuclei with pionic or photonic probes.

title: Central and noncentral components of the effective sd-shell interaction
abstract: The contributions of central as well as noncentral two-body interactions to the matrix elements of various effective interactions for the $\mathrm{sd}$ shell are studied in an SU(3) two-particle basis. The results show that their central parts agree rather well and exhibit an approximate SU(3) symmetry. However, large differences are found between the noncentral parts of microscopic and phenomenological interactions, respectively. The influence of noncentral components of the matrix elements of Glaudemans et al. on experimental data is investigated for the case of $^{28}\mathrm{Si}$, with the result that the $\mathrm{LS}$ component is very important to reproduce the correct ground state binding energy. Some effects introduced by higher order two-body interactions and many-body interactions are discussed.

title: Search for axions with the CDMS experiment.
abstract: We report on the first axion search results from the Cryogenic Dark Matter Search (CDMS) experiment at the Soudan Underground Laboratory. An energy threshold of 2 keV for electron-recoil events allows a search for possible solar axion conversion into photons or local galactic axion conversion into electrons in the germanium crystal detectors. The solar axion search sets an upper limit on the Primakov coupling g(agammagamma) of 2.4x10(-9) GeV-1 at the 95% confidence level for an axion mass less than 0.1 keV/c2. This limit benefits from the first precise measurement of the absolute crystal plane orientations in this type of experiment. The galactic axion search analysis sets a world-leading experimental upper limit on the axioelectric coupling g(aee) of 1.4x10(-12) at the 90% confidence level for an axion mass of 2.5 keV/c2.

title: X-ray selected galaxy clusters in the Pan-STARRS Medium Deep Survey
abstract: We present the results of a pilot study for the extended Massive Cluster Survey (eMACS), a comprehensive search for distant, X-ray luminous galaxy clusters at z > 0.5. Our pilot study applies the eMACS concept to the 71 deg2 area extended by the 10 fields of the Pan-STARRS1 (PS1) Medium Deep Survey (MDS). Candidate clusters are identified by visual inspection of PS1 images in the g, r, i and z bands in a 5 × 5 arcmin2 region around X-ray sources detected in the ROSAT All-Sky Survey (RASS). To test and optimize the eMACS X-ray selection criteria, our pilot study uses the largest possible RASS data base, i.e. all RASS sources listed in the Bright and Faint Source Catalogues (BSC and FSC) that fall within the MDS footprint. We apply no additional constraints regarding X-ray flux, spectral hardness ratio or photon statistics and lower the redshift threshold to z > 0.3 to extend the probed luminosity range to poorer systems. Scrutiny of PS1/MDS images for 41 BSC and 200 FSC sources combined with dedicated spectroscopic follow-up observations results in a sample of 11 clusters with estimated or spectroscopic redshifts of z > 0.3. In order to assess and quantify the degree of point source contamination of the observed RASS fluxes, we examine archival Chandra data obtained in targeted and serendipitous observations of six of the 11 clusters found. As expected, the diffuse emission from all six systems is contaminated by point sources to some degree, and for half of them active galactic nucleus emission dominates. X-ray follow-up observations will thus be crucial in order to establish robust cluster luminosities for eMACS clusters. Although the small number of distant X-ray luminous clusters in the MDS does not allow us to make firm predictions for the over 20 000 deg2 of extragalactic sky covered by eMACS, the identification of two extremely promising eMACS cluster candidates at z ≳ 0.6 (both yet to be observed with Chandra) in such a small solid angle is encouraging. Representing a tremendous gain over the presently known two dozen such systems from X-ray, optical and Sunyaev–Zel’dovich cluster surveys combined, the sample of over 100 extremely massive clusters at z > 0.5 expected from eMACS would be invaluable for the identification of the most powerful gravitational lenses in the Universe, as well as for in-depth and statistical studies of the physical properties of the most massive galaxy clusters out to z ∼ 1.

title: Surface Event Rejection Using Phonon Information in CDMS
abstract: The published CDMS analyses have used the shape of the phonon signal rising edge to reject low-ionization-yield surface events which produce acoustic phonons more quickly than bulk events do. To achieve better WIMP sensitivity with future larger exposures, we are using a simplified model of phonon production and propagation to construct event position estimators that help us to find more efficient surface event rejection cuts. We describe this model and the resulting new cuts, and summarize the surface event leakage rates and the sensitivity figures of merit of the five surface event rejection methods developed in the second CDMS II Soudan run data analysis.