Coulomb gauge confinement in the heavy quark limit

The relationship between the nonperturbative Green's functions of Yang-Mills theory and the confinement potential is investigated. By rewriting the generating functional of quantum chromodynamics in terms of a heavy quark mass expansion in Coulomb gauge, restricting to leading order in this expansion and considering only the two-point functions of the Yang-Mills sector, the rainbow-ladder approximation to the gap and Bethe-Salpeter equations is shown to be exact in this case and an analytic, nonperturbative solution is presented. It is found that there is a direct connection between the string tension and the temporal gluon propagator. Further, it is shown that for the 4-point quark correlation functions, only confined bound states of color-singlet quark-antiquark (meson) and quark-quark (baryon) pairs exist.Comment: 22 pages, 6 figure

Beyond the rainbow: effects from pion back-coupling

We investigate hadronic unquenching effects in light quarks and mesons. To this end we take into account the back-coupling of the pion onto the quark propagator within the non-perturbative continuum framework of Schwinger-Dyson equations (SDE) and Bethe-Salpeter equations (BSE). We improve on a previous approach by explicitly solving both the coupled system of DSEs and BSEs in the complex plane and the normalisation problem for Bethe-Salpeter kernels depending on the total momentum of the meson. As a result of our study we find considerable unquenching effects in the spectrum of light pseudoscalar, vector and axial-vector mesons.Comment: 9 pages, 5 figures. Minor typos corrected. Version to appear in PR

Probing Unquenching Effects in the Gluon Polarisation in Light Mesons

We introduce an extension to the ladder truncated Bethe-Salpeter equation for mesons and the rainbow truncated quark Dyson-Schwinger equations which includes quark-loop corrections to the gluon propagator. This truncation scheme obeys the axialvector Ward-Takahashi identity relating the quark self-energy and the Bethe-Salpeter kernel. Two different approximations to the Yang-Mills sector are used as input: the first is a sophisticated truncation of the full Yang-Mills Dyson-Schwinger equations, the second is a phenomenologically motivated form. We find that the spectra and decay constants of pseudoscalar and vector mesons are overall described well for either approach. Meson mass results for charge eigenstate vector and pseudoscalar meson masses are compared to lattice data. The effects of unquenching the system are small but not negligible.Comment: 26 pages, 13 figure

Probing the gluon self-interaction in light mesons

We investigate masses and decay constants of light mesons from a coupled system of Dyson--Schwinger and Bethe--Salpeter equations. We explicitly take into account dominant non-Abelian contributions to the dressed quark-gluon vertex stemming from the gluon self-interaction. We construct the corresponding Bethe-Salpeter kernel that satisfies the axial-vector Ward-Takahashi identity. Our numerical treatment fully includes all momentum dependencies with all equations solved completely in the complex plane. This approach goes well beyond the rainbow-ladder approximation and permits us to investigate the influence of the gluon self-interaction on the properties of mesons. As a first result we find indications of a nonperturbative cancellation of the gluon self-interaction contributions and pion cloud effects in the mass of the rho-meson.Comment: 4 pages, 5 figures. Matches published version in PR

Dyson-Schwinger Equations and Coulomb Gauge Yang-Mills Theory

Coulomb gauge Yang-Mills theory is considered within the first order formalism. It is shown that the action is invariant under both the standard BRS transform and an additional component. The Ward-Takahashi identity arising from this non-standard transform is shown to be automatically satisfied by the equations of motion.Comment: 3 pages, talk given at Quark Confinement and the Hadron Spectrum VII (2-7 Sep, 2006), Ponta Delgada, Azore

The metallicity of gamma-ray burst environments from high energy observations

Gamma-ray bursts (GRBs) and their early afterglows ionise their circumburst material. Only high-energy spectroscopy therefore, allows examination of the matter close to the burst itself. Soft X-ray absorption allows an estimate to be made of the total column density in metals. The detection of the X-ray afterglow can also be used to place a limit on the total gas column along the line of sight based on the Compton scattering opacity. Such a limit would enable, for the first time, the determination of lower limits on the metallicity in the circumburst environments of GRBs. In this paper, we determine the limits that can be placed on the total gas column density in the vicinities of GRBs based on the Compton scattering. We simulate the effects of Compton scattering on a collimated beam of high energy photons passing through a shell of high column density material to determine the expected lightcurves, luminosities, and spectra. We compare these predictions to observations, and determine what limits can realistically be placed on the total gas column density. The smearing out of pulses in the lightcurve from Compton scattering is not likely to be observable, and its absence does not place strong constraints on the Compton depth for GRBs. However, the distribution of observed luminosities of bursts allows us to place statistical, model-dependent limits that are typically <~1e25 cm^{-2} for less luminous bursts, and as low as ~1e24 cm$^{-2} for the most luminous. Using the shape of the high-energy broadband spectrum, however, in some favourable cases, limits as low as ~5e24 cm^{-2} can placed on individual bursts, implying metallicity lower limits from X- and gamma-rays alone from 0 up to 0.01 Z/Zsun. At extremely high redshifts, this limit would be at least 0.02 Z/Z_sun, enough to discriminate population III from non-primordial GRBs.Comment: 4 pages, 4 figures, submitted to A&A letter

The ghost propagator in Coulomb gauge

We present results for a numerical study of the ghost propagator in Coulomb gauge whereby lattice results for the spatial gluon propagator are used as input to solving the ghost Dyson-Schwinger equation. We show that in order to solve completely, the ghost equation must be supplemented by a boundary condition (the value of the inverse ghost propagator dressing function at zero momentum) which determines if the solution is critical (zero value for the boundary condition) or subcritical (finite value). The various solutions exhibit a characteristic behavior where all curves follow the same (critical) solution when going from high to low momenta until `forced' to freeze out in the infrared to the value of the boundary condition. The boundary condition can be interpreted in terms of the Gribov gauge-fixing ambiguity; we also demonstrate that this is not connected to the renormalization. Further, the connection to the temporal gluon propagator and the infrared slavery picture of confinement is discussed.Comment: 3 pages, 2 figures, talk presented at "Quark Confinement and the Hadron Spectrum IX", Madrid, August 30-September 3, 2010, to appear in the proceeding

Aspects of the confinement mechanism in Coulomb-gauge QCD

Phenomenological consequences of the infrared singular, instantaneous part of the gluon propagator in Coulomb gauge are investigated. The corresponding quark Dyson-Schwinger equation is solved, neglecting retardation and transverse gluons and regulating the resulting infrared singularities. While the quark propagator vanishes as the infrared regulator goes to zero, the frequency integral over the quark propagator stays finite and well-defined. Solutions of the homogeneous Bethe-Salpeter equation for the pseudoscalar and vector mesons as well as for scalar and axial-vector diquarks are obtained. In the limit of a vanishing infrared regulator the diquark masses diverge, while meson properties and diquark radii remain finite and well-defined. These features are interpreted with respect to the resulting aspects of confinement for colored quark-quark correlations.Comment: 4 pages, 6 figure