Mean field exponents and small quark masses

We demonstrate that the restoration of chiral symmetry at finite-T in a class of confining Dyson-Schwinger equation (DSE) models of QCD is a mean field transition, and that an accurate determination of the critical exponents using the chiral and thermal susceptibilities requires very small values of the current-quark mass: log_{10}(m/m_u) < -5. Other classes of DSE models characterised by qualitatively different interactions also exhibit a mean field transition. Incipient in this observation is the suggestion that mean field exponents are a result of the gap equation's fermion substructure and not of the interaction.Comment: 13 pages, 3 figures, REVTEX, epsfi

Chiral symmetry breaking in dimensionally regularized nonperturbative quenched QED

In this paper we study dynamical chiral symmetry breaking in dimensionally regularized quenched QED within the context of Dyson-Schwinger equations. In D < 4 dimensions the theory has solutions which exhibit chiral symmetry breaking for all values of the coupling. To begin with, we study this phenomenon both numerically and, with some approximations, analytically within the rainbow approximation in the Landau gauge. In particular, we discuss how to extract the critical coupling alpha_c = pi/3 relevant in four dimensions from the D dimensional theory. We further present analytic results for the chirally symmetric solution obtained with the Curtis-Pennington vertex as well as numerical results for solutions exhibiting chiral symmetry breaking. For these we demonstrate that, using dimensional regularization, the extraction of the critical coupling relevant for this vertex is feasible. Initial results for this critical coupling are in agreement with cut-off based work within the currently achievable numerical precision.Comment: 24 pages, including 5 figures; submitted to Phys. Rev.

Running coupling and fermion mass in strong coupling QED

Simple toy model is used in order to exhibit the technique of extracting the non-perturbative information about Green's functions in Minkowski space. The effective charge and the dynamical electron mass are calculated in strong coupling 3+1 QED by solving the coupled Dyson-Schwinger equations for electron and photon propagators. The minimal Ball-Chiu vertex was used for simplicity and we impose the Landau gauge fixing on QED action. The solution obtained separately in Euclidean and Minkowski space were compared, the latter one was extracted with the help of spectral technique.Comment: 23 pages, 4 figures, v4: revised and extended version, one introductory section adde

The π\pi, K+K^+, and K0K^0 electromagnetic form factors

The rainbow truncation of the quark Dyson-Schwinger equation is combined with the ladder Bethe-Salpeter equation for the meson amplitudes and the dressed quark-photon vertex in a self-consistent Poincar\'e-invariant study of the pion and kaon electromagnetic form factors in impulse approximation. We demonstrate explicitly that the current is conserved in this approach and that the obtained results are independent of the momentum partitioning in the Bethe-Salpeter amplitudes. With model gluon parameters previously fixed by the condensate, the pion mass and decay constant, and the kaon mass, the charge radii and spacelike form factors are found to be in good agreement with the experimental data.Comment: 8 pages, 6 figures, Revte

The Quark-Photon Vertex and the Pion Charge Radius

The rainbow truncation of the quark Dyson-Schwinger equation is combined with the ladder Bethe-Salpeter equation for the dressed quark-photon vertex to study the low-momentum behavior of the pion electromagnetic form factor. With model gluon parameters previously fixed by the pion mass and decay constant, the pion charge radius $r_\pi$ is found to be in excellent agreement with the data. When the often-used Ball-Chiu Ansatz is used to construct the quark-photon vertex directly from the quark propagator, less than half of $r_\pi^2$ is generated. The remainder of $r^2_\pi$ is seen to be attributable to the presence of the $\rho$-pole in the solution of the ladder Bethe-Salpeter equation.Comment: 21 pages, 9 figure

Multiplicative renormalizability and quark propagator

The renormalized Dyson-Schwinger equation for the quark propagator is studied, in Landau gauge, in a novel truncation which preserves multiplicative renormalizability. The renormalization constants are formally eliminated from the integral equations, and the running coupling explicitly enters the kernels of the new equations. To construct a truncation which preserves multiplicative renormalizability, and reproduces the correct leading order perturbative behavior, non-trivial cancellations involving the full quark-gluon vertex are assumed in the quark self-energy loop. A model for the running coupling is introduced, with infrared fixed point in agreement with previous Dyson-Schwinger studies of the gauge sector, and with correct logarithmic tail. Dynamical chiral symmetry breaking is investigated, and the generated quark mass is of the order of the extension of the infrared plateau of the coupling, and about three times larger than in the Abelian approximation, which violates multiplicative renormalizability. The generated scale is of the right size for hadronic phenomenology, without requiring an infrared enhancement of the running coupling.Comment: 17 pages; minor corrections, comparison to lattice results added; accepted for publication in Phys. Rev.

Confinement Phenomenology in the Bethe-Salpeter Equation

We consider the solution of the Bethe-Salpeter equation in Euclidean metric for a qbar-q vector meson in the circumstance where the dressed quark propagators have time-like complex conjugate mass poles. This approximates features encountered in recent QCD modeling via the Dyson-Schwinger equations; the absence of real mass poles simulates quark confinement. The analytic continuation in the total momentum necessary to reach the mass shell for a meson sufficiently heavier than 1 GeV leads to the quark poles being within the integration domain for two variables in the standard approach. Through Feynman integral techniques, we show how the analytic continuation can be implemented in a way suitable for a practical numerical solution. We show that the would-be qbar-q width to the meson generated from one quark pole is exactly cancelled by the effect of the conjugate partner pole; the meson mass remains real and there is no spurious qbar-q production threshold. The ladder kernel we employ is consistent with one-loop perturbative QCD and has a two-parameter infrared structure found to be successful in recent studies of the light SU(3) meson sector.Comment: Submitted for publication; 10.5x2-column pages, REVTEX 4, 3 postscript files making 3 fig

HIV Serostatus and Tumor Differentiation Among Patients with Cervical Cancer at Bugando Medical Centre.

Evidence for the association between Human immunodeficiency virus infection and cervical cancer has been contrasting, with some studies reporting increased risk of cervical cancer among HIV positive women while others report no association. Similar evidence from Tanzania is scarce as HIV seroprevalence among cervical cancer patients has not been rigorously evaluated. The purpose of this study was to determine the association between HIV and tumor differentiation among patients with cervical cancer at Bugando Medical Centre and Teaching Hospital in Mwanza, North-Western Tanzania. This was a descriptive analytical study involving suspected cervical cancer patients seen at the gynaecology outpatient clinic and in the gynaecological ward from November 2010 to March 2011. A total of 91 suspected cervical cancer patients were seen during the study period and 74 patients were histologically confirmed with cervical cancer. The mean age of those confirmed of cervical cancer was 50.5 ± 12.5 years. Most patients (39 of the total 74-52.7%) were in early disease stages (stages IA-IIA). HIV infection was diagnosed in 22 (29.7%) patients. On average, HIV positive women with early cervical cancer disease had significantly more CD4+ cells than those with advanced disease (385.8 ± 170.4 95% CI 354.8-516.7 and 266.2 ± 87.5, 95% CI 213.3-319.0 respectively p = 0.042). In a binary logistic regression model, factors associated with HIV seropositivity were ever use of hormonal contraception (OR 5.79 95% CI 1.99-16.83 p = 0.001), aged over 50 years (OR 0.09 95% CI 0.02-0.36 p = 0.001), previous history of STI (OR 3.43 95% CI 1.10-10.80 p = 0.035) and multiple sexual partners OR 5.56 95% CI 1.18-26.25 p = 0.030). Of these factors, only ever use of hormonal contraception was associated with tumor cell differentiation (OR 0.16 95% CI 0.06-0.49 p = 0.001). HIV seropositivity was weakly associated with tumor cell differentiation in an unadjusted analysis (OR 0.21 95% CI 0.04-1.02 p = 0.053), but strong evidence for the association was found after adjusting for ever use of hormonal contraception with approximately six times more likelihood of HIV infection among women with poorly differentiated tumor cells compared to those with moderately and well differentiated cells (OR 5.62 95% CI 1.76-17.94 p = 0.004).\ud Results from this study setting suggest that HIV is common among cervical cancer patients and that HIV seropositivity may be associated with poor tumour differentiation. Larger studies in this and similar settings with high HIV prevalence and high burden of cervical cancer are required to document this relationship

Facets of confinement and dynamical chiral symmetry breaking

The gap equation is a cornerstone in understanding dynamical chiral symmetry breaking and may also provide clues to confinement. A symmetry-preserving truncation of its kernel enables proofs of important results and the development of an efficacious phenomenology. We describe a model of the kernel that yields: a momentum-dependent dressed-quark propagator in fair agreement with quenched lattice-QCD results; and chiral limit values: f_pi= 68 MeV and = -(190 MeV)^3. It is compared with models inferred from studies of the gauge sector.Comment: 5 pages, 3 figures; contribution to the proceedings of Quark Nuclear Physics (QNP 2002), Juelich, Germany, 9-14 Jun 200

Analysis of a quenched lattice-QCD dressed-quark propagator

Quenched lattice-QCD data on the dressed-quark Schwinger function can be correlated with dressed-gluon data via a rainbow gap equation so long as that equation's kernel possesses enhancement at infrared momenta above that exhibited by the gluon alone. The required enhancement can be ascribed to a dressing of the quark-gluon vertex. The solutions of the rainbow gap equation exhibit dynamical chiral symmetry breaking and are consistent with confinement. The gap equation and related, symmetry-preserving ladder Bethe-Salpeter equation yield estimates for chiral and physical pion observables that suggest these quantities are materially underestimated in the quenched theory: |<bar-q q>| by a factor of two and f_pi by 30%.Comment: 9 pages, LaTeX2e, REVTEX4, 6 figure