Selected nucleon form factors and a composite scalar diquark

A covariant, composite scalar diquark, Fadde'ev amplitude model for the nucleon is used to calculate pseudoscalar, isoscalar- and isovector-vector, axial-vector and scalar nucleon form factors. The last yields the nucleon sigma-term and on-shell sigma-nucleon coupling. The calculated form factors are soft, and the couplings are generally in good agreement with experiment and other determinations. Elements in the dressed-quark-axial-vector vertex that are not constrained by the Ward-Takahashi identity contribute ~20% to the magnitude of g_A. The calculation of the nucleon sigma-term elucidates the only unambiguous means of extrapolating meson-nucleon couplings off the meson mass-shell.Comment: 12 pages, REVTEX, 5 figures, epsfi

K -> pi pi and a light scalar meson

We explore the Delta-I= 1/2 rule and epsilon'/epsilon in K -> pi pi transitions using a Dyson-Schwinger equation model. Exploiting the feature that QCD penguin operators direct K^0_S transitions through 0^{++} intermediate states, we find an explanation of the enhancement of I=0 K -> pi pi transitions in the contribution of a light sigma-meson. This mechanism also affects epsilon'/epsilon.Comment: 7 pages, REVTE

IR finiteness of the ghost dressing function from numerical resolution of the ghost SD equation

We solve numerically the Schwinger-Dyson (SD hereafter) ghost equation in the Landau gauge for a given gluon propagator finite at k=0 (alpha_gluon=1) and with the usual assumption of constancy of the ghost-gluon vertex ; we show that there exist two possible types of ghost dressing function solutions, as we have previously inferred from analytical considerations : one singular at zero momentum, satisfying the familiar relation alpha_gluon+2 alpha_ghost=0 between the infrared exponents of the gluon and ghost dressing functions(in short, respectively alpha_G and alpha_F) and having therefore alpha_ghost=-1/2, and another which is finite at the origin (alpha_ghost=0), which violates the relation. It is most important that the type of solution which is realized depends on the value of the coupling constant. There are regular ones for any coupling below some value, while there is only one singular solution, obtained only at a critical value of the coupling. For all momenta k<1.5 GeV where they can be trusted, our lattice data exclude neatly the singular one, and agree very well with the regular solution we obtain at a coupling constant compatible with the bare lattice value.Comment: 17 pages, 3 figures (one new figure and a short paragraph added

Nonperturbative structure of the quark-gluon vertex

The complete tensor structure of the quark--gluon vertex in Landau gauge is determined at two kinematical points (`asymmetric' and `symmetric') from lattice QCD in the quenched approximation. The simulations are carried out at beta=6.0, using a mean-field improved Sheikholeslami-Wohlert fermion action, with two quark masses ~ 60 and 115 MeV. We find substantial deviations from the abelian form at the asymmetric point. The mass dependence is found to be negligible. At the symmetric point, the form factor related to the chromomagnetic moment is determined and found to contribute significantly to the infrared interaction strength.Comment: 16 pages, 11 figures, JHEP3.cl

Valence-quark distributions in the pion

We calculate the pion's valence-quark momentum-fraction probability distribution using a Dyson-Schwinger equation model. Valence-quarks with an active mass of 0.30 GeV carry 71% of the pion's momentum at a resolving scale q_0=0.54 GeV = 1/(0.37 fm). The shape of the calculated distribution is characteristic of a strongly bound system and, evolved from q_0 to q=2 GeV, it yields first, second and third moments in agreement with lattice and phenomenological estimates, and valence-quarks carrying 49% of the pion's momentum. However, pointwise there is a discrepancy between our calculated distribution and that hitherto inferred from parametrisations of extant pion-nucleon Drell-Yan data.Comment: 8 pages, 3 figures, REVTEX, aps.sty, epsfig.sty, minor corrections, version to appear in PR

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.

Quark-gluon vertex in general kinematics

The original publication can be found at www.springerlink.com Submitted to Cornell University’s online archive www.arXiv.org in 2007 by Jon-Ivar Skullerud. Post-print sourced from www.arxiv.org.We compute the quark–gluon vertex in quenched lattice QCD in the Landau gauge, using an off-shell mean-field O(a)-improved fermion action. The Dirac-vector part of the vertex is computed for arbitrary kinematics. We find a substantial infrared enhancement of the interaction strength regardless of the kinematics.Ayse Kizilersu, Derek B. Leinweber, Jon-Ivar Skullerud and Anthony G. William

A dynamical gluon mass solution in a coupled system of the Schwinger-Dyson equations

We study numerically the Schwinger-Dyson equations for the coupled system of gluon and ghost propagators in the Landau gauge and in the case of pure gauge QCD. We show that a dynamical mass for the gluon propagator arises as a solution while the ghost propagator develops an enhanced behavior in the infrared regime of QCD. Simple analytical expressions are proposed for the propagators, and the mass dependency on the $\Lambda_{QCD}$ scale and its perturbative scaling are studied. We discuss the implications of our results for the infrared behavior of the coupling constant, which, according to fits for the propagators infrared behavior, seems to indicate that $\alpha_s (q^2) \to 0$ as $q^2 \to 0$.Comment: 17 pages, 7 figures - Revised version to be consistent with erratum to appear in JHE

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

Closed-Time Path Integral Formalism and Medium Effects of Non-Equilibrium QCD Matter

We apply the closed-time path integral formalism to study the medium effects of non-equilibrium gluon matter. We derive the medium modified resummed gluon propagator to the one loop level in non-equilibrium in the covariant gauge. The gluon propagator we derive can be used to remove the infrared divergences in the secondary parton collisions to study thermalization of minijet parton plasma at RHIC and LHC.Comment: Final version, To appear in Physical Review D, Minor modification, reference adde