Covariant QCD Modeling of Light Meson Physics

We summarize recent progress in soft QCD modeling based on the set of Dyson--Schwinger equations truncated to ladder-rainbow level. This covariant approach to hadron physics accommodates quark confinement and implements the QCD one-loop renormalization group behavior. We compare the dressed quark propagator, pseudoscalar and vector meson masses as a function of quark mass, and the rho -> pi pi coupling to recent lattice-QCD data. The error in the Gell-Mann--Oakes--Renner relation with increasing quark mass is quantified by comparison to the exact pseudoscalar mass relation as evaluated within the ladder-rainbow Dyson-Schwinger model.Comment: Presented at the International School on Nuclear Physics, 24th course: Quarks in Nuclei, Erice, Sicily, September 2002; to be published in Prog. Part. Nucl. Phys.; 6 pages, 6 fig

The quark-photon vertex and meson electromagnetic form factors

The ladder Bethe-Salpeter solution for the dressed photon-quark vertex is used to study the low-momentum behavior of the pion electromagnetic and the $\gamma^\star \pi^0 \gamma$ transition form factors. With model parameters previously fixed by light meson masses and decay constants, the low-momentum slope of both form factors is in excellent agreement with the data. In comparison, the often-used Ball-Chiu Ansatz for the vertex is found to be deficient; less than half of the obtained $r_\pi^2$ is generated by that Ansatz while the remainder of the charge radius could be attributed to the tail of the $\rho$ resonance.Comment: 4 pages, 2 figures, uses espcrc1.sty, talk presented at PANIC99, Uppsala, Swede

Dyson-Schwinger Equations: An Instrument for Hadron Physics

Dyson-Schwinger equations furnish a Poincare' covariant approach to hadron physics. They reveal that dynamical chiral symmetry breaking is tied to the long-range behaviour of the strong interaction and make predictions corroborated by modern lattice-QCD simulations. A hallmark in the contemporary use of DSEs is the existence of a nonperturbative, symmetry preserving truncation that enables the proof of exact results. The systematic error associated with the truncation's leading term has been quantified and this underpins an efficacious one-parameter model that is being employed to study meson excited states.Comment: 9 pages; LaTeX2e; Contribution to proceedings of "17th International Conference on Few-Body Problems in Physics," Duke University/TUNL, 5-10/June/200

Goldstone Boson's Valence-Quark Distribution

Dynamical chiral symmetry breaking (DCSB) is one of the keystones of low-energy hadronic phenomena. Dyson-Schwinger equations provide a model-independent quark-level understanding and correlate that with the behaviour of the pion's Bethe-Salpeter amplitude. This amplitude is a core element in the calculation of pion observables and combined with the dressed-quark Schwinger function required by DCSB it yields a valence-quark distribution function for the pion that behaves as (1-x)^2 for x~1, in accordance with perturbative analyses. This behaviour can be verified at contemporary experimental facilities.Comment: 7 pages, LaTeX2e, espcrc2.sty; Summary of a presentation at the 11th International Light-Cone Workshop: ``Light-cone Physics: Particles and Strings,'' ECT*, Trento, Italy, 3-11/Nov./200

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

QCD modeling of hadron physics

We review recent developments in the understanding of meson properties as solutions of the Bethe-Salpeter equation in rainbow-ladder truncation. Included are recent results for the pseudoscalar and vector meson masses and leptonic decay constants, ranging from pions up to c\bar{c} bound states; extrapolation to b\bar{b} states is explored. We also present a new and improved calculation of F_\pi(Q^2) and an analysis of the \pi\gamma\gamma transition form factor for both \pi(140) and \pi(1330). Lattice-QCD results for propagators and the quark-gluon vertex are analyzed, and the effects of quark-gluon vertex dressing and the three-gluon coupling upon meson masses are considered.Comment: 17 pages, 19 postscript figures, contribution to the proceedings of LC05, Cairns, Australia, July 200

Boolean Circuit Complexity of Regular Languages

In this paper we define a new descriptional complexity measure for Deterministic Finite Automata, BC-complexity, as an alternative to the state complexity. We prove that for two DFAs with the same number of states BC-complexity can differ exponentially. In some cases minimization of DFA can lead to an exponential increase in BC-complexity, on the other hand BC-complexity of DFAs with a large state space which are obtained by some standard constructions (determinization of NFA, language operations), is reasonably small. But our main result is the analogue of the "Shannon effect" for finite automata: almost all DFAs with a fixed number of states have BC-complexity that is close to the maximum.Comment: In Proceedings AFL 2014, arXiv:1405.527

Meson elastic and transition form factors

The Dyson-Schwinger equations of QCD, truncated to ladder-rainbow level, are used to calculate meson form factors in impulse approximation. The infrared strength of the ladder-rainbow kernel is described by two parameters fitted to the chiral condensate and f_pi; the ultraviolet behavior is fixed by the QCD running coupling. This obtained elastic form factors F_pi(Q^2) and F_K(Q^2) agree well with the available data. We also calculate the rho to pi gamma and K* to K gamma transition form factors, which are useful for meson-exchange models.Comment: 6 pages, contribution to the JLab workshop Exclusive processes at high-t, May 200