October 24, 2001
The dichotomy of the pion as QCD's Goldstone mode and a bound state of massive constituents is easily understood using the Dyson-Schwinger equations. That provides the foundation for an efficacious phenomenology, which correlates the pion's charge radius and electromagnetic form factor with its valence quark distribution function; and simultaneously provides a Poincare' covariant description of the nucleon, its form factors and, more recently, meson photoproduction processes. This well-constrained framework can also be used to eliminate candidates for an extension of the Standard Model by providing the relation between current-quark electric dipole moments and that of the neutron
Similar papers 1
November 1, 2000
The contemporary use of Dyson-Schwinger equations in hadronic physics is exemplified via applications to the calculation of pseudoscalar meson masses, and inclusive deep inelastic scattering with a determination of the pion's valence-quark distribution function.
January 15, 2003
Dyson-Schwinger equations furnish a Poincare' covariant framework within which to study hadrons. A particular feature is the existence of a nonperturbative, symmetry preserving truncation that enables the proof of exact results. The gap equation reveals that dynamical chiral symmetry breaking is tied to the long-range behaviour of the strong interaction, which is thereby constrained by observables, and the pion is precisely understood, and seen to exist simultaneously as a Go...
November 13, 2008
A synopsis exemplifying the employment of Dyson-Schwinger equations in the calculation and explanation of hadron electromagnetic form factors and related phenomena. In particular the contribution: presents the pion form factor computed simultaneously at spacelike and timelike momenta; reports aspects of the evolution of the nucleon and Delta masses with current-quark mass and the correlation of their mass difference with that between scalar and axial-vector diquarks; describe...
June 28, 2013
A novel method is employed to compute the pion electromagnetic form factor, F_\pi(Q^2), on the entire domain of spacelike momentum transfer using the Dyson-Schwinger equation (DSE) framework in quantum chromodynamics (QCD). The DSE architecture unifies this prediction with that of the pion's valence-quark parton distribution amplitude (PDA). Using this PDA, the leading-order, leading-twist perturbative QCD result for Q^2 F_\pi(Q^2) underestimates the full computation by just ...
September 3, 2009
This thesis presents an investigation of meson and baryon properties in the framework of covariant bound-state equations based on the Dyson-Schwinger equations of QCD. Pion and rho-meson, diquark, nucleon and delta-baryon masses are obtained as self-consistent solutions of the respective equations for $q\bar{q}$, $qq$, $qqq$ and $q(qq)$ systems. The common parenthesis is given by a rainbow-ladder truncation in the quark-(anti-)quark channel. It includes an effective quark-glu...
May 25, 2000
A perspective on the contemporary use of Dyson-Schwinger equations, focusing on some recent phenomenological applications: a description and unification of light-meson observables using a one-parameter model of the effective quark-quark interaction, and studies of leptonic and nonleptonic nucleon form factors.
October 6, 2000
We illustrate the contemporary application of Dyson-Schwinger equations using two examples: the calculation of pseudoscalar meson masses, an associated model-independent mass formula and the approach to the heavy-quark limit; and the study of nucleon observables, including a calculation of its mass, $M$, via a covariant Fadde'ev equation and an estimate of pion-loop contributions to $M$.
August 26, 1994
The nonperturbative, Dyson-Schwinger equation approach to solving QCD provides a straightforward, microscopic description of dynamical chiral symmetry breaking and confinement. It is an ideal tool for the study of pion observables. This is illustrated via its application to the calculation of: the $\pi$-$\pi$ scattering lengths $a_0^0$, $a_0^2$, $a_1^1$, $a_2^0$, $a_2^2$ and associated partial wave amplitudes; the $\pi^0\rightarrow \gamma\gamma$ decay width; and the charged p...
February 12, 2003
There have been many demonstrations of the utility of the Dyson-Schwinger equations of QCD as a systematic, phenomenological framework for describing the perturbative and non-perturbative dynamics of hadrons in terms of Euclidean Green functions of quarks and gluons. Still, there remain some unanswered questions regarding the theoretical underpinnings of the approach. I review several studies that are shedding light on how these questions might be resolved and review predicti...
July 2, 2014
We describe results for the pion distribution amplitude (PDA) at the non-perturbative scale $\mu=~$2GeV by projecting the Poincar\'e-covariant Bethe-Salpeter wave-function onto the light-front and use it to investigate the ultraviolet behavior of the electromagnetic form factor, $F_\pi(Q^2)$, on the entire domain of spacelike $Q^2$. The significant dilation of this PDA compared to the known asymptotic PDA is a signature of dynamical chiral symmetry breaking (DCSB) on the ligh...