Craig D. Roberts

Dyson-Schwinger equations and their application to hadronic physics

We review the current status of nonperturbative studies of gauge field theory using the Dyson-Schwinger equation formalism and its application to hadronic physics. We begin with an introduction to the formalism and a discussion of renormalisation in this approach. We then review the current status of studies of Abelian gauge theories [e.g., strong coupling quantum electrodynamics] before turning our attention to the non-Abelian gauge theory of the strong interaction, quantum chromodynamics. We discuss confinement, dynamical chiral symmetry breaking and the application and contribution of these techniques to our understanding of the strong interactions.

Dyson-Schwinger equations: A Tool for hadron physics

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 behavior of the strong interaction, which is thereby constrained by observables, and the pion is precisely understood, and seen to exist simultaneously as a Goldstone mode and a bound state of strongly dressed quarks. The systematic error associated with the simplest truncation has been quantified, and it underpins a one-parameter model efficacious in describing an extensive body of mesonic phenomena. Incipient applications to baryons have brought successes and encountered challenges familiar from early studies of mesons, and promise a covariant field theory upon which to base an understanding of contemporary large momentum transfer data.

Pion mass and decay constant

Independent of assumptions about the form of the quark-antiquark scattering kernel we derive the explicit relation between the pion Bethe-Salpeter amplitude, {Gamma}{pi}, and the quark propagator in the chiral limit; {Gamma}{pi} necessarily involves a non-negligible {gamma}{sub 5}{gamma} x P term (P is the pion four-momentum). We also obtain exact expressions for the pion decay constant, f{sub {pi}}, and mass, both of which depend on {Gamma}{sub {pi}}; and demonstrate the equivalence between f{sub {pi}} and the pion Bethe-Salpeter normalization constant in the chiral limit. We stress the importance of preserving the axial-vector Ward-Takahashi identity in any study of the pion itself, and in any study whose goal is a unified understanding of the properties of the pion and other hadronic bound states.

Goldstone theorem and diquark confinement beyond rainbow ladder approximation

Abstract The quark Dyson-Schwinger equation and meson Bethe-Salpeter equation are studied in a truncation scheme that extends the rainbow-ladder approximation such that, in the chiral limit, the isovector, pseudoscalar meson remains massless. Repulsive contributions, which appear at higher order in the Bethe-Salpeter kernel, eliminate the bound state pole in the quark-quark (diquark) channel that is present in rainbow-ladder approximation. The net effect of higher order terms on the meson bound state masses is small.

Collective perspective on advances in Dyson-Schwinger Equation QCD

We survey contemporary studies of hadrons and strongly interacting quarks using QCDs Dyson—Schwinger equations, addressing the following aspects: confinement and dynamical chiral symmetry breaking; the hadron spectrum; hadron elastic and transition form factors, from small- to large-Q2; parton distribution functions; the physics of hadrons containing one or more heavy quarks; and properties of the quark gluon plasma.

Sketching the Bethe-Salpeter kernel

An exact form is presented for the axial-vector Bethe-Salpeter equation, which is valid when the quark-gluon vertex is fully dressed. A Ward-Takahashi identity for the Bethe-Salpeter kernel is derived therefrom and solved for a class of dressed quark-gluon-vertex models. The solution provides a symmetry-preserving closed system of gap and vertex equations. The analysis can be extended to the vector equation. This enables a comparison between the responses of pseudoscalar and scalar meson masses to nonperturbatively dressing the quark-gluon vertex. The result indicates that dynamical chiral symmetry breaking enhances spin-orbit splitting in the meson spectrum.

Explanation and Prediction of Observables using Continuum Strong QCD

Abstract The last five years have brought considerable progress in the study of the bound-state problem in continuum quantum field theory. We highlight a subset of that progress; viz., that made within the context of Dyson–Schwinger equation analyses of cold, sparse hadrons. Our focus is primarily on advances in the reliable computation, explanation and prediction of quantities that are truly measurable; but we also review aspects of a new paradigm that has condensates contained within hadrons, and explain that the asymptotic form of parton distribution amplitudes and functions are practically unreachable with terrestrial facilities. Given the pace of expansion in experiment and improvement in theory, it appears possible that the next five years will bring profound growth in our store of knowledge about hadrons and nuclei.

STUDIES OF NUCLEON RESONANCE STRUCTURE IN EXCLUSIVE MESON ELECTROPRODUCTION

Studies of the structure of excited baryons are key factors to the N* program at Jefferson Lab (JLab). Within the first year of data taking with the Hall B CLAS12 detector following the 12 GeV upgrade, a dedicated experiment will aim to extract the N* electrocouplings at high photon virtualities Q2. This experiment will allow exploration of the structure of N* resonances at the highest photon virtualities ever achieved, with a kinematic reach up to Q2 = 12 GeV2. This high-Q2 reach will make it possible to probe the excited nucleon structures at distance scales ranging from where effective degrees of freedom, such as constituent quarks, are dominant through the transition to where nearly massless bare-quark degrees of freedom are relevant. In this document, we present a detailed description of the physics that can be addressed through N* structure studies in exclusive meson electroproduction. The discussion includes recent advances in reaction theory for extracting N* electrocouplings from meson electropro...

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 equations 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;

Pair creation and an x-ray free electron laser

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