https://hal.archives-ouvertes.fr/jpa-00239583/document

Il nuovo cimento

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.

QCD and strongly coupled gauge theories: challenges and perspectives

A method to calculate the elastic scattering amplitude at low energies in two-dimensional quantum field theories is proposed and tested in a numerical simulation of the 0(3) non-linear if-model on a simple square lattice. We also compute the isospin current form factor in this model and compare our results with the known exact expressions for the S-matrix and the form factor in the continuum limit. As a technical improvement, we introduce a two-cluster simulation algorithm which leads to significantly reduced statistical errors in the calculation of four-point correlation functions.

https://physics.ucsd.edu/students/courses/spring2013/physics142/labs/finalprojects/luscherwolff.pdf

HOW TO CALCULATETHE ELASTICSCATFERINGMATRiX IN TWO-DIMENSIONALQUANTUMFIELD THEORIES BY NUMERICAL SIMULATION

I review recent results on the infrared properties of QCD from Dyson-Schwinger equations. The topics include infrared exponents of one-particle irreducible Green's functions, the fixed point behaviour of the running coupling at zero momentum, the pattern of dynamical quark mass generation and properties of light mesons.

http://iopscience.iop.org/article/10.1088/0954-3899/32/8/R02/pdf

Infrared properties of QCD from Dyson-Schwinger equations

The quark model was formulated in 1964 to classify mesons as bound states made of a quark-antiquark pair, and baryons as bound states made of three quarks. For a long time all known mesons and baryons could be classified within this scheme. Quantum Chromodynamics (QCD), however, in principle also allows the existence of more complex structures, generically called exotic hadrons or simply exotics. These include four-quark hadrons (tetraquarks and hadronic molecules), five-quark hadrons (pentaquarks) and states with active gluonic degrees of freedom (hybrids), and even states of pure glue (glueballs). Exotic hadrons have been systematically searched for in numerous experiments for many years. Remarkably, in the past fifteen years, many new hadrons that do not exhibit the expected properties of ordinary (not exotic) hadrons have been discovered in the quarkonium spectrum. These hadrons are collectively known as $XYZ$ states. Some of them, like the charged states, are undoubtedly exotic. Parallel to the experimental progress, the last decades have also witnessed an enormous theoretical effort to reach a theoretical understanding of the $XYZ$ states. Theoretical approaches include not only phenomenological extensions of the quark model to exotics, but also modern non-relativistic effective field theories and lattice QCD calculations. The present work aims at reviewing the rapid progress in the field of exotic $XYZ$ hadrons over the past few years both in experiments and theory. It concludes with a summary on future prospects and challenges.

The $XYZ$ states: experimental and theoretical status and perspectives

We report the first study of the nucleon where the full Poincare-covariant structure of the three-quark amplitude is implemented in the Faddeev equation. We employ an interaction kernel which is consistent with contemporary studies of meson properties and aspects of chiral symmetry and its dynamical breaking, thus yielding a comprehensive approach to hadron physics. The resulting current-mass evolution of the nucleon mass compares well with lattice data and deviates only by ∼5% from the quark-diquark result obtained in previous studies.

Nucleon mass from a covariant three-quark Faddeev equation.

Features of the dressed-quark-gluon vertex and their role in the gap and Bethe-Salpeter equations are explored. It is argued that quenched lattice data indicate the existence of net attraction in the color-octet projection of the quark-antiquark scattering kernel. The study employs a vertex model whose diagrammatic content is explicitly enumerable. That enables the systematic construction of a vertex-consistent Bethe-Salpeter kernel and thereby an exploration of the consequences for the strong interaction spectrum of attraction in the color-octet channel. With rising current-quark mass the rainbow-ladder truncation is shown to provide an increasingly accurate estimate of a bound state's mass. Moreover, the calculated splitting between vector and pseudoscalar meson masses vanishes as the current-quark mass increases, which argues for the mass of the pseudoscalar partner of the $\ensuremath{\Upsilon}(1S)$ to be above $9.4\phantom{\rule{0.3em}{0ex}}\mathrm{GeV}$. With the amount of attraction suggested by lattice data color-antitriplet diquarks are absent from the strong interaction spectrum.

https://arxiv.org/pdf/nucl-th/0403012.pdf

Aspects and consequences of a dressed-quark-gluon vertex

We present a Poincar\'e covariant Faddeev equation, which enables the simultaneous prediction of meson and baryon observables using the leading order in a truncation of the Dyson-Schwinger equations that can systematically be improved. The solution describes a nucleon's dressed-quark core. The evolution of the nucleon mass with current-quark mass is discussed. A nucleon-photon current, which can produce nucleon form factors with realistic ${Q}^{2}$ evolution, is described. Axial-vector diquark correlations lead to a neutron Dirac form factor that is negative, with ${r}_{1}^{\mathit{nu}}g{r}_{1}^{\mathit{nd}}$. The proton electric-magnetic form factor ratio falls with increasing ${Q}^{2}$.

Toward unifying the description of meson and baryon properties

Goldstone modes are the only pseudoscalar mesons to possess a nonzero leptonic decay constant in the chiral limit when chiral symmetry is dynamically broken. The decay constants of their radial excitations vanish. These features and aspects of their impact on the meson spectrum are illustrated using a manifestly covariant and symmetry-preserving model of the kernels in the gap and Bethe-Salpeter equations.

https://arxiv.org/pdf/nucl-th/0406030.pdf

Pseudoscalar meson radial excitations

A Poincare' covariant Faddeev equation, which describes baryons as composites of confined-quarks and -nonpointlike-diquarks, is solved to obtain masses and Faddeev amplitudes for the nucleon and Delta. The amplitudes are a component of a nucleon-photon vertex that automatically fulfills the Ward-Takahashi identity for on-shell nucleons. These elements are sufficient for the calculation of a quark core contribution to the nucleons' electromagnetic form factors. An accurate description of the static properties is not possible with the core alone but the error is uniformly reduced by the incorporation of meson-loop contributions. Such contributions to form factors are noticeable for Q^2 < ~2 GeV^2 but vanish with increasing momentum transfer. Hence, larger Q^2 experiments probe the quark core. The calculated behaviour of G_E^p(Q^2)/G_M^p(Q^2) on Q^2 \in [2,6] GeV^2 agrees with that inferred from polarisation transfer data. Moreover, \sqrt{Q^2} F_2(Q^2)/F_1(Q^2) is approximately constant on this domain. These outcomes result from correlations in the proton's amplitude.

Andreas Krassnigg

Papers

Nucleon mass from a covariant three-quark Faddeev equation.

Aspects and consequences of a dressed-quark-gluon vertex

Toward unifying the description of meson and baryon properties

Pseudoscalar meson radial excitations

On Nucleon Electromagnetic Form Factors