Electromagnetic Form Factors of Charged and Neutral Kaons

The charged and neutral kaon form factors are calculated as a phenomenological application of the QCD Dyson-Schwinger equations. The results are compared with the pion form factor calculated in the same framework and yield \mbox{$F_{K^\pm}(Q^2) > F_{\pi^\pm}(Q^2)$} on \mbox{$Q^2\in[0,3]$~GeV$^2$}; and a neutral kaon form factor that is similar in form and magnitude to the neutron charge form factor. These results are sensitive to the difference between the kaon and pion Bethe-Salpeter amplitude and the $u$- and $s$-quark propagation characteristics.Comment: 11 Pages, 2 figures, REVTEX, uses epsfig. No chang

K_{l 3} and \pi_{e 3} transition form factors

$K_{\ell 3}$ and $\pi_{e 3}$ transition form factors are calculated as an application of Dyson-Schwinger equations. The role of nonanalytic contributions to the quark--W-boson vertex is elucidated. A one-parameter model for this vertex provides a uniformly good description of these transitions, including the value of the scalar form factor of the kaon at the Callan-Treiman point. The $K_{\ell 3}$ form factors, $f_\pm^K$, are approximately linear on $t\in [m_e^2,m_\mu^2]$ and have approximately the same slope. $f_-^K(0)$ is a measure of the Euclidean constituent-quark mass ratio: $M^E_s/M^E_u$. In the isospin symmetric limit: $-f_+^\pi(0)= F_\pi(t)$, the electromagnetic pion form factor, and $f_-^\pi(t)\equiv 0$.Comment: 11 pages (incl. 3 figures), elsart.sty, epsf.st

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

Nucleon form factors and a nonpointlike diquark

Nucleon form factors are calculated on q^2 in [0,3] GeV^2 using an Ansatz for the nucleon's Fadde'ev amplitude motivated by quark-diquark solutions of the relativistic Fadde'ev equation. Only the scalar diquark is retained, and it and the quark are confined. A good description of the data requires a nonpointlike diquark correlation with an electromagnetic radius of 0.8 r_pi. The composite, nonpointlike nature of the diquark is crucial. It provides for diquark-breakup terms that are of greater importance than the diquark photon absorption contribution.Comment: 5 pages, REVTEX, epsfig, 3 figure

Goldstone Theorem and Diquark Confinement Beyond Rainbow-Ladder Approximation

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. Quark-quark (diquark) correlations, which are bound in rainbow-ladder approximation, are destabilised by repulsive contributions that only appear at higher order in the Bethe-Salpeter kernel. The net effect of higher order terms on the meson bound-state masses is small.Comment: 11 pages, LaTeX, elsart.sty, 3 EPS figure

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

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

A continuum order parameter for deconfinement

Dyson-Schwinger equations are presented as a non-perturbative tool for the study and modeling of QCD at finite-{ital T}. An order parameter for deconfinement, applicable for both light and heavy quarks, is introduced. In a simple Dyson-Schwinger equation model of two-flavor QCD, coincident, 2nd-order chiral symmetry restoration and deconfinement transitions occur at {ital T} {approx} 150 MeV, with the same critical exponent, {Beta} {approx} 0.33

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

Looking into the matter of light-quark hadrons

In tackling QCD, a constructive feedback between theory and extant and forthcoming experiments is necessary in order to place constraints on the infrared behaviour of QCD's \beta-function, a key nonperturbative quantity in hadron physics. The Dyson-Schwinger equations provide a tool with which to work toward this goal. They connect confinement with dynamical chiral symmetry breaking, both with the observable properties of hadrons, and hence provide a means of elucidating the material content of real-world QCD. This contribution illustrates these points via comments on: in-hadron condensates; dressed-quark anomalous chromo- and electro-magnetic moments; the spectra of mesons and baryons, and the critical role played by hadron-hadron interactions in producing these spectra.Comment: 11 pages, 7 figures. Contribution to the Proceedings of "Applications of light-cone coordinates to highly relativistic systems - LIGHTCONE 2011," 23-27 May, 2011, Dallas. The Proceedings will be published in Few Body System