A. Höll

Aspects and consequences of a dressed-quark-gluon vertex

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 states 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 {upsilon}(1S) to be above 9.4 GeV. With the amount of attraction suggested by lattice data color-antitriplet diquarks are absent from the strong interaction spectrum.

Pseudoscalar meson radial excitations

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.

Electromagnetic properties of ground-state and excited-state pseudoscalar mesons

The axial-vector Ward-Takahashi identity places constraints on particular properties of every pseudoscalar meson. For example, in the chiral limit all pseudoscalar mesons, except the Goldstone mode, decouple from the axial-vector current. Nevertheless, all neutral pseudoscalar mesons couple to two photons. The strength of the {pi}{sub n}{sup 0}{gamma}{gamma} coupling, where n=0 denotes the Goldstone mode, is affected by the Abelian anomalys continuum contribution. The effect is material for n{ne}0. The {gamma}*{pi}{sub n}{gamma}* transition form factor, T{sub {pi}{sub n}}(Q{sup 2}), is nonzero for all n, and T{sub {pi}{sub n}}(Q{sup 2}){approx_equal}(4{pi}{sup 2}/3)(f{sub {pi}{sub n}}/Q{sup 2}) at large Q{sup 2}. For all pseudoscalars but the Goldstone mode, this leading contribution vanishes in the chiral limit. In this instance the ultraviolet power-law behavior is 1/Q{sup 4} for n{ne}0, and we find numerically T{sub {pi}{sub 1}}(Q{sup 2}){approx_equal}(4{pi}{sup 2}/3)(- /Q{sup 4}). This subleading power-law behavior is always present. In general its coefficient is not simply related to f{sub {pi}{sub n}}n. The properties of n{ne}0 pseudoscalar mesons are sensitive to the pointwise behavior of the long-range piece of the interaction between light quarks.

On nucleon electromagnetic form-factors

Abstract.A Poincaré-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 Δ. 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 Q2 ≲ 2 GeV2 but vanish with increasing momentum transfer. Hence, larger Q2 experiments probe the quark core. The calculated behaviour of GEp(Q2)/GMp(Q2) on Q2 ∈ [2,6] GeV2 agrees with that inferred from polarization transfer data. Moreover,

Sigma terms of light-quark hadrons

\sqrt{Q^2} F_2(Q^2)/F_1(Q^2)\hskip-1pt\approx

Schwinger functions and light-quark bound states

constant on this domain. These outcomes result from correlations in the proton’s amplitude.

Schwinger functions and light-quark bound states, and sigma terms

Abstract.A calculation of the current-quark mass dependence of hadron masses can help in using observational data to place constraints on the variation of nature’s fundamental parameters. A hadron’s σ-term is a measure of this dependence. The connection between a hadron’s σ-term and the Feynman-Hellmann theorem is illustrated with an explicit calculation for the pion using a rainbow-ladder truncation of the Dyson-Schwinger equations: in the vicinity of the chiral limit σπ = mπ/2. This truncation also provides a decent estimate of σρ because the two dominant self-energy corrections to the ρ-meson’s mass largely cancel in their contribution to σρ. The truncation is less accurate for the ω, however, because there is little to compete with an ω → ρπ self-energy contribution that magnifies the value of σω by ≲25%. A Poincaré-covariant Faddeev equation, which describes baryons as composites of confined-quarks and -nonpointlike-diquarks, is solved to obtain the current-quark mass dependence of the masses of the nucleon and Δ, and thereby σN and σΔ. This “quark-core” piece is augmented by the “pion cloud” contribution, which is positive. The analysis yields σN ≃ 60 MeV and σΔ ≃ 50 MeV.

ON THE COMPLEXION OF PSEUDOSCALAR MESONS

Abstract.We examine the applicability and viability of methods to obtain knowledge about bound states from information provided solely in Euclidean space. Rudimentary methods can be adequate if one only requires information about the ground and first excited state and assumptions made about analytic properties are valid. However, to obtain information from Schwinger functions about higher mass states, something more sophisticated is necessary. A method based on the correlator matrix can be dependable when operators are carefully tuned and errors are small. This method is nevertheless not competitive when an unambiguous analytic continuation of even a single Schwinger function to complex momenta is available.

Current quark-mass dependence of nucleon magnetic moments and radii

We explore the viability of using solely spacelike information about a Schwinger function to extract properties of bound states. In a concrete example it is not possible to determine properties of states with masses {approx}> 1.2 GeV. Modern Dyson-Schwinger equation methods supply a well-constrained tool that provides access to hadron masses and {sigma}-terms. We report values of the latter for a range of hadrons. Of interest is an analysis relating to a u,d scalar meson, which is compatible with a picture of the lightest 0{sup ++} as a bound state of a dressed-quark and -antiquark supplemented by a material pion cloud. A constituent-quark {sigma}-term is defined, which affords a means for assessing the flavor-dependence of dynamical chiral symmetry breaking.

Theory and phenomenology of hadrons

A strongly momentum-dependent dressed-quark mass function is basic to QCD. It is central to the appearance of a constituent-quark mass-scale and an existential prerequisite for Goldstone modes. Dyson-Schwinger equation (DSEs) studies have long emphasised this importance, and have proved that QCDs Goldstone modes are the only pseudoscalar mesons to possess a nonzero leptonic decay constant in the chiral limit when chiral symmetry is dynamically broken, while the decay constants of their radial excitations vanish. Such features are readily illustrated using a rainbow-ladder truncation of the DSEs. In this connection we find (in GeV): fηc(1S)=0.233, mηc(2S)=3.42; and support for interpreting η(1295), η(1470) as the first radial excitations of η(548), η′(958), respectively, and K(1460) as the first radial excitation of the kaon. Moreover, such radial excitations have electromagnetic diameters greater than 2 fm. This exceeds the spatial length of lattices used typically in contemporary lattice-QCD.