Understanding the nucleon as a Borromean bound-state

Analyses of the three valence-quark bound-state problem in relativistic quantum field theory predict that the nucleon may be understood primarily as a Borromean bound-state, in which binding arises mainly from two separate effects. One originates in non-Abelian facets of QCD that are expressed in the strong running coupling and generate confined but strongly-correlated colour-antitriplet diquark clusters in both the scalar-isoscalar and pseudovector-isotriplet channels. That attraction is magnified by quark exchange associated with diquark breakup and reformation. Diquark clustering is driven by the same mechanism which dynamically breaks chiral symmetry in the Standard Model. It has numerous observable consequences, the complete elucidation of which requires a framework that also simultaneously expresses the running of the coupling and masses in the strong interaction. Planned experiments are capable of validating this picture.Comment: 7 pages, 7 figure

Ward-Green-Takahashi identities and the axial-vector vertex

The colour-singlet axial-vector vertex plays a pivotal role in understanding dynamical chiral symmetry breaking and numerous hadronic weak interactions, yet scant model-independent information is available. We therefore use longitudinal and transverse Ward-Green-Takahashi (WGT) identities, together with kinematic constraints, in order to ameliorate this situation and expose novel features of the axial vertex: amongst them, Ward-like identities for elements in the transverse piece of the vertex, which complement and shed new light on identities determined previously for components in its longitudinal part. Such algebraic results are verified via solutions of the Bethe-Salpeter equation for the axial vertex obtained using two materially different kernels for the relevant Dyson-Schwinger equations. The solutions also provide insights that suggest a practical Ansatz for the axial-vector vertex.Comment: 7 pages, 3 figure

Nucleon spin structure at very high-x

Dyson-Schwinger equation treatments of the strong interaction show that the presence and importance of nonpointlike diquark correlations within the nucleon are a natural consequence of dynamical chiral symmetry breaking. Using this foundation, we deduce a collection of simple formulae, expressed in terms of diquark appearance and mixing probabilities, from which one may compute ratios of longitudinal-spin-dependent u- and d-quark parton distribution functions on the domain x =1. A comparison with predictions from other approaches plus a consideration of extant and planned experiments shows that the measurement of nucleon longitudinal spin asymmetries on x =1 can add considerably to our capacity for discriminating between contemporary pictures of nucleon structure.Comment: 6 pages, 1 table, 3 figures. To appear in Phys. Lett.

Parton distribution amplitudes of light vector mesons

A rainbow-ladder truncation of QCD's Dyson-Schwinger equations is used to calculate rho- and phi-meson valence-quark (twist-two parton) distribution amplitudes (PDAs) via a light-front projection of their Bethe-Salpeter wave functions, which possess S- and D-wave components of comparable size in the meson rest frame. All computed PDAs are broad concave functions, whose dilation with respect to the asymptotic distribution is an expression of dynamical chiral symmetry breaking. The PDAs can be used to define an ordering of valence-quark light-front spatial-extent within mesons: this size is smallest within the pion and increases through the perp-polarisation to the parallel-polarisation of the vector mesons; effects associated with the breaking of SU(3)-flavour symmetry are significantly smaller than those associated with altering the polarisation of vector mesons. Notably, the predicted pointwise behaviour of the rho-meson PDAs is in quantitative agreement with that inferred recently via an analysis of diffractive vector-meson photoproduction experiments.Comment: 13 pages, 4 figures, 4 table

Reflections upon the Emergence of Hadronic Mass

With discovery of the Higgs boson, science has located the source for $\lesssim 2$% of the mass of visible matter. The focus of attention can now shift to the search for the origin of the remaining $\gtrsim 98$%. The instruments at work here must be capable of simultaneously generating the 1 GeV mass-scale associated with the nucleon and ensuring that this mass-scale is completely hidden in the chiral-limit pion. This hunt for an understanding of the emergence of hadronic mass (EHM) has actually been underway for many years. What is changing are the impacts of QCD-related theory, through the elucidation of clear signals for EHM in hadron observables, and the ability of modern and planned experimental facilities to access these observables. These developments are exemplified in a discussion of the evolving understanding of pion and kaon parton distributions.Comment: 13 pages, 9 figures. Invited contribution to EPJ ST Issue "Strong Correlations in Dense Matter Physics

Practical corollaries of transverse Ward-Green-Takahashi identities

The gauge principle is fundamental in formulating the Standard Model. Fermion--gauge-boson couplings are the inescapable consequence and the primary determining factor for observable phenomena. Vertices describing such couplings are simple in perturbation theory and yet the existence of strong-interaction bound-states guarantees that many phenomena within the Model are nonperturbative. It is therefore crucial to understand how dynamics dresses the vertices and thereby fundamentally alters the appearance of fermion--gauge-boson interactions. We consider the coupling of a dressed-fermion to an Abelian gauge boson, and describe a unified treatment and solution of the familiar longitudinal Ward-Green-Takahashi identity and its less well known transverse counterparts. Novel consequences for the dressed-fermion--gauge-boson vertex are exposed.Comment: 5 pages, 1 figur