πandρmesons, and their diquark partners, from a contact interaction

Abstract

We present a unified Dyson-Schwinger equation treatment of static and electromagnetic properties of pseudoscalar and vector mesons, and scalar and axial-vector diquark correlations, based upon a vector-vector contact-interaction. A basic motivation for this study is the need to document a comparison between the electromagnetic form factors of mesons and those diquarks which play a material role in nucleon structure. A notable result, therefore, is the large degree of similarity between related meson and diquark form factors. The simplicity of the interaction enables computation of the form factors at arbitrarily large spacelike-Q 2 , which enables us to expose a zero in the ρ-meson electric form factor at z, where rρ, rD are, respectively, the electric radii of the ρ-meson and deuteron.

Features and flaws of a contact interaction treatment of the kaon

“…First, as also observed elsewhere [15][16][17][18][19][20], in connection with observables determined by probes with |Q 2 | M 2 , results obtained using a symmetry-preserving regularisation of the contact-interaction are not realistically distinguishable from those produced by the most sophisticated QCD renormalisation-group-improved kernels currently available. In addition, available data on the charged-kaon form factor do not extend into the domain whereupon one could distinguish between contact-interaction results and those obtained with QCD-like kernels.…”

“…(A3), and Eqs. (16), (18). Equation (27) is a particular example of a general identity that is true irrespective of the interaction.…”

“…There is a fundamental mathematical similarity between diquark correlations and uniquely identified meson analogues [25]. Hence, computing the properties of these analogues is principally equivalent to producing results for the diquark correlations [18]; and form factors for diquark correlations are a necessary piece in the computation of baryon form factors [19].…”

“…This need is readily explained [18]. Many properties of baryons are successfully described via a Poincaré covariant Faddeev equation that expresses the presence of nonpointlike diquark correlations [21], evidence for the existence of which is accumulating [19,[22][23][24].…”

“…This study is an integral part of a larger programme, aimed at charting the interaction between light-quarks by explicating the impact of differing assumptions about the behaviour of the Bethe-Salpeter kernel upon the spectrum of hadrons, and also upon their elastic and transition form factors on a large domain of momentum transfer. Material progress has been made in connection with u, d-quark systems [15][16][17][18][19]; and a spectrum of mesons and baryons with one or more s-quarks was recently computed [20]. In order to extend the latter to predictions for elastic and transition form factors of baryons containing s-quarks, it is necessary to compute such form factors for mesons containing s-quarks.…”