Features and flaws of a contact interaction treatment of the kaon

Abstract

Elastic and semileptonic transition form factors for the kaon and pion are calculated using the leading-order in a global-symmetry-preserving truncation of the Dyson-Schwinger equations and a momentum-independent form for the associated kernels in the gap and Bethe-Salpeter equations. The computed form factors are compared both with those obtained using the same truncation but an interaction that preserves the one-loop renormalisation-group behaviour of QCD and with data. The comparisons show that: in connection with observables revealed by probes with |Q^2|<~ M^2, where M~0.4GeV is an infrared value of the dressed-quark mass, results obtained using a symmetry-preserving regularisation of the contact-interaction are not realistically distinguishable from those produced by more sophisticated kernels; and available data on kaon form factors do not extend into the domain whereupon one could distinguish between the interactions. The situation is different if one includes the domain Q^2>M^2. Thereupon, a fully consistent treatment of the contact interaction produces form factors that are typically harder than those obtained with QCD renormalisation-group-improved kernels. Amongst other things also described are a Ward identity for the inhomogeneous scalar vertex, similarity between the charge distribution of a dressed-u-quark in the K^+ and that of the dressed-u-quark in the pi^+, and reflections upon the point whereat one might begin to see perturbative behaviour in the pion form factor. Interpolations of the form factors are provided, which should assist in working to chart the interaction between light-quarks by explicating the impact on hadron properties of differing assumptions about the behaviour of the Bethe-Salpeter kernel.