Current-hadron scattering and scaling in a dual relativistic quark model

Abstract

A meromorphic amplitude with satisfactory high-energy behaviour and scaling propertics is constructed for the scattering of a current off a pseudoscalar hadron. The amplitude has a quark model mass spectrum and factorization properties on the leading trajectory. The current-hadron coupling is mediated by an infinite number of vector mesons and the hadron form factors obtained are satisfactory. The divergence conditions on the amplitude are examined and the possible ways of implementing gauge invariance are mentioned. The light-cone structure of our amplitude is then discussed particularly with respect to the relevance of the light-cone for the derivation of fixed-mass sum rules. It is found that besides the usual singularity there is an additional one associated with the discontinuity on the external current legs. Lastly the conditions for which the quark model relation between the deep inelastic structure functions emerges and the behaviour of the structure functions for ω(=−q2/p·q)→2 are discussed.