Light cone and mass shells
Abstract
We propose a hypothesis which generalizes the notion of duality to offmassshell current matrix elements. The hypothesis, referred to as strong lightcone dominance, is formulated in terms of the lightcone sum rules, which reflect causality and the lightcone structure of current commutators: We postulate that these sum rules are saturated quasilocally by individual resonance peaks, in a similar manner as duality requires resonances to saturate the FESR for the hadronic onshell amplitudes. This reconstitutes scaling in an average sense in regions where the leading lightcone singularity does not dominate. In coordinate space this hypothesis implies that the leading lightcone singularity regulates (tames) the entire lightcone expansion in a neighbourhood of the surface of the lightcone, whose extension is of the order of an inverse mass difference between consecutive resonances. We investigate the hypothesis of strong lightcone dominance in the framework of narrow resonance models for the vertex and show that the leading lightcone singularity indeed normalizes the single particle contributions by means of a relation of the DrellYanWest type. A simple Venezianolike vertex model is exhibited, which is strongly lightcone dominated. Furthermore, we show how to exploitthe hypothesis in a rather modelindependent way. We present some applications to the nonforward fourpoint function and show in particular that strong lightcone dominancerequires scaling for exclusive electroproduction processes like γ ^{∗} + N → π + N.
 Publication:

Nuclear Physics B
 Pub Date:
 July 1973
 DOI:
 10.1016/05503213(73)901119
 Bibcode:
 1973NuPhB..57..413J