Quantum chromodynamics and Bloom-Gilman duality

Abstract

We study the quantum-chromodynamic explanation of the long-established empirical connection, called Bloom-Gilman duality, between scaling and resonance regimes of the inelastic structure function $\ensuremath{\nu}{W}_{2}({\ensuremath{\omega}}^{\ensuremath{'}})$, where $\ensuremath{\nu}$ and ${\ensuremath{\omega}}^{\ensuremath{'}}$ are the usual kinematic variables. We show how QCD expectations for the baryon transition form factors lead to the observed constancy with momentum transfer of the resonance/"background" ratio. We can also understand why the resonance contribution follows with changing ${Q}^{2}$, a curve whose shape is the same as the scaling-limit curve. We comment on the longitudinal response function and on possible contrasts in exciting resonances with different isospins. These await experimental scrutiny in newer-generation electron facilities.