Duality in the inelastic structure function and the disappearing<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Δ</mml:mi></mml:math>resonance

Abstract

We study the dual relationship between the resonances and the scaling curve for the inelastic structure function $\ensuremath{\nu}{W}_{2}$ in the ${Q}^{2}$ range 1 to 17 ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$. We focus on an exception to the rule that resonance bumps fall with increasing ${Q}^{2}$ at the same rate as the background, namely, the $\ensuremath{\Delta}(1232)$, for which the resonance falls faster than the background. We show that $\ensuremath{\nu}{W}_{2}$, averaged over suitable ranges of $x$, yields the smooth scaling curve seen at higher values of ${Q}^{2}$ at the same values of $x$, for all resonance regions. The fall of the $\ensuremath{\Delta}(1232)$ and corresponding rise of the background hints at a common dynamics for both.