Trouble with ξ scaling?

We review our analysis of inclusive lepton-hadron scattering, which is based on the use of the variable ξ that incorporates target- and constituent-mass effects in a color-gauge theory [quantum chromodynamics (QCD)]. We show that the apparent paradoxes recently encountered by several groups in connection with ξ scaling are not paradoxes at all, but rather are based on misunderstanding of our analysis. Paradoxes arise when the ξ-scaling analysis is applied for all ξ, but, as we stated in earlier work, QCD predicts that corrections (due to twist-greater-than-2 operators) are negligible only for W well above the proton mass. We restate our previous analysis in which we introduced a smooth function Fs that ξ-scales up to explicit logarithmic corrections. Fs has no thresholds (it is nonzero for 0<ξ<1). QCD predicts that Fs describes the data in the sense of Bloom-Gilman local duality. More constructively, we use the parton-model language to interpret the field-theoretic operator-product expansion in successive "twists" and develop an intuitive physical interpretation of twist. We reanalyze the "paradoxes" in parton language. We resolve (to our satisfaction) the question of nonperturbative effects in the analysis of electroproduction.