Scaling and the nucleon form factors: information on Z2 and the Drell--Yan--West relation

New rigorous bounds on the discontinuities of off-shell nucleon form factors are system-atically derived and used in two applications. First, upper limits of between 0 and 0.3 are set on Z₂, the proton's wave-function renormalization constant, under different assumptions about R, the ratio of longitudinal to transverse virtual photoabsorption cross sections, in the Bjorken limit, and about possible subtraction constants in the sideways dispersion relations for nucleon form factors. The bounds on Z₂⁻¹-1 represent an improvement by factors of 8 and 32 over previous results and permit a conclusion without neglect of a subtraction constant. If the $J^{\pi }={\frac{1}{2}}^{+}$ contributions to deep-inelastic scattering do not scale, Z₂=0 in any case. Second, it is suggested that the Drell-Yan-West relation is the extremum of an inequality imposed by unitarity and analyticity. This is the case if the off-shell Dirac form factor F(s,Q²), near s=m², is a smooth but nontrivial function of s, as Q²→∞, whether or not the $J^{\pi }={\frac{1}{2}}^{+}$ contributions scale.