Rigorous relation for structure functions

A theorem in field theory, due to Lehmann, Symanzik, and Zimmermann, implies that a certain combination of proper structure functions for eē annihilation scales trivially. This result is valid for experimental structure functions if the charge renormalization constant Z₃⁻¹ is finite. If W₁ and νW₂ scale separately, we find that their scale functions satisfy the relation F₁(ω)=1/3ωF₂(ω). The constraints imposed by the theorem are exemplified by a soluble model.