Inclusive annihilation in Yukawa theory

In the model of Yukawa field theory we consider the inclusive process e⁺+e^-→γ(p)→π(k)+anything. We find, by summing up the logarithms, that certain transforms H⁽ⁿ⁾ of the amplitude, which in the high-energy limit u≡p²→∞ may be identified with the moments ∫0¹dω ωⁿ⁺¹F̅ (ω,p²) of the structure functions F̅ (ω,p²), have simple leading behavior. At a fixed point of the renormalization group the H⁽ⁿ⁾ would grow like a fractional power δ_n of p². δ_n is a property of the underlying theory (Yukawa) rather than the structure of the pion, treated as a bound state, and may be calculated in perturbation theory.