Gluonic corrections to spin dependent weak structure functions

Abstract

We compute gluonic corrections to the spin dependent weak structure functions g₁, g₃ and g₄. g₁^WP is found o be directly proportional to the singlet part of g₁^µP and is Σ_i(Δ_qi+Δq^-i-α_sΔ_g/2π). In the gluon sector, g₃ and g₄ are both free from infrared and collinear divergences since they do not receive any gluonic corrections. Hence the Callan-Gross relation in the weak sector is nor corrected by the g→q, q^- subprocess. g₃^WP measures Δu_v + Δd_v. The distribution functions are identified with corresponding OPE matrix elements.