An Analysis of the Next-to-Leading Order Corrections to the g_T(=g_1+g_2) Scaling Function

Abstract

We present a general method for obtaining the quantum chromodynamical radiative corrections to the higher-twist (power-suppressed) contributions to inclusive deep-inelastic scattering in terms of light-cone correlation functions of the fundamental fields of quantum chromodynamics. Using this procedure, we calculate the previously unknown $\mathcal{O}({\alpha }_s)$ corrections to the twist-three part of the spin scaling function $g_T(x_B,Q^2)(=g_1(x_B,Q^2)+g_2(x_B,Q^2))$ and the corresponding forward Compton amplitude $S_T(\nu ,Q^2)$. Expanding our result about the unphysical point $x_B=\infty$, we arrive at an operator product expansion of the nonlocal product of two electromagnetic current operators involving twist-two and -three operators valid to $\mathcal{O}({\alpha }_s)$ for forward matrix elements. We find that the Wandzura-Wilczek relation between $g_1(x_B,Q^2)$ and the twist-two part of $g_T(x_B,Q^2)$ is respected in both the singlet and non-singlet sectors at this order, and argue its validity to all orders. The large-$N_c$ limit does not appreciably simplify the twist-three Wilson coefficients.

Comments: 41 pages, 9 figures, corrected minor error