Spin-dependent non-singlet structure functions in next-to-leading order

TL;DR

The paper develops a complete next-to-leading order framework for spin-dependent non-singlet structure functions, focusing on the $Q^2$-evolution of first moments and the role of $SU(2)$ and $SU(3)$ breaking. It derives and analyzes the Mellin-$n$ evolution with Wilson coefficients $\Delta C_q^i(n)$ and anomalous dimensions $\Delta\gamma_{NS}^1(n)$, including regularization-scheme considerations and axial-current conservation constraints. The authors show that the first moments $\Delta A_3(1)$ and $\Delta A_8(1)$ are conserved while polarized valence densities evolve via two-loop NS evolution, and they incorporate charm-mass effects in charged-current transitions. Numerical results indicate potential experimental access to SU(3) breaking and dynamical SU(2) breaking in the polarized sea via polarized DIS and CC/NC measurements at facilities like HERA, with predictions sensitive to the input sea and valence densities.

Abstract

We study in detail the flavor-non-singlet component of polarized structure functions in the framework of a consistent and complete next-to-leading order (${\cal O}(α_s))$ analysis. In this context, we discuss some important features of the calculation of the next-to-leading order corrections. Particular emphasis is put on the $Q^2$-evolution of sum-rules for the first moments of the non-singlet structure functions which, as we show, could serve to explore $SU(2)$ and $SU(3)$ breaking effects in relations between baryonic $β$-decay matrix elements and in the proton's polarized sea. Furthermore we make predictions for polarized non-singlet structure functions measurable in a conceivable $\vec{e}\vec{p}$ collider mode of HERA.