On the Anomalous Dimension of the Transversity Distribution $h_1(x,Q^2)$

TL;DR

The paper resolves a dispute over the leading-order anomalous dimension of the transversity distribution h1(x,Q^2) by computing it with three independent methods: forward local light-cone expansion, non-forward scattering analysis, and a forward Compton amplitude approach via Ioffe-Khodjamirian. All methods reproduce the established LO result, yielding the Mellin-space anomalous dimensions gamma_n^{h1} and the splitting function P_{h1}(z). The work further demonstrates the versatility of the Ioffe-Khodjamirian technique for extracting anomalous dimensions and discusses subtleties at NLO, including gauge-sensitive delta(1-z) terms. Overall, the findings reinforce the correctness of the LO evolution for h1 and outline pathways for extending the methodology to higher orders.

Abstract

We calculate the leading order anomalous dimension of the transversity structure function directly using three different methods, the local light-cone expansion in the forward case, the non-forward case, and the short-distance expansion of the forward Compton amplitude. Our results agree with the original calculation by Artru and Mekhfi [Z. Phys. {\bf 45} (1990) 669], which has been doubted recently. We also comment on the next-to-leading order anomalous dimension.