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Advances in High Energy Physics
Volume 2019, Article ID 4825790, 15 pages
Review Article

Introduction to the Transverse-Momentum-Weighted Technique in the Twist-3 Collinear Factorization Approach

Institute of Quantum Matter and School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China

Correspondence should be addressed to Hongxi Xing; nc.ude.uncs.m@gnixh and Shinsuke Yoshida; moc.liamg@58adihsoynihs

Received 21 December 2018; Accepted 31 March 2019; Published 2 June 2019

Guest Editor: Alexei Prokudin

Copyright © 2019 Hongxi Xing and Shinsuke Yoshida. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.


The twist-3 collinear factorization framework has drawn much attention in recent decades as a successful approach in describing the data for single spin asymmetries (SSAs). Many SSAs data have been experimentally accumulated in a variety of energies since the first measurement was done in the late 1970s and it is expected that the future experiments like Electron-Ion-Collider will provide us with more data. In order to perform a consistent and precise description of the data taken in different kinematic regimes, the scale evolution of the collinear twist-3 functions and the perturbative higher-order hard part coefficients are mandatory. In this paper, we introduce the techniques for next-to-leading order (NLO) calculation of transverse-momentum-weighted SSAs, which can be served as a useful tool to derive the QCD evolution equation for twist-3 functions and to verify the QCD collinear factorization for twist-3 observables at NLO, as well as obtain the finite NLO hard part coefficients.