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.

中文翻译：

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Twist-3共线分解方法中的横向动量加权技术简介

作为描述单自旋不对称性（SSA）数据的成功方法，twist-3共线性分解框架在最近几十年引起了很多关注。自从1970年代末进行首次测量以来，许多SSA的数据已经在各种能量下进行了实验性积累，并且预计未来的实验（如Electron-Ion-Collider）将为我们提供更多数据。为了对在不同运动学状态下获取的数据进行一致而精确的描述，共线Twist-3函数的尺度演化和扰动的高阶硬零件系数是强制性的。在本文中，我们介绍了用于横向动量加权SSA的次至领先阶（NLO）计算的技术，