# Introduction to the transverse-momentum-weighted technique in the twist-3 collinear factorization approach

## TL;DR

This paper introduces a technique for NLO calculations of transverse-momentum-weighted SSAs within the twist-3 collinear factorization framework, aiding in the evolution and verification of twist-3 functions.

## Contribution

It presents a new method for NLO calculations of SSAs, facilitating the derivation of QCD evolution equations and verification of factorization at twist-3 level.

## Key findings

- Developed a technique for NLO calculations of transverse-momentum-weighted SSAs.
- Provided a way to derive QCD evolution equations for twist-3 functions.
- Enabled verification of collinear factorization at NLO for twist-3 observables.

## Abstract

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 late 70s 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 to obtain the finite NLO hard part coefficients.