# New approach to the Sivers effect in the collinear twist-3 formalism

## TL;DR

This paper introduces a new non-pole calculation method for the Sivers effect within the collinear twist-3 formalism, demonstrating its consistency with traditional pole methods and highlighting its technical advantages.

## Contribution

It extends the non-pole technique to the Sivers effect and clarifies its consistency and advantages over the conventional pole calculation method.

## Key findings

- The non-pole method is consistent with pole calculations at $\\mathcal{O}(\alpha_s)$.
- The pole calculation implicitly uses equations of motion and Lorentz invariance.
- The non-pole method offers technical advantages in evaluating the Sivers effect.

## Abstract

The single-transverse spin asymmetry(SSA) for hadron production in the transversely polarized proton scattering receives major contribution from Sivers effect, which can be systematically described within the collinear twist-3 factorization framework in various processes. Conventional method in the evaluation of the Sivers effect known as pole calculation is technically quite different from non-pole calculation which is another method used in evaluating the final state twist-3 effect. In this paper, we extend the non-pole technique to the Sivers effect, and show the consistency with the conventional method through an explicit calculation of $\mathcal{O}(\alpha_s)$ correction in semi-inclusive deep inelastic scattering. As a result, we clarify that the conventional pole calculation is implicitly using the equation of motion and the Lorentz invariant relations whose importance became widely known in the non-pole calculation. We also clarify some technical advantages in using the new non-pole method.