# Phenomenological constraints on $A_N$ in $p^\uparrow p\to \pi\, X$ from Lorentz invariance relations

## TL;DR

This paper analyzes the single-spin asymmetry $A_N$ in polarized proton-proton collisions producing pions, using collinear twist-3 formalism and Lorentz invariance relations to incorporate TMD function inputs and constrain less known correlators.

## Contribution

It introduces a novel analysis combining Lorentz invariance relations with TMD evolution inputs to better constrain twist-3 contributions to $A_N$ in $p^
rrow p^\uparrow p \to \pi X$.

## Key findings

- Constraints on dynamical twist-3 correlators derived.
- Utilization of latest Sivers and Collins function extractions.
- Enhanced understanding of $A_N$ contributions in polarized collisions.

## Abstract

We present a new analysis of $A_N$ in $p^\uparrow p\to \pi\, X$ within the collinear twist-3 factorization formalism. We incorporate recently derived Lorentz invariance relations into our calculation and focus on input from the kinematical twist-3 functions, which are weighted integrals of transverse momentum dependent (TMD) functions. In particular, we use the latest extractions of the Sivers and Collins functions with TMD evolution to compute certain terms in $A_N$. Consequently, we are able to constrain the remaining contributions from the lesser known dynamical twist-3 correlators.