# Quasi-real photon contribution to $A_N$ in $\ell p^\uparrow \to \pi\,$ X within a TMD approach

## TL;DR

This paper investigates the contribution of quasi-real photons to the transverse single-spin asymmetry in lepton-proton collisions producing pions, using a TMD framework and updated data fits, improving previous models.

## Contribution

It extends prior work by including quasi-real photon effects in TMD calculations of $A_N$, providing more accurate predictions and a step towards unified TMD descriptions of SSAs.

## Key findings

- Good agreement with experimental data
- Improved description over previous models
- Supports unified TMD approach for different processes

## Abstract

Within a TMD approach we discuss the impact of quasi-real (Weizs\"acker-Williams) photon contribution to the transverse single-spin asymmetry, $A_N$, for the inclusive process $\ell p^\uparrow \to \pi\, X$. This study extends a previous one where only the leading-order contribution was taken into account. Predictions are obtained adopting the Sivers and transversity distributions and the Collins fragmentation functions as extracted from fits to the azimuthal asymmetries measured in semi-inclusive deep inelastic scattering and $e^+e^-$ annihilation processes. The description of the available data is very good, showing a clear general improvement with respect to the previous analysis (already quite promising). This result represents a further step towards a unified TMD treatment of SSAs in $\ell\,p^\uparrow \to\ell'\, h\, X$ and $\ell \,p^\uparrow \to h\, X$ processes.