Role of transverse momentum dependence of unpolarised parton distribution and fragmentation functions in the analysis of azimuthal spin asymmetries

TL;DR

This paper examines how the transverse momentum dependence of unpolarised parton distribution and fragmentation functions influences the analysis of azimuthal spin asymmetries, highlighting the importance of correlations in SIDIS, Drell-Yan, and $e^+e^-$ processes.

Contribution

It introduces a simple Gaussian model to analyze the correlation effects of transverse momentum dependence on spin asymmetries across different processes.

Findings

Correlation effects can significantly impact asymmetry measurements.

Neglecting these effects may lead to inaccurate extraction of distribution functions.

Careful consideration of transverse momentum dependence is essential for precise predictions.

Abstract

Information on the Sivers distribution and the Collins fragmentation functions and their transverse momentum dependence is mainly based on fitting single spin asymmetry data from semi-inclusive deep inelastic scattering (SIDIS). Independent information, respectively on the Sivers distribution and the Collins fragmentation, can be obtained from Drell-Yan and $e^+e^-$ annihilation processes. In the SIDIS case, the transverse momentum of the final observed hadron, which is the quantity measured, is generated both by the average transverse momentum in the distribution and in the fragmentation functions. As a consequence, these are strongly correlated and a separate extraction is made difficult. In this paper we investigate, in a simple kinematical Gaussian configuration, this correlation, its role on the transverse single spin asymmetries in SIDIS and the consequences for predictions of the Sivers asymmetry in Drell-Yan processes and for the Collins asymmetry in $e^+e^-$ annihilation. We find that, in some cases, these effects can be relevant and must be carefully taken into account.