Bessel-weighted asymmetries and the Sivers effect

TL;DR

This paper introduces Bessel-weighted asymmetries in Fourier space to simplify the analysis of the Sivers effect, providing a model-independent way to study spin-momentum correlations in nucleons.

Contribution

It proposes a novel Bessel-weighting method that suppresses high transverse momentum contributions and cancels soft factors, linking experimental observables to theoretical evolution equations and lattice QCD.

Findings

Bessel weights suppress divergent high transverse momentum contributions.

Soft factors cancel in Bessel-weighted asymmetries.

Expressions connect to evolution equations and lattice QCD results.

Abstract

We consider the cross section in Fourier space, conjugate to the outgoing hadron's transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. Advantages of employing these Bessel weights are that they suppress (divergent) contributions from high transverse momentum and that soft factors cancel in (Bessel-) weighted asymmetries. Also, the resulting compact expressions immediately connect to previous work on evolution equations for transverse momentum dependent parton distribution and fragmentation functions and to quantities accessible in lattice QCD. Bessel-weighted asymmetries are thus model independent observables that augment the description and our understanding of correlations of spin and momentum in nucleon structure.