Weighted $\sin\left(3\phi_h -\phi_S\right)$ asymmetry from pretzelosity in SIDIS at electron ion colliders

TL;DR

This paper predicts a measurable azimuthal asymmetry in charged pion production at electron ion colliders, which can reveal the pretzelosity distribution in the proton, using existing parametrizations and numerical methods.

Contribution

It provides the first numerical prediction of the weighted $ ext{sin}(3 ext{phi}_h - ext{phi}_S)$ asymmetry in SIDIS at EICs based on pretzelosity and Collins functions.

Findings

Weighted asymmetry around 2% in EIC kinematics

Feasibility of accessing pretzelosity at future colliders

Numerical prediction based on existing parametrizations

Abstract

We investigate the transverse momentum weighted azimuthal asymmetry with a $\sin\left(3\phi_h -\phi_S\right)$ modulation in electroproduction of charged pion production off the transversely polarized proton. The asymmetry is contributed by the product of the second transverse-moment of the pretzelosity distribution function and the first transverse-moment of the Collins function. Using the extracted result for the proton pretzelosity and the available parametrization for the pion Collins function, we numerically predict the $P_{hT}^3$-weighted $\sin\left(3\phi_h -\phi_S\right)$ asymmetry for charged pion production at electron ion colliders (EICs). It is found that the weighted asymmetry is around 2 percent in the kinematics region of EICs. Our results show that the planned high luminosity electron ion colliders could be feasible to access pretzelosity in the near future.