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

Abstract

We investigate the transverse momentum weighted azimuthal asymmetry with a sin (3φ h − φS) 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 3 hT -weighted sin (3φ h − φS) 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.