The $g_T(x)$ contribution to single spin asymmetries in SIDIS

TL;DR

This paper introduces a new two-loop perturbative contribution involving the $g_T(x)$ distribution to single spin asymmetries in SIDIS, providing parameter-free predictions for future Electron-Ion Collider measurements.

Contribution

It identifies a novel two-loop contribution involving $g_T(x)$ and $ riangle G(x)$ to SSA, expressed solely through twist-two functions, enabling unambiguous predictions.

Findings

$A_{UT}$ asymmetries can reach 1-2% at the EIC.

New two-loop contributions involve $g_T(x)$ and $ riangle G(x)$.

Predictions are parameter-free within the Wandzura-Wilczek approximation.

Abstract

Motivated by a novel origin of transverse single spin asymmetry (SSA) in semi-inclusive Deep Inelastic Scattering (SIDIS) uncovered by some of us, we quantitatively investigate its impact on the theoretical understanding of the mechanism responsible for SSA. This new contribution from the quark-initiated channel first appears in two-loop perturbation theory and involves the $g_T(x)$ distribution. We point out another entirely analogous piece from the gluon-initiated channel proportional to the gluon helicity distribution $\Delta G(x)$. Both contributions are solely expressed in terms of twist-two polarized parton distribution functions and twist-two fragmentation functions in the Wandzura-Wilczek approximation, such that they can be unambiguously evaluated without introducing free parameters. We make predictions for measurements of the asymmetries $A_{UT}$ at the future Electron-Ion Collider (EIC), and find that $A_{UT}$ associated with the $\sin (\phi_h-\phi_S)$, $\sin \phi_S$ and $\sin (2\phi_h-\phi_S)$ harmonics can reach up to 1-2\% even at the top EIC energy.