Elastic Dijet Production in Electron Scattering on a Longitudinally Polarized Proton at Small $x$: A Portal to Orbital Angular Momentum Distributions

TL;DR

This paper demonstrates that elastic dijet production in electron-proton scattering at small x can serve as a powerful tool to access quark and gluon orbital angular momentum distributions, advancing the understanding of proton spin structure.

Contribution

It provides the first detailed calculation showing that the longitudinal double spin asymmetry is a robust observable for probing quark and gluon OAM at small x, using the light-cone operator formalism.

Findings

DSA is a reliable probe for quark and gluon OAM distributions.

SSA sensitivity to OAM requires further theoretical development.

Potential to measure OAM distributions at future Electron-Ion Collider.

Abstract

We calculate the elastic production of dijets from electron collisions with a longitudinally polarized proton target at small values of the Bjorken $x$ variable. Building on the pioneering proposals of \cite{Hatta:2016aoc,Bhattacharya:2022vvo, Bhattacharya:2023hbq, Bhattacharya:2024sck} for measuring the quark and gluon orbital angular momentum (OAM) distributions, our focus is on both the longitudinal double spin asymmetry (DSA) and longitudinal single spin asymmetry (SSA). We compute the numerators of these asymmetries in the small-$x$ formalism of the light-cone operator treatment. Utilizing the small-$x$ expressions for the OAM distributions derived in our earlier paper, we demonstrate that the DSA provides a robust probe for both the quark and gluon OAM distributions within the proton. In contrast, we find that while the SSA is also sensitive to the OAM distributions, extraction of the latter from the SSA would require new developments in small-$x$ theory and phenomenology, and is probably not feasible at this point in time. These findings highlight the potential of DSA measurements in elastic dijet production at the future Electron-Ion Collider to provide the first-ever direct access to the quark and gluon OAM distributions at small $x$, paving the way for new insights into the proton spin puzzle.