Exploring orbital angular momentum and spin-orbit correlations for gluons at the Electron-Ion Collider

In our previous work [S. Bhattacharya , ], we introduced a pioneering observable aimed at experimentally detecting the orbital angular momentum (OAM) of gluons. Our focus was on the longitudinal double spin asymmetry observed in exclusive dijet production during electron-proton scattering. We demonstrated the sensitivity of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>cos</a:mi><a:mi>ϕ</a:mi></a:math> angular correlation between the scattered electron and proton as a probe for gluon OAM at small <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>x</c:mi></c:math> and its intricate interplay with gluon helicity. This current work provides a comprehensive exposition, diving further into the aforementioned calculation with added elaboration and in-depth analysis. We reveal that, in addition to the gluon OAM, one also gains access to the spin-orbit correlation of gluons. We supplement our work with a detailed numerical analysis of our observables for the kinematics of the Electron-Ion Collider. In addition to dijet production, we also consider the recently proposed semi-inclusive diffractive deep inelastic scattering process, which potentially offers experimental advantages over dijet measurements. Finally, we investigate quark-channel contributions to these processes and find an unexpected breakdown of collinear factorization.