Updated numerical study of transverse single-spin asymmetries in single-inclusive pion production from lepton-nucleon collisions

We revisit the analysis of transverse single-spin asymmetries $A_N$ in lepton-nucleon scattering where only a single pion is detected in the final state, $\ell\,N^\uparrow\to h\, X$. This observable is the Electron-Ion Collider (EIC) analogue to $A_N$ in proton-proton collisions, $p^\uparrow p\to h\,X$, that has been studied intensely for decades, especially at the Relativistic Heavy Ion Collider (RHIC). We incorporate new theoretical developments in the collinear twist-3 framework and utilize recent extractions of (Sivers-like and Collins-like) quark-gluon-quark correlators in the numerical computations. We compare our calculations to HERMES measurements as well as make predictions for Jefferson Lab, COMPASS, and EIC kinematics. We further explore the role of next-to-leading order (NLO) corrections to the (twist-2) unpolarized cross section (denominator of $A_N$) and consider what can be deduced empirically about the potential numerical significance of the full NLO calculation of $A_N$ in this process. We consider sources of theoretical uncertainty in our predictions, which present potential opportunities then for future measurements to improve our understanding of $A_N$ and multi-parton correlations in hadrons.