Extraction of transverse-momentum-dependent helicity distributions of the nucleon

We present an updated global analysis of the transverse-momentum-dependent (TMD) helicity distributions of the nucleon from measurements of the longitudinal double-spin asymmetry $A_{LL}$ in semi-inclusive deep-inelastic scattering (SIDIS). The analysis incorporates target- and detected-hadron-mass corrections, next-to-next-to-leading-order matching in the small-$b_T$ operator product expansion, and an improved treatment of correlated systematic uncertainties. The present data constrain the up- and down-quark helicity TMDs, whereas the sea-quark and gluon distributions remain weakly constrained. After integration over transverse momenta up to the hard scale, the up- and down-quark distributions agree with collinear helicity distributions within uncertainties. Using the extracted TMDs and the Wandzura-Wilczek-type approximation, we predict the $\cos {\phi }_h$ modulation of $A_{LL}$ and find agreement with the HERMES and CLAS measurements. We also provide predictions for SIDIS $A_{LL}$ at CLAS12 and for longitudinal single-spin asymmetries in $W^{\pm }$ production with leptonic decays at STAR kinematics. An impact study with pseudodata for the proposed Electron-Ion Collider in China (EicC) indicates substantial potential to improve constraints on helicity TMDs at intermediate $x$, including the presently weakly constrained sea-quark sector.