Semi-inclusive deep-inelastic scattering in Wandzura-Wilczek-type approximation

We present the complete cross-section for the production of unpolarized hadrons in semi-inclusive deep-inelastic scattering up to power-suppressed $$ \mathcal{O}\left(1/{Q}^2\right) $$ O 1 / Q 2 terms in the Wandzura-Wilczek-type approximation, which consists in systematically assuming that $$ \overline{q}gq $$ q ¯ g q -terms are much smaller than $$ \overline{q}q $$ q ¯ q -correlators. We compute all twist-2 and twist-3 structure functions and the corresponding asymmetries, and discuss the applicability of the Wandzura-Wilczek-type approximations on the basis of available data. We make predictions that can be tested by data from COMPASS, HERMES, Jefferson Lab, and the future Electron-Ion Collider. The results of this paper can be readily used for phenomenology and for event generators, and will help to improve the description of semi-inclusive deep-inelastic processes in terms of transverse momentum dependent parton distribution functions and fragmentation functions beyond the leading twist.