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 $O\left(1/Q^2\right)$ terms in the Wandzura-Wilczek-type approximation, which consists in systematically assuming that $\overline{q}gq$-terms are much smaller than $\overline{q}q$-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.