We present the complete cross-section for the production of unpolarized hadrons in semi-inclusive deep-inelastic scattering up to power-suppressed O(1/Q 2) terms in the Wandzura-Wilczek-type approximation, which consists in systematically assuming thatqgq-terms are much smaller thanqq-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.

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The Drell-Yan process provides important information on the internal struc- ture of hadrons including transverse momentum dependent parton distribution functions (TMDs). In this work we present calculations for all leading twist structure functions de- scribing the pion induced Drell-Yan process. The non-perturbative input for the TMDs is taken from the light-front constituent quark model, the spectator model, and available parametrizations of TMDs extracted from the experimental data. TMD evolution is im- plemented at Next-to-Leading Logarithmic precision for the first time for all asymmetries. Our results are compatible with the first experimental information, help to interpret the data from ongoing experiments, and will allow one to quantitatively assess the models in future when more precise data will become available.

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We present the complete cross-section for the production of unpolarized hadrons in semi-inclusive deep-inelastic scattering up to power-suppressed O(1/Q 2 ) terms in the Wandzura-Wilczek-type approximation, which consists in systematically assuming thatqgq-terms are much smaller thanqq-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.