We explore the complete cross-section for the production of unpolarized hadrons in semi-inclusive deep-inelastic scattering up to power-suppressed $mathcal{O}(1/Q^2)$ terms in the Wandzura-Wilczek-type (WW-type) approximation, which consists in systematically assuming that $bar{q}gq$-correlators are much smaller than $bar{q}q$-correlators. Under the applicability of WW-type approximations, certain relations among transverse momentum dependent parton distribution functions (TMDs) and fragmentation functions (FFs) occur which are used to approximate SIDIS cross-section in terms of a smaller subset of TMDs and FFs. We discuss the applicability of the WW-type approximations on the basis of available data.
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