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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 that qgqbar-terms are much smaller than qqbar -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. 

A bstract Charged-lepton-flavor-violation is predicted in several new physics scenarios. We update the analysis of τ lepton decays into a light charged lepton ( ℓ = e ± or μ ± ) and a vector meson ( V 0 = ρ 0 , ϕ , ω , K *0 , or $$ \overline{K} $$ K ¯ *0 ) using 980 fb − 1 of data collected with the Belle detector at the KEKB collider. No significant excess of such signal events is observed, and thus 90% credibility level upper limits are set on the τ → ℓV 0 branching fractions in the range of (1.7–4 . 3) × 10 − 8 . These limits are improved by 30% on average from the previous results.