Kinematic power corrections for TMD factorization theorem of semi-inclusive deep-inelastic scattering

We evaluate the complete set of kinematic power corrections (KPCs) to the leading power (LP) term of the transverse momentum dependent (TMD) factorization theorem for semi-inclusive deep-inelastic scattering (SIDIS) with a polarized target. This formulation restores the contributions of twist-two TMD distributions to all structure functions, including those that vanish at leading power, such as contributions of longitudinal photons. The resulting expressions are explicitly gauge- and frame-invariant, and inherit all key features of the standard TMD factorization framework, including the coefficient functions and the evolution equations. Numerical estimations show that KPCs contribute only a few percent at $Q\sim 10$GeV, but can reach several tens of percents when $Q\sim 2$GeV. Consequently, accounting for kinematic power corrections can be vital for an accurate theoretical description of current SIDIS measurements.