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Interplay of Threshold Resummation and Hadron Mass Corrections in Deep Inelastic Processes

We discuss hadron mass corrections and threshold resummation for deep-inelastic scattering $\ell N\rightarrow\ell' X$ and semi-inclusive annihilation $e^+e^-\rightarrow h X$ processes, and provide a prescription how to consistently combine these two corrections respecting all kinematic thresholds. We find an interesting interplay between threshold resummation and target mass corrections for deep-inelastic scattering at large values of Bjorken $x_B$. In semi-inclusive annihilation, on the contrary, the two considered corrections are relevant in different kinematic regions and do not affect each other. A detailed analysis is nonetheless of interest in the light of recent high precision data from BaBar and Belle on pion and kaon production, with which we compare our calculations. For both deep inelastic scattering and single inclusive annihilation, the size of the combined corrections compared to the precision of world data is shown to be large. Therefore, we conclude that these theoretical corrections are relevant for global QCD fits in order to extract precise parton distributions at large Bjorken $x_B$, and fragmentation functions over the whole kinematic range.