O(αs2)QCD corrections to the electroproduction of hadrons with high transverse momentum

We compute the order ${\alpha }_s^2$ corrections to the one particle inclusive electroproduction cross section of hadrons with nonvanishing transverse momentum. We perform the full calculation analytically, and obtain the expression of the factorized (finite) cross section at this order. We compare our results with H1 data on forward production of ${\pi }^0$, and discuss the phenomenological implications of the rather large higher order contributions obtained in that case. Specifically, we analyze the cross section sensitivity to the factorization and renormalization scales, and to the input fragmentation functions, over the kinematical region covered by data. We conclude that the data is well described by the $\mathcal{O}({\alpha }_s^2)$ predictions within the theoretical uncertainties and without the inclusion of any physics content beyond the Dokshitzer-Grivov-Lipatov-Altarelli-Parisi (DGLAP) approach.