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the precise measurement of final state hadrons in lepton nucleon deep inelastic scattering constitutes an excellent benchmark for different features of perturbative quantum chromodynamics . among them , the calculation of higher order corrections , which have been explored and validated for most processes up to next to leading order ( nlo ) accuracy . for the one particle inclusive processes
only very recently there has been progress beyond the leading order ( lo ) @xcite .
and up to now there were no analytic computation of the @xmath2 corrections for the electroproduction of hadrons with non vanishing transverse momentum .
the analytic computation of the @xmath2 corrections allows us to check factorization in a direct way , which means that collinear singularities showing up in the partonic cross section factorize into parton densities ( pdfs ) and fragmentation functions ( ffs ) . as a consequence of this explicit cancellation ,
the resulting cross section is finite and can be straightforwardly convoluted with pdfs and ffs in a fast and stable numerical codes .
the analytical result is still sufficiently exclusive and keeps the dependence on the rapidity and the transverse momentum of the produced hadron , allowing a detailed comparison with the experimental data . in the following
we summarize the results obtained in ref .
we consider the process @xmath3 where a lepton of momentum @xmath4 scatters off a nucleon of momentum @xmath5 with a lepton of momentum @xmath6 and a hadron @xmath7 of momentum @xmath8 tagged in the final state . omitting target fragmentation at zero transverse momentum , which has been discussed at length in @xcite ,
the cross section for this process can be written as @xmath9\ ] ] where @xmath10 is the partonic level cross section corresponding to the process and is calculated order by order in perturbation theory through the related parton - photon squared matrix elements @xmath11 for the @xmath12 processes @xmath13 in terms of the standard kinematical variables @xcite .    at order-@xmath0 ,
the partonic cross sections receive contributions from the following reactions : @xmath14 where any of the outgoing partons can fragment into the final state hadron @xmath7 .    at variance with the @xmath15 case , where the integration over final states leads to overlapping singularities along various curves in the residual phase space , here
the only remaining singularities are found at @xmath16 and thus they can be dealt with the standard method . after combining real and virtual contributions to a given partonic process , the cross section can be written as @xmath17 where the coefficient of the single poles , @xmath18 , as well as the finite contributions @xmath19 , include ` delta ' and ` plus ' distributions in @xmath20 .
the ir double poles present in the individual real and virtual contributions cancel out in the sum , providing the first straightforward check on the angular integration of real amplitudes and the loop integrals in the virtual case . in the real terms
, the above mentioned double poles come from the product of a pole arising in the integration over the spectators phase space and a single pole coming from the expansion of @xmath21 factors .
double poles in the virtual contributions always arise from loop integrals .
the remaining singularities , contributing to the single pole , are of uv and collinear origin .
the former are removed by means of coupling constant renormalization , whereas the latter have to be factorized in the redefinition of parton densities and fragmentation functions .
in figure [ fig : x_bj ] we show the lo and nlo predictions for the electroproduction of neutral pions as a function of @xmath22 and @xmath23 , respectively , in the kinematical range of the h1 experiment @xcite , together with the most recent data for the range @xmath24 .
the cross sections are computed as described in the previous sections , applying h1 cuts and using mrst02 parton densities @xcite .
similar results are found using other sets of modern pdfs . for the input fragmentation functions , we use two different sets , the ones from reference @xcite denoted as kkp and those from @xcite referenced as k. we set the renormalization and factorization scales as the average between @xmath25 and @xmath26 , and we compute @xmath27 at nlo(lo ) fixing @xmath28 as in the mrst analysis .
the plots clearly show that the nlo cross sections are much larger than the lo ones , even by the required order of magnitude in certain kinematical regions .
another interesting feature is that the uncertainty due to the choice of a fragmentation functions set is also quite noticeable , this fact driven by the different gluon content of the two sets considered here .
low @xmath25 bins seem to prefer kkp set , which have a larger gluon - fragmentation content , whereas for larger @xmath25 both sets agree with the data within errors .
lo estimates show a much smaller sensitivity on the choice of fragmentation functions , since gluon fragmentation does not contribute significantly to the cross section at this order .
the rather large size of the k - factor can , then , be understood as a consequence of the opening of a new dominant ( ` leading - order ' ) channel , and not to the ` genuine ' increase in the partonic cross section that might otherwise threaten perturbative stability .
the dominance of the new channel is due to the size of the gluon distribution at small @xmath22 and to the fact that the h1 selection cuts highlight the kinematical region dominated by the @xmath29 partonic process .      in figure
[ fig : discri ] we show the different contributions to the cross section discriminated by the underlying partonic process .
notice that at very small @xmath22 the @xmath30 term can be by itself several times larger than the lo contribution , remaining larger or comparable even for higher @xmath22 values .
the forward selection is also responsible of the scale sensitivity of the cross section , as it supresses large components with small scale dependence whereas it stresses components as @xmath30 whose scale dependence would be partly canceled only at nnlo        a. daleo , c. garca canal , r. sassot , _ nucl .
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we compute the order @xmath0 corrections to the one particle inclusive electroproduction cross section of hadrons with non vanishing transverse momentum . 
 we compare our results with h1 data on forward production of @xmath1 , and conclude that the data is well described by the dglap approach . within the theoretical uncertainties .     
 address = institut fr theoretische physik , universitt zrich , winterthurerstrasse 190 , ch-8057 zrich , switzerland     address = departamento de fsica , universidad de buenos aires , ciudad universitaria , pab.1 ( 1428 ) buenos aires , argentina     address = departamento de fsica , universidad de buenos aires , ciudad universitaria , pab.1 ( 1428 ) buenos aires , argentina