Abstract
We determine approximate next-to-next-to-leading order (NNLO) corrections to unpolarized and polarized semi-inclusive DIS. They are derived using the threshold resummation formalism, which we fully develop to next-to-next-to-leading logarithmic (NNLL) accuracy, including the two-loop hard factor. The approximate NNLO terms are obtained by expansion of the resummed expression. They include all terms in Mellin space that are logarithmically enhanced at threshold, or that are constant. In terms of the customary SIDIS variables $x$ and $z$ they include all double distributions (that is, "plus" distributions and $\delta$-functions) in the partonic variables. We also investigate corrections that are suppressed at threshold and we determine the dominant terms among these. Our numerical estimates suggest much significance of the approximate NNLO terms, along with a reduction in scale dependence.
Highlights
Data taken in the semi-inclusive deep-inelastic scattering (SIDIS) process lp → lhX offer powerful insights into QCD and hadronic structure
We determine approximate next-to-next-to-leading order (NNLO) corrections to unpolarized and polarized semi-inclusive deep-inelastic scattering. They are derived using the threshold resummation formalism, which we fully develop to next-to-next-to-leading logarithmic accuracy, including the two-loop hard factor
SIDIS might in principle offer important complementary information on, for example, the flavor structure of the sea quarks, the analyses usually do not include information from SIDIS. One reason for this is the fact that the NNLO partonic hard-scattering functions for SIDIS are not yet available, so that computations of the SIDIS cross section are currently restricted to next-to-leading order (NLO)
Summary
Data taken in the semi-inclusive deep-inelastic scattering (SIDIS) process lp → lhX offer powerful insights into QCD and hadronic structure Among their main uses are extractions of fragmentation functions [1,2,3,4,5], (polarized) parton distributions [6,7], or even combinations thereof [8,9]. SIDIS might in principle offer important complementary information on, for example, the flavor structure of the sea quarks, the analyses usually do not include information from SIDIS One reason for this is the fact that the NNLO partonic hard-scattering functions for SIDIS are not yet available (a few first steps toward their calculation have been taken in [10,11,12]), so that computations of the SIDIS cross section are currently restricted to next-to-leading order (NLO).
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