Threshold resummation at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">N</mml:mi><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>LL</mml:mi></mml:mrow><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow></mml:mrow></mml:math> accuracy and approximate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup><mml:mi>LO</mml:mi></mml:mrow></mml:math> corrections to semi-inclusive DIS
Maurizio Abele, Daniel de Florian, Werner Vogelsang
Abstract
We advance the threshold resummation formalism for semi-inclusive deep-inelastic scattering (SIDIS) to next-to-next-to-next-to-leading logarithmic ($\mathrm{N}^{3}\mathrm{LL}$) order, including the three-loop hard factor. We expand the results in the strong coupling to obtain approximate next-to-next-to-next-to-leading order (${\mathrm{N}}^{3}\mathrm{LO}$) corrections for the SIDIS cross section. In Mellin moment space, these corrections include all terms that are logarithmically enhanced at threshold, or that are constant. We also consider a set of corrections that are suppressed near threshold. Our numerical estimates show modest changes of the cross section by the approximate ${\mathrm{N}}^{3}\mathrm{LO}$ terms, suggesting a very good perturbative stability of the SIDIS process.