Dynamical next-to-next-to-leading order parton distributions

Abstract

Utilizing recent deep inelastic scattering measurements $({\ensuremath{\sigma}}_{r},{F}_{2,3,L})$ and data on hadronic dilepton production we determine at next-to-next-to-leading order (NNLO) (3-loop) of QCD the dynamical parton distributions of the nucleon generated radiatively from valencelike positive input distributions at an optimally chosen low resolution scale (${Q}_{0}^{2}<1\text{ }\text{ }{\mathrm{GeV}}^{2}$). These are compared with ``standard'' NNLO distributions generated from positive input distributions at some fixed and higher resolution scale (${Q}_{0}^{2}>1\text{ }\text{ }{\mathrm{GeV}}^{2}$). Although the NNLO corrections imply in both approaches an improved value of ${\ensuremath{\chi}}^{2}$, typically ${\ensuremath{\chi}}_{\mathrm{NNLO}}^{2}\ensuremath{\simeq}0.9{\ensuremath{\chi}}_{\mathrm{NLO}}^{2}$, present deep inelastic scattering data are still not sufficiently accurate to distinguish between NLO results and the minute NNLO effects of a few percent, despite the fact that the dynamical NNLO uncertainties are somewhat smaller than the NLO ones and both are, as expected, smaller than those of their standard counterparts. The dynamical predictions for ${F}_{L}(x,{Q}^{2})$ become perturbatively stable already at ${Q}^{2}=2--3\text{ }\text{ }{\mathrm{GeV}}^{2}$ where precision measurements could even delineate NNLO effects in the very small-$x$ region. This is in contrast to the common standard approach but NNLO/NLO differences are here less distinguishable due to the larger $1\ensuremath{\sigma}$ uncertainty bands. Within the dynamical approach we obtain ${\ensuremath{\alpha}}_{s}({M}_{Z}^{2})=0.1124\ifmmode\pm\else\textpm\fi{}0.0020$, whereas the somewhat less constrained standard fit gives ${\ensuremath{\alpha}}_{s}({M}_{Z}^{2})=0.1158\ifmmode\pm\else\textpm\fi{}0.0035$.