Resummation of small-x double logarithms in QCD: inclusive deep-inelastic scattering

Abstract

We present a comprehensive study of high-energy double logarithms in inclusive DIS. They appear parametrically as alpha_s^n ln^{2n-k} x at the n-th order in perturbation theory in the splitting functions for the parton evolution and the coefficient functions for the hard scattering process, and represent the leading corrections at small $x$ in the flavour non-singlet case. We perform their resummation, in terms of modified Bessel functions, to all orders in full QCD up to NNLL accuracy, and partly to N^3LL and beyond in the large-n_c limit, and provide fixed-order expansions up to five loops. In the flavour-singlet sector, where these double logarithms are sub-dominant at small x compared to single-logarithmic alpha_s^n x^{-1} ln^{n-k} x BFKL contributions, we construct fixed-order expansions up to five loops at NNLL accuracy in full QCD. The results elucidate the analytic small-x structure underlying inclusive DIS results in fixed-order perturbation theory and provide important information for present and future numerical and analytic calculations of these quantities.

43 pages, LaTeX, 3 figures. Analytical results in ancillary FORM file

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• Four-loop splitting functions in QCD -- The quark-quark case
• Analytic Solution for the Revised Helicity Evolution at Small $x$ and Large $N_c$: New Resummed Gluon-Gluon Polarized Anomalous Dimension and Intercept
• The $N_f{C}_F^3$ contribution to the non-singlet splitting function at four-loop order
• Complete $N_f^2$ contributions to four-loop pure-singlet splitting functions
• Helicity Evolution at Small $x$: Revised Asymptotic Results at Large $N_c\&N_f$
• Global analysis of polarized DIS & SIDIS data with improved small-$x$ helicity evolution
• An FONLL prescription with coexisting flavor number PDFs
• Four-loop large-n_f contributions to the non-singlet structure functions F_2 and F_L
• Combination of aN${}^3$LO PDFs and implications for Higgs production cross-sections at the LHC
• Anomalous dimensions at small spins