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

Davies, J.; Kom, C.-H.; Moch, S.; Vogt, Andreas

Preprint

PUBDB-2022-05057

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

Davies, J. ; Kom, C.-H. ; Moch, S.Extern* ; Vogt, A. (Corresponding author)Extern*

2022

(2022) [10.3204/PUBDB-2022-05057]

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Please use a persistent id in citations: doi:10.3204/PUBDB-2022-05057

Report No.: DESY 21-225; LTH 1289; arXiv:2202.10362

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$^{3}$LL 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.

Keyword(s): deep inelastic scattering: inclusive reaction ; renormalization group ; factorization ; perturbation theory: higher-order ; quantum chromodynamics ; resummation ; small-x ; splitting function ; hard scattering ; parton ; flavor ; BFKL equation ; singlet ; numerical calculations ; Deep Inelastic Scattering or Small-x Physics ; Factorization ; Renormalization Group ; Higher-Order Perturbative Calculations ; Resummation