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

Josh Davies, C.-H. Kom, Sven-Olaf Moch, Andreas Vogt
2021 Journal of high energy physics 2022(8)  
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,
more » ... d 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.
doi:10.3204/pubdb-2021-05484 fatcat:xfsg5rbpnvd5jpzlu2ovvj3cq4