Transverse momentum broadening from NLL BFKL to all orders in pQCD

Abstract

We study, to all orders in perturbative QCD, the universal behavior of the saturation momentum Qs(L) controlling the transverse momentum distribution of a fast parton propagating through a dense QCD medium with large size L. Due to the double logarithmic nature of the quantum evolution of the saturation momentum, its large L asymptotics is obtained by slightly departing from the double logarithmic limit of either next-to-leading log (NLL) BFKL or leading order DGLAP evolution equations. At fixed coupling, or in conformal N = 4 SYM theory, we derive the large L expansion of Qs(L) up to order α 3/2 s . In QCD with massless quarks, where conformal symmetry is broken by the running of the strong coupling constant, the one-loop QCD β-function fully accounts for the universal terms in the Qs(L) expansion. Therefore, the universal coefficients of this series are known exactly to all orders in αs.