Transverse momentum broadening from NLL BFKL to all orders in pQCD

TL;DR

This paper investigates the universal behavior of the saturation momentum in dense QCD media at all orders in perturbative QCD, revealing how quantum evolution affects transverse momentum broadening and deriving exact universal coefficients.

Contribution

It provides a comprehensive all-orders analysis of the saturation momentum's asymptotics in QCD, including the effects of running coupling and conformal theories, extending previous approximations.

Findings

Derived the large L expansion of Q_s(L) up to order α_s^{3/2}.

Identified universal coefficients in the Q_s(L) expansion that are exact to all orders in α_s.

Connected the effects of the QCD β-function to the universal behavior of saturation momentum.

Abstract

We study, to all orders in perturbative QCD, the universal behavior of the saturation momentum $Q_s(L)$ 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 $\mathcal{N}=4$ SYM theory, we derive the large $L$ expansion of $Q_s(L)$ up to order $\alpha_s^{3/2}$. In QCD with massless quarks, where conformal symmetry is broken by the running of the strong coupling constant, the one-loop QCD $\beta$-function fully accounts for the universal terms in the $Q_s(L)$ expansion. Therefore, the universal coefficients of this series are known exactly to all orders in $\alpha_s$.