Radiative pT-broadening of high-energy quarks and gluons in QCD matter

TL;DR

This paper investigates how high-energy quarks gain transverse momentum through gluon radiation when passing through QCD matter, revealing significant logarithmic corrections and resummation effects that impact momentum broadening.

Contribution

It extends Zakharov's formalism to include radiative effects on transverse momentum broadening, identifying double and single logarithmic contributions and their resummation.

Findings

Radiative corrections significantly increase p⊥-broadening.

Double logarithmic terms dominate the radiative contributions.

Resummation of these terms alters the expected broadening values.

Abstract

We study radiative $p_{\perp}$-broadening of high energy quarks passing through hot and cold QCD matter. With $L$ the length of the matter and $l_{0}$ the size of constituents of the matter we find $\avg{p_{\perp}^{2}}$ has both double logarithmic terms, $\ln^{2}(L/l_{0})$, and single logarithmic terms, $\ln(L/l_{0})$, coming from gluon radiation induced by the matter. We use a (slight) extension of a formalism developed by B. Zakharov for studying energy loss, a formalism which, for much of our calculation, reduces to a simple dipole scattering analysis. We estimate the radiative contribution to be a sizable correction to the nonradiative value of $\avg{p_{\perp}^{2}}$. We also carry out a resummation of the double logarithmic terms that we find, and we briefly discuss running coupling effects which appear here in a rather unusual way.