The Transverse-momentum-dependent Parton Distribution Function and Jet Transport in Medium

TL;DR

The authors develop a gauge-invariant framework to describe nuclear transverse momentum broadening of quarks using transverse-momentum-dependent distributions. They show that, under a maximal two-gluon correlation approximation, the nuclear TMD quark distribution is a convolution of the nucleon TMD with a Gaussian broadening governed by the transport parameter hat{q}_F, effectively solving a 2-D diffusion equation in transverse momentum. By extending the formalism to arbitrary gauges and incorporating higher-twist nucleon gluon matrix elements, they reveal transverse-distance dependent corrections and connect to the TDD gluon distribution. The study extends to hot media, relates the results to the dipole model, and contrasts with strong-coupling results in N=4 SYM, where multiple-gluon correlations gain importance, underscoring the role of multi-parton correlations in medium-modified jet transport.

Abstract

We show that the gauge-invariant transverse-momentum-dependent (TMD) quark distribution function can be expressed as a sum of all higher-twist collinear parton matrix elements in terms of a transport operator. From such a general expression, we derive the nuclear broadening of the transverse momentum distribution. Under the maximal two-gluon correlation approximation, in which all higher-twist nuclear multiple-parton correlations with the leading nuclear enhancement are given by products of twist-two nucleon parton distributions, we find the nuclear transverse momentum distribution as a convolution of a Gaussian distribution and the nucleon TMD quark distribution. The width of the Gaussian, or the mean total transverse momentum broadening squared, is given by the path integral of the quark transport parameter $\hat q_F$ which can also be expressed in a gauge invariant form and is given by the gluon distribution density in the nuclear medium. We further show that contributions from higher-twist nucleon gluon distributions can be resummed under the extended adjoint two-gluon correlation approximation and the nuclear transverse momentum distribution can be expressed in terms of a transverse scale dependent quark transport parameter or gluon distribution density. We extend the study to hot medium and compare to dipole model approximation and ${\cal N}=4$ Supersymmetric Yang-Mills (SYM) theory in the strong coupling limit. We find that multiple gluon correlations become important in the strongly coupled system such as ${\cal N}=4$ SYM plasma.

Figures (2)

• Figure 1: Multiple soft gluon interaction between the struck quark and the remnant of the target nucleus in DIS.
• Figure 2: Splitting the cap-like gauge link into chains of closed plaquette linked by short Wilson lines.