Higher twist jet broadening and classical propagation

TL;DR

This paper develops a resummed higher twist approach to jet broadening in deep-inelastic scattering, deriving a diffusion equation for jet transverse momentum and comparing it with classical Langevin dynamics, clarifying the relation between diffusion constants.

Contribution

It introduces a novel resummation method for higher twist corrections leading to a diffusion equation for jet transverse momentum, connecting quantum and classical descriptions.

Findings

Resummation yields a 2D diffusion equation for jet transverse momentum.

Derived explicit relation between diffusion constant D and transport coefficient .

Compared quantum resummation results with classical Langevin analysis, showing their agreement.

Abstract

The transverse broadening of jets produced in deep-inelastic scattering (DIS) off a large nucleus is studied in the collinear limit. A class of medium enhanced higher twist corrections are re-summed to calculate the transverse momentum distribution of the produced collinear jet. In contrast to previous approaches, resummation of the leading length enhanced higher twist corrections is shown to lead to a two dimensional diffusion equation for the transverse momentum of the propagating jet. Results for the average transverse momentum obtained from this approach are then compared to the broadening expected from a classical Langevin analysis for the propagation of the jet under the action of the fluctuating color Lorentz force inside the nucleons. The set of approximations that lead to identical results from the two approaches are outlined. The relationship between the momentum diffusion constant $D$ and the transport coefficient $\hat{q}$ is explicitly derived.