Transverse Momentum Broadening and the Jet Quenching Parameter, Redux

TL;DR

This paper employs Soft Collinear Effective Theory to define and analyze the jet quenching parameter , providing a field theoretical perspective on transverse momentum broadening of energetic partons in quark-gluon plasma, and revisits calculations in strongly coupled plasma.

Contribution

It introduces a field theoretical definition of the jet quenching parameter  using Wilson lines and clarifies its interpretation as a diffusion constant, revisiting previous calculations in strongly coupled plasma.

Findings

Derived the effective Lagrangian for parton-Glauber mode interaction.

Provided a field theoretical definition of  via Wilson lines.

Revised previous  calculations for N=4 SYM plasma.

Abstract

We use Soft Collinear Effective Theory (SCET) to analyze the transverse momentum broadening, or diffusion in transverse momentum space, of an energetic parton propagating through quark-gluon plasma. Since we neglect the radiation of gluons from the energetic parton, we can only discuss momentum broadening, not parton energy loss. The interaction responsible for momentum broadening in the absence of radiation is that between the energetic (collinear) parton and the Glauber modes of the gluon fields in the medium. We derive the effective Lagrangian for this interaction, and we show that the probability for picking up transverse momentum k_\perp is given by the Fourier transform of the expectation value of two transversely separated light-like path-ordered Wilson lines. This yields a field theoretical definition of the jet quenching parameter \hat q, and shows that this can be interpreted as a diffusion constant. We close by revisiting the calculation of \hat q for the strongly coupled plasma of N=4 SYM theory, showing that previous calculations need some modifications that make them more straightforward and do not change the result.