Thermal field theory derivation of the source term induced by a fast parton from the quark energy-momentum tensor

TL;DR

This paper derives the energy-momentum distribution transmitted by a fast parton to a thermalized quark medium using thermal field theory, revealing how local excitations diminish with increasing parton energy and affecting observable Mach cone signals.

Contribution

It provides a direct derivation of the source term from the quark energy-momentum tensor in thermal field theory, linking microscopic interactions to macroscopic medium responses.

Findings

Local excitations decrease sharply with parton energy

Implications for the trigger $p_T$ dependence in heavy-ion collisions

Conical emission patterns are less likely at higher trigger $p_T$

Abstract

I derive the distribution of energy and momentum transmitted from a fast parton to a medium of thermalized quarks, or the source term, in perturbative thermal field theory directly from the quark energy-momentum tensor. The fast parton is coupled to the medium by adding an interaction term to the Lagrangian. The thermal expectation value of the energy-momentum tensor source term is then evaluated using standard Feynman rules at finite temperature. It is found that local excitations, which are important for exciting an observable Mach cone structure, fall sharply as a function of the energy of the fast parton. This may have implications for the trigger $p_T$ dependence of measurements of azimuthal dihadron particle correlations in heavy-ion collisions. In particular, a conical emission pattern would be less likely to be observed for increasing trigger $p_T$. I show that the results presented in this paper can be generalized to more realistic modeling of fast parton propagation, such as through a time dependent interaction term, in future studies.