Hard collinear gluon radiation and multiple scattering in a medium

TL;DR

This paper calculates the gluon radiation and energy loss of high-energy jets in a nuclear medium, extending the higher-twist scheme to include multiple scatterings and the LPM effect, with resummation of leading contributions.

Contribution

It introduces a comprehensive resummation of multiple scatterings in the higher-twist scheme, incorporating the LPM effect and retaining all gluon momentum fractions, improving understanding of jet quenching in nuclear media.

Findings

Leading $1/Q^2$ contribution matches single scattering results after integration.

Resummation of multiple scatterings captures the LPM interference effects.

Formalism can be extended to Monte Carlo simulations.

Abstract

The energy loss of hard jets produced in the Deep-Inelastic scattering (DIS) off a large nucleus is considered in the collinear limit. In particular, the single gluon emission cross section due to multiple scattering in the medium is calculated. Calculations are carried out in the higher-twist scheme, which is extended to include contributions from multiple transverse scatterings on both the produced quark and the radiated gluon. The leading length enhanced parts of these power suppressed contributions are resummed. Various interferences between such diagrams lead to the Landau-Pomeranchuk-Migdal (LPM) effect. We resum the corrections from an arbitrary number of scatterings and isolate the leading contributions which are suppressed by one extra power of the hard scale $Q^{2}$. All powers of the emitted gluon forward momentum fraction $y$ are retained. We compare our results with the previous calculation of single scattering per emission in the higher-twist scheme as well as with multiple scattering resummations in other schemes. It is found that the leading ($1/Q^2$) contribution to the double differential gluon production cross section, in this approach, is equivalent to that obtained from the single scattering calculation once the transverse momentum of the final quark is integrated out. We comment on the generalization of this formalism to Monte-Carlo routines.