Improved opacity expansion for medium-induced parton splitting

TL;DR

This paper introduces a new expansion scheme for calculating parton splitting rates in dense QCD media, improving upon the standard opacity expansion by incorporating harmonic oscillator approximations and extending the regime of validity.

Contribution

It develops a generalized opacity expansion around the harmonic oscillator, capturing both high and low frequency regimes beyond the leading logarithmic approximation.

Findings

Accounts for Bethe-Heitler regime effects

Matches full numerical results from prior studies

Provides insights for Monte Carlo event generator implementation

Abstract

We present a new expansion scheme to compute the rate for parton splittings in dense and finite QCD media. In contrast to the standard opacity expansion, our expansion is performed around the harmonic oscillator whose characteristic frequency depends on the typical transverse momentum scale generated in the splitting. The first two orders account for the high frequency regime that is dominated by single hard scatterings together with the regime of multiple soft scatterings at low frequency. This work generalizes the findings of Ref. \cite{Mehtar-Tani:2019tvy} beyond the leading logarithmic approximation allowing to account also for the Bethe-Heitler regime and compare to the full numerical results from Ref. \cite{CaronHuot:2010bp}. We investigate the sensitivity of our results to varying the separation scale that defines the leading order. Finally, the application to Monte Carlo event generators is discussed.