The LPM Effect in sequential bremsstrahlung: $1/N_c^2$ corrections

Abstract

An important question concerning in-medium high-energy parton showers in a quark-gluon plasma or other QCD medium is whether consecutive splittings of the partons in a given shower can be treated as quantum mechanically independent, or whether the formation times for two consecutive splittings instead have significant overlap. Various previous calculations of the effect of overlapping formation times have either (i) restricted attention to a soft bremsstrahlung limit, or else (ii) used the large-$N_c$ limit (where $N_c=3$ is the number of quark colors). In this paper, we make a first study of the accuracy of the large-$N_c$ limit used by those calculations of overlap effects that avoid a soft bremsstrahlung approximation. Specifically, we calculate the $1/N_c^2$ correction to previous $N_c=\infty$ results for overlap $g\to gg\to ggg$ of two consecutive gluon splittings $g\to gg$. At order $1/N_c^2$, there is interesting and non-trivial color dynamics that must be accounted for during the overlap of the formation times.

arXiv comment47 pages, 19 figures. Changes from v1: some clarification added through new footnotes and a new figure

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Cited by in corpus (3)

• Classical vs quantum corrections to jet broadening in a weakly-coupled Quark-Gluon Plasma
• Jet substructure observables for jet quenching in Quark Gluon Plasma: a Machine Learning driven analysis
• The LPM effect in sequential bremsstrahlung: incorporation of "instantaneous'' interactions for QCD