The LPM effect in sequential bremsstrahlung: 1/ N c 2 $$ {\mathrm{N}}_{\mathrm{c}}^2 $$ corrections

Peter Arnold (Department of Physics, University of Virginia, Charlottesville, VA, 22904, USA) ; Omar Elgedawy (Department of Physics, University of Virginia, Charlottesville, VA, 22904, USA)

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 $$ {N}_{\mathrm{c}}^2 $$ correction to previous N c = ∞ results for overlap g → gg → ggg of two consecutive gluon splittings g → gg. At order 1/ N c 2 $$ {N}_{\mathrm{c}}^2 $$ , there is interesting and non-trivial color dynamics that must be accounted for during the overlap of the formation times.

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      "value": "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/   <math> <msubsup> <mi>N</mi> <mi>c</mi> <mn>2</mn> </msubsup> </math>  $$ {N}_{\\mathrm{c}}^2 $$  correction to previous N c = \u221e results for overlap g \u2192 gg \u2192 ggg of two consecutive gluon splittings g \u2192 gg. At order 1/   <math> <msubsup> <mi>N</mi> <mi>c</mi> <mn>2</mn> </msubsup> </math>  $$ {N}_{\\mathrm{c}}^2 $$ , there is interesting and non-trivial color dynamics that must be accounted for during the overlap of the formation times."
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Published on:
19 August 2022
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2022 (2022)
Issue 8
Pages 1-51
DOI:
https://doi.org/10.1007/JHEP08(2022)194
arXiv:
2202.04662
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: