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Title: The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts

Abstract

Here, we develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. Furthermore, this equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We also compute the decay width analytically, giving a closed form expression, and find it to be jet geometry independent, up to the number of legs of the dipole in the active jet. By enabling the asymptotic expansion we find that the perturbative seed is correct; we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. This must be supplemented with the correct application of the BFKL approximation to the BMS equation in collinear limits. Comparing to the asymptotics of the conformally related evolution equation encountered in small-x physics, the Balitisky-Kovchegov (BK) equation, we find that the asymptotic form of the non-global logarithms directly maps to the black-discmore » unitarity limit of the BK equation, despite the contrasting physical pictures. Indeed, we recover the equations of saturation physics in the final state dynamics of QCD.« less

Authors:
 [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1360709
Report Number(s):
LA-UR-16-27653
Journal ID: ISSN 1029-8479; TRN: US1702168
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 1; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 97 MATHEMATICS AND COMPUTING; Perturbative QCD; Resummation

Citation Formats

Neill, Duff. The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts. United States: N. p., 2017. Web. doi:10.1007/JHEP01(2017)109.
Neill, Duff. The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts. United States. doi:10.1007/JHEP01(2017)109.
Neill, Duff. Wed . "The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts". United States. doi:10.1007/JHEP01(2017)109. https://www.osti.gov/servlets/purl/1360709.
@article{osti_1360709,
title = {The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts},
author = {Neill, Duff},
abstractNote = {Here, we develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. Furthermore, this equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We also compute the decay width analytically, giving a closed form expression, and find it to be jet geometry independent, up to the number of legs of the dipole in the active jet. By enabling the asymptotic expansion we find that the perturbative seed is correct; we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. This must be supplemented with the correct application of the BFKL approximation to the BMS equation in collinear limits. Comparing to the asymptotics of the conformally related evolution equation encountered in small-x physics, the Balitisky-Kovchegov (BK) equation, we find that the asymptotic form of the non-global logarithms directly maps to the black-disc unitarity limit of the BK equation, despite the contrasting physical pictures. Indeed, we recover the equations of saturation physics in the final state dynamics of QCD.},
doi = {10.1007/JHEP01(2017)109},
journal = {Journal of High Energy Physics (Online)},
number = 1,
volume = 2017,
place = {United States},
year = {Wed Jan 25 00:00:00 EST 2017},
month = {Wed Jan 25 00:00:00 EST 2017}
}

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