The asymptotic form of nonglobal logarithms, black disc saturation, and gluonic deserts
Abstract
Here, we develop an asymptotic perturbation theory for the large logarithmic behavior of the nonlinear integrodifferential equation describing the soft correlations of QCD jet measurements, the BanfiMarchesiniSmye (BMS) equation. Furthermore, this equation captures the latetime evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the nonglobal logarithm, a function of the infrared 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 smallx physics, the BalitiskyKovchegov (BK) equation, we find that the asymptotic form of the nonglobal logarithms directly maps to the blackdiscmore »
 Authors:
 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):
 LAUR1627653
Journal ID: ISSN 10298479; TRN: US1702168
 Grant/Contract Number:
 AC5206NA25396
 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 10298479
 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 nonglobal 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 nonglobal logarithms, black disc saturation, and gluonic deserts. United States. doi:10.1007/JHEP01(2017)109.
Neill, Duff. Wed .
"The asymptotic form of nonglobal 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 nonglobal 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 nonlinear integrodifferential equation describing the soft correlations of QCD jet measurements, the BanfiMarchesiniSmye (BMS) equation. Furthermore, this equation captures the latetime evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the nonglobal logarithm, a function of the infrared 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 smallx physics, the BalitiskyKovchegov (BK) equation, we find that the asymptotic form of the nonglobal logarithms directly maps to the blackdisc 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}
}
Web of Science

Nonglobal logarithms (NGLs) are the leading manifestation of correlations between distinct phase space regions in QCD and gauge theories and have proven a challenge to understand using traditional resummation techniques. Recently, the dressed gluon expansion was introduced that enables an expansion of the NGL series in terms of a “dressed gluon” building block, defined by an allorders factorization theorem. Here, we clarify the nature of the dressed gluon expansion, and prove that it has an infinite radius of convergence as a solution to the leading logarithmic and largeN _{c} master equation for NGLs, the BanfiMarchesiniSmye (BMS) equation. The dressed gluonmore »Cited by 6

The analytic structure of nonglobal logarithms: Convergence of the dressed gluon expansion
Nonglobal logarithms (NGLs) are the leading manifestation of correlations between distinct phase space regions in QCD and gauge theories and have proven a challenge to understand using traditional resummation techniques. Recently, the dressed gluon expansion was introduced that enables an expansion of the NGL series in terms of a “dressed gluon” building block, defined by an allorders factorization theorem. Here, we clarify the nature of the dressed gluon expansion, and prove that it has an infinite radius of convergence as a solution to the leading logarithmic and largeN _{c} master equation for NGLs, the BanfiMarchesiniSmye (BMS) equation. The dressed gluonmore »Cited by 6 
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