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Title: The analytic structure of non-global logarithms: Convergence of the dressed gluon expansion

Non-global 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 ex-pansion was introduced that enables an expansion of the NGL series in terms of a “dressed gluon” building block, defined by an all-orders 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 large-N c master equation for NGLs, the Banfi-Marchesini-Smye (BMS) equation. The dressed gluon expansion therefore provides an expansion of the NGL series that can be truncated at any order, with reliable uncertainty estimates. In contrast, manifest in the results of the fixed-order expansion of the BMS equation up to 12-loops is a breakdown of convergence at a finite value of α slog. We explain this finite radius of convergence using the dressed gluon expansion, showing how the dynamics of the buffer region, a region of phase space near the boundary of the jet that was identified in early studies of NGLs, leads to large contributions to the fixed order expansion. We also usemore » the dressed gluon expansion to discuss the convergence of the next-to-leading NGL series, and the role of collinear logarithms that appear at this order. Finally, we show how an understanding of the analytic behavior obtained from the dressed gluon expansion allows us to improve the fixed order NGL series using conformal transformations to extend the domain of analyticity. Furthermore, this allows us to calculate the NGL distribution for all values of α slog from the coefficients of the fixed order expansion.« less
Authors:
 [1] ;  [2] ; ORCiD logo [3]
  1. Harvard Univ., Cambridge, MA (United States); Reed College, Portland, OR (United States)
  2. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
  3. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Report Number(s):
LA-UR-16-26925
Journal ID: ISSN 1029-8479; TRN: US1701251
Grant/Contract Number:
AC52-06NA25396; AC02-05CH11231
Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 11; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org:
USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; atomic and nuclear physics; perturbative QCD; resummation; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Perturbative QCD
OSTI Identifier:
1377586
Alternate Identifier(s):
OSTI ID: 1346845

Larkoski, Andrew J., Moult, Ian, and Neill, Duff Austin. The analytic structure of non-global logarithms: Convergence of the dressed gluon expansion. United States: N. p., Web. doi:10.1007/JHEP11(2016)089.
Larkoski, Andrew J., Moult, Ian, & Neill, Duff Austin. The analytic structure of non-global logarithms: Convergence of the dressed gluon expansion. United States. doi:10.1007/JHEP11(2016)089.
Larkoski, Andrew J., Moult, Ian, and Neill, Duff Austin. 2016. "The analytic structure of non-global logarithms: Convergence of the dressed gluon expansion". United States. doi:10.1007/JHEP11(2016)089. https://www.osti.gov/servlets/purl/1377586.
@article{osti_1377586,
title = {The analytic structure of non-global logarithms: Convergence of the dressed gluon expansion},
author = {Larkoski, Andrew J. and Moult, Ian and Neill, Duff Austin},
abstractNote = {Non-global 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 ex-pansion was introduced that enables an expansion of the NGL series in terms of a “dressed gluon” building block, defined by an all-orders 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 large-Nc master equation for NGLs, the Banfi-Marchesini-Smye (BMS) equation. The dressed gluon expansion therefore provides an expansion of the NGL series that can be truncated at any order, with reliable uncertainty estimates. In contrast, manifest in the results of the fixed-order expansion of the BMS equation up to 12-loops is a breakdown of convergence at a finite value of αslog. We explain this finite radius of convergence using the dressed gluon expansion, showing how the dynamics of the buffer region, a region of phase space near the boundary of the jet that was identified in early studies of NGLs, leads to large contributions to the fixed order expansion. We also use the dressed gluon expansion to discuss the convergence of the next-to-leading NGL series, and the role of collinear logarithms that appear at this order. Finally, we show how an understanding of the analytic behavior obtained from the dressed gluon expansion allows us to improve the fixed order NGL series using conformal transformations to extend the domain of analyticity. Furthermore, this allows us to calculate the NGL distribution for all values of αslog from the coefficients of the fixed order expansion.},
doi = {10.1007/JHEP11(2016)089},
journal = {Journal of High Energy Physics (Online)},
number = 11,
volume = 2016,
place = {United States},
year = {2016},
month = {11}
}