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Title: Collinear limit of the energy-energy correlator

Abstract

The energy-energy-correlator (EEC) observable in e+e annihilation measures the energy deposited in two detectors as a function of the angle between the detectors. The collinear limit, where the angle between the two detectors approaches zero, is of particular interest for describing the substructure of jets produced at hadron colliders as well as in e+e annihilation. We derive a factorization formula for the leading power asymptotic behavior in the collinear limit of a generic quantum field theory, which allows for the resummation of logarithmically enhanced terms to all orders by renormalization group evolution. The relevant anomalous dimensions are expressed in terms of the timelike data of the theory, in particular the moments of the timelike splitting functions, which are known to high perturbative orders. We relate the small angle and back-to-back limits to each other via the total cross section and an integral over intermediate angles. This relation, for the EEC in e+e and in Higgs decay to gluons, provides us with the initial conditions for quark and gluon jet functions at order α2s. In QCD and in N = 1 super-Yang-Mills theory, we then perform the resummation to next-to-next-to-leading logarithm, improving previous calculations by two perturbative orders. We highlight themore » important role played by the nonvanishing β function in these theories, which while subdominant for Higgs decays to gluons, dominates the behavior of the EEC in the collinear limit for e+e annihilation, and in N = 1 super-Yang-Mills theory. In conformally invariant N = 4 super-Yang-Mills theory, reciprocity between timelike and spacelike evolution can be used to express our factorization formula as a power law with exponent equal to the spacelike twist-two spin-three anomalous dimensions, thus providing a connection between timelike and spacelike approaches.« less

Authors:
; ;
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1532582
Alternate Identifier(s):
OSTI ID: 1546714
Grant/Contract Number:  
AC02-76SF00515; AC02-05CH11231; 107201*172210191
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 1; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Dixon, Lance J., Moult, Ian, and Zhu, Hua Xing. Collinear limit of the energy-energy correlator. United States: N. p., 2019. Web. doi:10.1103/PhysRevD.100.014009.
Dixon, Lance J., Moult, Ian, & Zhu, Hua Xing. Collinear limit of the energy-energy correlator. United States. doi:10.1103/PhysRevD.100.014009.
Dixon, Lance J., Moult, Ian, and Zhu, Hua Xing. Tue . "Collinear limit of the energy-energy correlator". United States. doi:10.1103/PhysRevD.100.014009.
@article{osti_1532582,
title = {Collinear limit of the energy-energy correlator},
author = {Dixon, Lance J. and Moult, Ian and Zhu, Hua Xing},
abstractNote = {The energy-energy-correlator (EEC) observable in e+e– annihilation measures the energy deposited in two detectors as a function of the angle between the detectors. The collinear limit, where the angle between the two detectors approaches zero, is of particular interest for describing the substructure of jets produced at hadron colliders as well as in e+e– annihilation. We derive a factorization formula for the leading power asymptotic behavior in the collinear limit of a generic quantum field theory, which allows for the resummation of logarithmically enhanced terms to all orders by renormalization group evolution. The relevant anomalous dimensions are expressed in terms of the timelike data of the theory, in particular the moments of the timelike splitting functions, which are known to high perturbative orders. We relate the small angle and back-to-back limits to each other via the total cross section and an integral over intermediate angles. This relation, for the EEC in e+e– and in Higgs decay to gluons, provides us with the initial conditions for quark and gluon jet functions at order α2s. In QCD and in N = 1 super-Yang-Mills theory, we then perform the resummation to next-to-next-to-leading logarithm, improving previous calculations by two perturbative orders. We highlight the important role played by the nonvanishing β function in these theories, which while subdominant for Higgs decays to gluons, dominates the behavior of the EEC in the collinear limit for e+e– annihilation, and in N = 1 super-Yang-Mills theory. In conformally invariant N = 4 super-Yang-Mills theory, reciprocity between timelike and spacelike evolution can be used to express our factorization formula as a power law with exponent equal to the spacelike twist-two spin-three anomalous dimensions, thus providing a connection between timelike and spacelike approaches.},
doi = {10.1103/PhysRevD.100.014009},
journal = {Physical Review D},
number = 1,
volume = 100,
place = {United States},
year = {2019},
month = {7}
}

Journal Article:
Free Publicly Available Full Text
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DOI: 10.1103/PhysRevD.100.014009

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Cited by: 3 works
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