Simplicity from recoil: the three-loop soft function and factorization for the energy-energy correlation

Moult, Ian; Zhu, Hua Xing

doi:10.1007/JHEP08(2018)160

Title: Simplicity from recoil: the three-loop soft function and factorization for the energy-energy correlation

Abstract

We derive an operator based factorization theorem for the energy-energy correlation (EEC) observable in the back-to-back region, allowing the cross section to be written as a convolution of hard, jet and soft functions. We prove the equivalence of the soft functions for the EEC and color singlet transverse-momentum resummation to all-loop order, and give their analytic result to three-loops. Large logarithms appearing in the perturbative expansion of the EEC can be resummed to all orders using renormalization group evolution. We give analytic results for all required anomalous dimensions to three-loop order, providing the first example of a transverse-momentum (recoil) sensitive e⁺e^- event shape whose anomalous dimensions are known at this order. The EEC can now be computed to next-to-next-to-next-to-leading logarithm matched to next-to-next-to-leading order, making it a prime candidate for precision QCD studies and extractions of the strong coupling constant. Lastly, we anticipate that our factorization theorem will also be crucial for understanding non-perturbative power corrections for the EEC, and their relationship to those appearing in other observables.

Authors:

Moult, Ian ^[1]; Zhu, Hua Xing ^[2]

Univ. of California, Berkeley, CA (United States). Berkeley Center for Theoretical Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Theoretical Physics Group
Zhejiang Univ., Hangzhou (China). Zhejiang Institute of Modern Physics, Department of Physics

Publication Date:: Mon Aug 27 00:00:00 EDT 2018

Research Org.:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1480820

Grant/Contract Number:: AC02-05CH11231

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 8; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; Jets; NLO Computations

Citation Formats


                    Moult, Ian, and Zhu, Hua Xing. Simplicity from recoil: the three-loop soft function and factorization for the energy-energy correlation.  United States: N. p., 2018. 
Web.  doi:10.1007/JHEP08(2018)160.

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                    Moult, Ian, & Zhu, Hua Xing. Simplicity from recoil: the three-loop soft function and factorization for the energy-energy correlation.  United States.  https://doi.org/10.1007/JHEP08(2018)160

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                    Moult, Ian, and Zhu, Hua Xing. Mon .  
"Simplicity from recoil: the three-loop soft function and factorization for the energy-energy correlation".  United States.  https://doi.org/10.1007/JHEP08(2018)160.  https://www.osti.gov/servlets/purl/1480820.

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@article{osti_1480820,

  title        = {Simplicity from recoil: the three-loop soft function and factorization for the energy-energy correlation},

  author       = {Moult, Ian and Zhu, Hua Xing},

  abstractNote = {We derive an operator based factorization theorem for the energy-energy correlation (EEC) observable in the back-to-back region, allowing the cross section to be written as a convolution of hard, jet and soft functions. We prove the equivalence of the soft functions for the EEC and color singlet transverse-momentum resummation to all-loop order, and give their analytic result to three-loops. Large logarithms appearing in the perturbative expansion of the EEC can be resummed to all orders using renormalization group evolution. We give analytic results for all required anomalous dimensions to three-loop order, providing the first example of a transverse-momentum (recoil) sensitive e+e- event shape whose anomalous dimensions are known at this order. The EEC can now be computed to next-to-next-to-next-to-leading logarithm matched to next-to-next-to-leading order, making it a prime candidate for precision QCD studies and extractions of the strong coupling constant. Lastly, we anticipate that our factorization theorem will also be crucial for understanding non-perturbative power corrections for the EEC, and their relationship to those appearing in other observables.},

  doi          = {10.1007/JHEP08(2018)160},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 8,

  volume       = 2018,

  place        = {United States},

  year         = {Mon Aug 27 00:00:00 EDT 2018},

  month        = {Mon Aug 27 00:00:00 EDT 2018}

}

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Works referencing / citing this record:

Transverse parton distribution and fragmentation functions at NNLO: the gluon case
journal, January 2020

Luo, Ming-Xing; Yang, Tong-Zhi; Zhu, Hua Xing
Journal of High Energy Physics, Vol. 2020, Issue 1
DOI: 10.1007/jhep01(2020)040

Subleading Power Rapidity Divergences and Power Corrections for $q_T$
text, January 2019

Ebert, Markus A.; Moult, Ian; Stewart, Iain W.
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2019-02279

Generic dijet soft functions at two-loop order: correlated emissions
text, January 2018

Bell, Guido; Rahn, Rudi; Talbert, Jim
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2019-00961

New insights on an old problem: resummation of the D-parameter
journal, February 2019

Larkoski, Andrew J.; Procita, Aja
Journal of High Energy Physics, Vol. 2019, Issue 2
DOI: 10.1007/jhep02(2019)104

Transverse parton distribution and fragmentation functions at NNLO: the quark case
journal, October 2019

Luo, Ming-Xing; Wang, Xing; Xu, Xiaofeng
Journal of High Energy Physics, Vol. 2019, Issue 10
DOI: 10.1007/jhep10(2019)083

Subleading power rapidity divergences and power corrections for qT
journal, April 2019

Ebert, Markus A.; Moult, Ian; Stewart, Iain W.
Journal of High Energy Physics, Vol. 2019, Issue 4
DOI: 10.1007/jhep04(2019)123

Generic dijet soft functions at two-loop order: correlated emissions
text, January 2019

Bell, Guido; Rahn, Rudi Michael; Talbert, Jim
Springer
DOI: 10.7892/boris.134180

Subleading Power Rapidity Divergences and Power Corrections for $q_T$
text, January 2018

Ebert, Markus A.; Moult, Ian; Stewart, Iain W.
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2019-00610

Generic dijet soft functions at two-loop order: correlated emissions
text, January 2019

Bell, Guido; Rahn, Rudi; Talbert, Jim
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2019-02906

New Insights on an Old Problem: Resummation of the D-parameter
text, January 2018

Larkoski, Andrew J.; Procita, Aja
arXiv
DOI: 10.48550/arxiv.1810.06563

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