The Energy-Energy Correlation in the back-to-back limit at N3LO and N3LL'

Ebert, Markus A.; Mistlberger, Bernhard; Vita, Gherardo

doi:10.1007/jhep08(2021)022

Title: The Energy-Energy Correlation in the back-to-back limit at N³LO and N³LL'

Abstract

We present the analytic formula for the Energy-Energy Correlation (EEC) in electron-positron annihilation computed in perturbative QCD to next-to-next-to-next-to-leading order (N³LO) in the back-to-back limit. In particular, we consider the EEC arising from the annihilation of an electron-positron pair into a virtual photon as well as a Higgs boson and their subsequent inclusive decay into hadrons. Our computation is based on a factorization theorem of the EEC formulated within Soft-Collinear Effective Theory (SCET) for the back-to-back limit. We obtain the last missing ingredient for our computation — the jet function — from a recent calculation of the transverse-momentum dependent fragmentation function (TMDFF) at N³LO. We combine the newly obtained N³LO jet function with the well known hard and soft function to predict the EEC in the back-to-back limit. The leading transcendental contribution of our analytic formula agrees with previously obtained results in N = 4 supersymmetric Yang-Mills theory. We obtain the N = 2 Mellin moment of the bulk region of the EEC using momentum sum rules. Finally, we obtain the first resummation of the EEC in the back-to-back limit at N³LL' accuracy, resulting in a factor of ~ 4 reduction of uncertainties in the peak region compared to N³LLmore » predictions.« less

Authors:

Ebert, Markus A. ^[1]; Mistlberger, Bernhard ^[2];

^[2]

Max Planck Inst. fuer Physik, Munich (Germany); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
SLAC National Accelerator Lab., Menlo Park, CA (United States)

Publication Date:: Wed Aug 04 00:00:00 EDT 2021

Research Org.:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

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

OSTI Identifier:: 1819452

Grant/Contract Number:: AC02-76SF00515; SC0011090

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: 2021; Journal Issue: 8; Journal ID: ISSN 1029-8479

Publisher:: Springer Nature

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Effective Field Theories; Perturbative QCD; Resummation

Citation Formats


                    Ebert, Markus A., Mistlberger, Bernhard, and Vita, Gherardo. The Energy-Energy Correlation in the back-to-back limit at N3LO and N3LL'.  United States: N. p., 2021. 
Web.  doi:10.1007/jhep08(2021)022.

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                    Ebert, Markus A., Mistlberger, Bernhard, & Vita, Gherardo. The Energy-Energy Correlation in the back-to-back limit at N3LO and N3LL'.  United States.  https://doi.org/10.1007/jhep08(2021)022

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                    Ebert, Markus A., Mistlberger, Bernhard, and Vita, Gherardo. Wed .  
"The Energy-Energy Correlation in the back-to-back limit at N3LO and N3LL'".  United States.  https://doi.org/10.1007/jhep08(2021)022.  https://www.osti.gov/servlets/purl/1819452.

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@article{osti_1819452,

  title        = {The Energy-Energy Correlation in the back-to-back limit at N3LO and N3LL'},

  author       = {Ebert, Markus A. and Mistlberger, Bernhard and Vita, Gherardo},

  abstractNote = {We present the analytic formula for the Energy-Energy Correlation (EEC) in electron-positron annihilation computed in perturbative QCD to next-to-next-to-next-to-leading order (N3LO) in the back-to-back limit. In particular, we consider the EEC arising from the annihilation of an electron-positron pair into a virtual photon as well as a Higgs boson and their subsequent inclusive decay into hadrons. Our computation is based on a factorization theorem of the EEC formulated within Soft-Collinear Effective Theory (SCET) for the back-to-back limit. We obtain the last missing ingredient for our computation — the jet function — from a recent calculation of the transverse-momentum dependent fragmentation function (TMDFF) at N3LO. We combine the newly obtained N3LO jet function with the well known hard and soft function to predict the EEC in the back-to-back limit. The leading transcendental contribution of our analytic formula agrees with previously obtained results in N = 4 supersymmetric Yang-Mills theory. We obtain the N = 2 Mellin moment of the bulk region of the EEC using momentum sum rules. Finally, we obtain the first resummation of the EEC in the back-to-back limit at N3LL' accuracy, resulting in a factor of ~ 4 reduction of uncertainties in the peak region compared to N3LL predictions.},

  doi          = {10.1007/jhep08(2021)022},

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

  number       = 8,

  volume       = 2021,

  place        = {United States},

  year         = {Wed Aug 04 00:00:00 EDT 2021},

  month        = {Wed Aug 04 00:00:00 EDT 2021}

}

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Event shapes in <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math> super-Yang–Mills theory
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Belitsky, A. V.; Hohenegger, S.; Korchemsky, G. P.
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Single logarithm effects in electron-positron annihilation
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From correlation functions to event shapes in QCD
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Title: The Energy-Energy Correlation in the back-to-back limit at N3LO and N3LL'

Abstract

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A subtraction scheme for computing QCD jet cross sections at NNLO: regularization of doubly-real emissions journal, January 2007

Transverse momentum dependent PDFs at N3LO journal, September 2020

Transverse energy–energy correlations of jets in the electron–proton deep inelastic scattering at HERA journal, November 2020

Two-loop quark and gluon form factors in dimensional regularisation journal, September 2005

Invariant operators in collinear effective theory journal, September 2001

Transverse-energy-energy correlations in deep inelastic scattering journal, November 2020

Back-to-back jets in QCD journal, December 1981

Higher-order Sudakov resummation in coupled gauge theories journal, March 2020

Energy Correlations in Electron-Positron Annihilation: Testing Quantum Chromodynamics journal, December 1978

Bootstrapping Rapidity Anomalous Dimensions for Transverse-Momentum Resummation journal, January 2017

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Analytic integration of real-virtual counterterms in NNLO jet cross sections I journal, September 2008

A complete basis of helicity operators for subleading factorization journal, November 2017

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Simplicity from recoil: the three-loop soft function and factorization for the energy-energy correlation journal, August 2018

Back-to-back jets: Fourier transform from b to kT journal, April 1982

A toolbox for $$q_{T}$$ and 0-jettiness subtractions at $$\hbox {N}^3\hbox {LO}$$ journal, February 2021

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A formalism for the systematic treatment of rapidity logarithms in Quantum Field Theory journal, May 2012

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The quark form factor at higher orders journal, August 2005

The gell-mann-low function of QCD in the three-loop approximation journal, June 1980

A Subleading Operator Basis and Matching for $gg \to H$ text, January 2017

Four-loop non-singlet splitting functions in the planar limit and beyond journal, October 2017

The three-loop splitting functions in QCD: the non-singlet case journal, June 2004

The full four-loop cusp anomalous dimension in $$ \mathcal{N} $$ = 4 super Yang-Mills and QCD journal, April 2020

Universal structure of subleading infrared poles in gauge theory amplitudes journal, August 2008

Renormalization of the Wilson loops beyond the leading order journal, January 1987

Rapidity renormalized TMD soft and beam functions at two loops journal, March 2016

Quark and gluon form factors to three loops text, January 2009

Self-Contained Definition of the Collins-Soper Kernel journal, November 2020

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Title: The Energy-Energy Correlation in the back-to-back limit at N³LO and N³LL'

Towards quasi-transverse momentum dependent PDFs computable on the lattice
journal, September 2019

A subtraction scheme for computing QCD jet cross sections at NNLO: regularization of real-virtual emission
journal, January 2007

Matter dependence of the four-loop QCD cusp anomalous dimension: from small angles to all angles
journal, May 2019

Virtual corrections to gg→H to two loops in the heavy top limit
journal, October 2000

An exponential regulator for rapidity divergences
journal, November 2020

Power corrections to event shapes and factorization
journal, August 1999

Three-Jet Production in Electron-Positron Collisions at Next-to-Next-to-Leading Order Accuracy
journal, October 2016

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

Power corrections to event shapes and factorization
text, January 1999

The large $N$ limit of superconformal field theories and supergravity
journal, January 1998

Energy-Energy Correlations in $N = 4$ Supersymmetric Yang-Mills Theory
journal, February 2014

Energy correlations in the end-point region
journal, January 2020

Gluon jet function at three loops in QCD
journal, November 2018

Four-loop photon quark form factor and cusp anomalous dimension in the large-N c limit of QCD
journal, March 2017

Universality of Soft and Collinear Factors in Hard-Scattering Factorization
journal, December 2004

Transverse-momentum-dependent factorization for lattice observables
journal, April 2020

Higgs production with a central jet veto at NNLL+NNLO
journal, April 2011

Matter dependence of the four-loop cusp anomalous dimension
text, January 2019

Adler Function, Sum Rules and Crewther Relation of Order O(alpha_s^4): the Singlet Case
text, January 2012

Higher-spin correlators
journal, October 2013

Determining the nonperturbative Collins-Soper kernel from lattice QCD
journal, February 2019

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journal, April 2020

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journal, January 2007

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journal, September 2020

Transverse energy–energy correlations of jets in the electron–proton deep inelastic scattering at HERA
journal, November 2020

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journal, September 2005

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journal, September 2001

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journal, November 2020

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journal, December 1981

Higher-order Sudakov resummation in coupled gauge theories
journal, March 2020

Energy Correlations in Electron-Positron Annihilation: Testing Quantum Chromodynamics
journal, December 1978

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journal, January 2017

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journal, June 2021

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journal, January 2005

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journal, July 1984

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journal, September 2008

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journal, July 2020

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journal, January 2020

Simplicity from recoil: the three-loop soft function and factorization for the energy-energy correlation
journal, August 2018

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journal, April 1982

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journal, February 2021

Two-jet cross section ine + e − annihilation
journal, December 1987

A formalism for the systematic treatment of rapidity logarithms in Quantum Field Theory
journal, May 2012

Energy-energy correlators in deep inelastic scattering
journal, May 2021

The quark form factor at higher orders
journal, August 2005

The gell-mann-low function of QCD in the three-loop approximation
journal, June 1980

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text, January 2017

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journal, October 2017

The three-loop splitting functions in QCD: the non-singlet case
journal, June 2004

The full four-loop cusp anomalous dimension in $$ \mathcal{N} $$ = 4 super Yang-Mills and QCD
journal, April 2020

Universal structure of subleading infrared poles in gauge theory amplitudes
journal, August 2008

Renormalization of the Wilson loops beyond the leading order
journal, January 1987

Rapidity renormalized TMD soft and beam functions at two loops
journal, March 2016

Quark and gluon form factors to three loops
text, January 2009

Self-Contained Definition of the Collins-Soper Kernel
journal, November 2020

Analytical Computation of Energy-Energy Correlation at Next-to-Leading Order in QCD
journal, March 2018

Lattice QCD Calculations of Transverse-Momentum-Dependent Soft Function through Large-Momentum Effective Theory
journal, November 2020

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journal, September 2020

Second order logarithmic corrections to the Drell-Yan cross-section
journal, December 1988

Analytic next-to-leading order calculation of energy-energy correlation in gluon-initiated Higgs decays
journal, June 2019

From correlation functions to event shapes
journal, July 2014

Summing soft emission in QCD
journal, April 1982

Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond
journal, October 2005

QCD evolution of (un)polarized gluon TMDPDFs and the Higgs qT -distribution
journal, July 2015

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journal, March 2014

The four-loop β-function in quantum chromodynamics
journal, May 1997

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journal, April 2019

Fermionic Glauber operators and quark reggeization
journal, February 2018

An effective field theory for collinear and soft gluons: Heavy to light decays
journal, May 2001

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journal, March 2020

A precise determination of α _s from LEP thrust data using effective field theory
journal, July 2008

Correspondence between Soft and Rapidity Anomalous Dimensions
journal, February 2017

The quark beam function at NNLL
journal, September 2010

Collins-Soper kernel for TMD evolution from lattice QCD
journal, July 2020

Precise determination of $$\alpha _{S}(M_Z)$$ α S ( M Z ) from a global fit of energy–energy correlation to NNLO+NNLL predictions
journal, June 2018

A subtraction scheme for computing QCD jet cross sections at NNLO: regularization of real-virtual emission
journal, January 2007

QCD evolution of (un)polarized gluon TMDPDFs and the Higgs $q_T$-distribution
text, January 2015

Single logarithm effects in electron-positron annihilation
journal, April 1983