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Title: Non-global logarithms, factorization, and the soft substructure of jets

Abstract

An outstanding problem in QCD and jet physics is the factorization and resummation of logarithms that arise due to phase space constraints, so-called non-global logarithms (NGLs). In this paper, we show that NGLs can be factorized and resummed down to an unresolved infrared scale by making sufficiently many measurements on a jet or other restricted phase space region. Resummation is accomplished by renormalization group evolution of the objects in the factorization theorem and anomalous dimensions can be calculated to any perturbative accuracy and with any number of colors. To connect with the NGLs of more inclusive measurements, we present a novel perturbative expansion which is controlled by the volume of the allowed phase space for unresolved emissions. Arbitrary accuracy can be obtained by making more and more measurements so to resolve lower and lower scales. We find that even a minimal number of measurements produces agreement with Monte Carlo methods for leading-logarithmic resummation of NGLs at the sub-percent level over the full dynamical range relevant for the Large Hadron Collider. Here, we also discuss other applications of our factorization theorem to soft jet dynamics and how to extend to higher-order accuracy.

Authors:
 [1];  [1];  [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1455239
Grant/Contract Number:  
SC0011090; SC0012567
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: 2015; Journal Issue: 9; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Resummation; QCD

Citation Formats

Larkoski, Andrew J., Moult, Ian, and Neill, Duff. Non-global logarithms, factorization, and the soft substructure of jets. United States: N. p., 2015. Web. doi:10.1007/JHEP09(2015)143.
Larkoski, Andrew J., Moult, Ian, & Neill, Duff. Non-global logarithms, factorization, and the soft substructure of jets. United States. doi:10.1007/JHEP09(2015)143.
Larkoski, Andrew J., Moult, Ian, and Neill, Duff. Tue . "Non-global logarithms, factorization, and the soft substructure of jets". United States. doi:10.1007/JHEP09(2015)143. https://www.osti.gov/servlets/purl/1455239.
@article{osti_1455239,
title = {Non-global logarithms, factorization, and the soft substructure of jets},
author = {Larkoski, Andrew J. and Moult, Ian and Neill, Duff},
abstractNote = {An outstanding problem in QCD and jet physics is the factorization and resummation of logarithms that arise due to phase space constraints, so-called non-global logarithms (NGLs). In this paper, we show that NGLs can be factorized and resummed down to an unresolved infrared scale by making sufficiently many measurements on a jet or other restricted phase space region. Resummation is accomplished by renormalization group evolution of the objects in the factorization theorem and anomalous dimensions can be calculated to any perturbative accuracy and with any number of colors. To connect with the NGLs of more inclusive measurements, we present a novel perturbative expansion which is controlled by the volume of the allowed phase space for unresolved emissions. Arbitrary accuracy can be obtained by making more and more measurements so to resolve lower and lower scales. We find that even a minimal number of measurements produces agreement with Monte Carlo methods for leading-logarithmic resummation of NGLs at the sub-percent level over the full dynamical range relevant for the Large Hadron Collider. Here, we also discuss other applications of our factorization theorem to soft jet dynamics and how to extend to higher-order accuracy.},
doi = {10.1007/JHEP09(2015)143},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2015,
place = {United States},
year = {2015},
month = {9}
}

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Cited by: 51 works
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Works referenced in this record:

Super-leading logarithms in non-global observables in QCD: colour basis independent calculation
journal, September 2008


Energy and Color Flow in Dijet Rapidity Gaps
journal, October 1998


Relating e + e annihilation to high energy scattering at weak and strong coupling
journal, November 2008


Single soft gluon emission at two loops
journal, November 2013


Non-global jet evolution at finite Nc
journal, May 2004


Multipole-expanded soft-collinear effective theory with non-Abelian gauge symmetry
journal, February 2003


Toward multi-differential cross sections: measuring two angularities on a single jet
journal, September 2014

  • Larkoski, Andrew J.; Moult, Ian; Neill, Duff
  • Journal of High Energy Physics, Vol. 2014, Issue 9
  • DOI: 10.1007/JHEP09(2014)046

Webs in multiparton scattering using the replica trick
journal, November 2010

  • Gardi, Einan; Laenen, Eric; Stavenga, Gerben
  • Journal of High Energy Physics, Vol. 2010, Issue 11
  • DOI: 10.1007/JHEP11(2010)155

Estimate of B ( B ¯ X s γ ) at O ( α s 2 )
journal, January 2007


Identifying boosted objects with N-subjettiness
journal, March 2011


Heavy jet mass distribution in e+e− annihilation
journal, December 1991


Resummation of the jet broadening in DIS
journal, June 2002

  • Dasgupta, M.; Salam, G. P.
  • The European Physical Journal C, Vol. 24, Issue 2
  • DOI: 10.1007/s100520200915

N Jettiness: An Inclusive Event Shape to Veto Jets
journal, August 2010


Double non-global logarithms in-n-out of jets
journal, January 2012

  • Hornig, Andrew; Lee, Christopher; Walsh, Jonathan R.
  • Journal of High Energy Physics, Vol. 2012, Issue 1
  • DOI: 10.1007/JHEP01(2012)149

Enhanced nonperturbative effects in Z decays to hadrons
journal, August 2004


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

  • Berger, Carola F.; Marcantonini, Claudio; Stewart, Iain W.
  • Journal of High Energy Physics, Vol. 2011, Issue 4
  • DOI: 10.1007/JHEP04(2011)092

The b → se+e− and b → sγ decays with next-to-leading logarithmic QCD-corrections
journal, March 1993


Non-global logarithms in filtered jet algorithms
journal, May 2010


Weak decays beyond leading logarithms
journal, October 1996

  • Buchalla, Gerhard; Buras, Andrzej J.; Lautenbacher, Markus E.
  • Reviews of Modern Physics, Vol. 68, Issue 4
  • DOI: 10.1103/RevModPhys.68.1125

Invariant operators in collinear effective theory
journal, September 2001


Gauge fields as rings of glue
journal, January 1980


Maximizing boosted top identification by minimizing N-subjettiness
journal, February 2012


The renormalization group equation for the color glass condensate
journal, June 2001


Super-leading logarithms in non-global observables in QCD?
journal, August 2006

  • Forshaw, Jeffrey R.; Kyrieleis, Albrecht; Seymour, Michael H.
  • Journal of High Energy Physics, Vol. 2006, Issue 08
  • DOI: 10.1088/1126-6708/2006/08/059

Resummed C-parameter distribution in e+e− annihilation
journal, May 1998


Energy correlation functions for jet substructure
journal, June 2013

  • Larkoski, Andrew J.; Salam, Gavin P.; Thaler, Jesse
  • Journal of High Energy Physics, Vol. 2013, Issue 6
  • DOI: 10.1007/JHEP06(2013)108

Energy flow in interjet radiation
journal, May 2002


Jet observables without jet algorithms
journal, April 2014

  • Bertolini, Daniele; Chan, Tucker; Thaler, Jesse
  • Journal of High Energy Physics, Vol. 2014, Issue 4
  • DOI: 10.1007/JHEP04(2014)013

Factorization for short distance hadron-hadron scattering
journal, January 1985


Infrared factorization of tree-level QCD amplitudes at the next-to-next-to-leading order and beyond
journal, March 2000


Summation of large corrections to short-distance hadronic cross sections
journal, January 1987


Renormalization-group improved prediction for Higgs production at hadron colliders
journal, April 2009


Improving Jet Distributions with Effective Field Theory
journal, October 2006


NLL+NNLO predictions for jet-veto efficiencies in Higgs-boson and Drell-Yan production
journal, June 2012

  • Banfi, Andrea; Salam, Gavin P.; Zanderighi, Giulia
  • Journal of High Energy Physics, Vol. 2012, Issue 6
  • DOI: 10.1007/JHEP06(2012)159

Hard scattering factorization from effective field theory
journal, July 2002


Resummation of non-global logarithms at finite <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:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:math>
journal, September 2013


Non-global logarithms at finite N c beyond leading order
journal, March 2015

  • Khelifa-Kerfa, Kamel; Delenda, Yazid
  • Journal of High Energy Physics, Vol. 2015, Issue 3
  • DOI: 10.1007/JHEP03(2015)094

Jet shapes with the broadening axis
journal, April 2014

  • Larkoski, Andrew J.; Neill, Duff; Thaler, Jesse
  • Journal of High Energy Physics, Vol. 2014, Issue 4
  • DOI: 10.1007/JHEP04(2014)017

The non-Abelian exponentiation theorem for multiple Wilson lines
journal, June 2013

  • Gardi, Einan; Smillie, Jennifer M.; White, Chris D.
  • Journal of High Energy Physics, Vol. 2013, Issue 6
  • DOI: 10.1007/JHEP06(2013)088

Transverse momentum distribution in Drell-Yan pair and W and Z boson production
journal, January 1985


Higgs- and Z -boson Production with a Jet Veto
journal, November 2012


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

  • Chiu, Jui-Yu; Jain, Ambar; Neill, Duff
  • Journal of High Energy Physics, Vol. 2012, Issue 5
  • DOI: 10.1007/JHEP05(2012)084

Effective field theory and matching in nonrelativistic gauge theories
journal, January 1998


Non-global logarithms in inter-jet energy flow with kt clustering requirement
journal, December 2002


Asymptotics of the Altarelli-Parisi-Lipatov Evolution Kernels of Parton Distributions
journal, July 1989


Dijet rapidity gaps in photoproduction from perturbative QCD
journal, November 1999


Renormalon resummation and exponentiation of soft and collinear gluon radiation in the thrust distribution
journal, August 2001


Weak radiative B-meson decay beyond leading logarithms
journal, May 1997


The two-loop soft current in dimensional regularization
journal, December 2013


Factorization and momentum-space resummation in deep-inelastic scattering
journal, January 2007


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


Exact solution of BFKL equation in jet-physics
journal, July 2004


Jet shapes and jet algorithms in SCET
journal, November 2010

  • Ellis, Stephen D.; Vermilion, Christopher K.; Walsh, Jonathan R.
  • Journal of High Energy Physics, Vol. 2010, Issue 11
  • DOI: 10.1007/JHEP11(2010)101

The anti- k t jet clustering algorithm
journal, April 2008


The first calculation of fractional jets
journal, May 2015

  • Bertolini, Daniele; Thaler, Jesse; Walsh, Jonathan R.
  • Journal of High Energy Physics, Vol. 2015, Issue 5
  • DOI: 10.1007/JHEP05(2015)008

Non-global logarithms and jet algorithms in high-p T jet shapes
journal, August 2010

  • Banfi, Andrea; Dasgupta, Mrinal; Khelifa-Kerfa, Kamel
  • Journal of High Energy Physics, Vol. 2010, Issue 8
  • DOI: 10.1007/JHEP08(2010)064

BFKL dynamics in jet evolution
journal, November 2003


Intrinsic glue distribution at very small x
journal, May 1997

  • Jalilian-Marian, Jamal; Kovner, Alex; McLerran, Larry
  • Physical Review D, Vol. 55, Issue 9
  • DOI: 10.1103/PhysRevD.55.5414

Power counting to better jet observables
journal, December 2014

  • Larkoski, Andrew J.; Moult, Ian; Neill, Duff
  • Journal of High Energy Physics, Vol. 2014, Issue 12
  • DOI: 10.1007/JHEP12(2014)009

When does the gluon reggeize?
journal, May 2015


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


Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
journal, September 2012


Boosted objects: a probe of beyond the standard model physics
journal, June 2011


Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
journal, September 2012


Operator expansion for high-energy scattering
journal, March 1996


On the structure of infrared singularities of gauge-theory amplitudes
journal, June 2009


The dijet cross section with a jet veto
journal, August 2011

  • Delgado, Rosa María Durán; Forshaw, Jeffrey R.; Marzani, Simone
  • Journal of High Energy Physics, Vol. 2011, Issue 8
  • DOI: 10.1007/JHEP08(2011)157

Resummation of large logarithms in e+e− event shape distributions
journal, October 1993


Transverse momentum moments of hadron distributions in QCD jets
journal, November 1981


Away-from-jet energy flow
journal, August 2002


Jet Vetoes interfering with H → WW
journal, September 2014


Boosted objects and jet substructure at the LHC. Report of BOOST2012, held at IFIC Valencia, 23rd–27th of July 2012
journal, March 2014


Quantum Chromodynamics Test for Jets
journal, December 1977


Factorization and NNLL Resummation for Higgs production with a jet veto
journal, July 2012

  • Becher, Thomas; Neubert, Matthias
  • Journal of High Energy Physics, Vol. 2012, Issue 7
  • DOI: 10.1007/JHEP07(2012)108

On soft singularities at three loops and beyond
journal, February 2010

  • Dixon, Lance J.; Gardi, Einan; Magnea, Lorenzo
  • Journal of High Energy Physics, Vol. 2010, Issue 2
  • DOI: 10.1007/JHEP02(2010)081

The perturbative calculation of jet structure in e+e− annihilation
journal, February 1981


Jet trimming
journal, February 2010

  • Krohn, David; Thaler, Jesse; Wang, Lian-Tao
  • Journal of High Energy Physics, Vol. 2010, Issue 2
  • DOI: 10.1007/JHEP02(2010)084

Jet vetoing at the LHC
journal, July 2009


Factorization and N3LLp+NNLO predictions for the Higgs cross section with a jet veto
journal, October 2013

  • Becher, Thomas; Neubert, Matthias; Rothen, Lorena
  • Journal of High Energy Physics, Vol. 2013, Issue 10
  • DOI: 10.1007/JHEP10(2013)125

Soft-gluon resummation for Higgs boson production at hadron colliders
journal, July 2003

  • Catani, Stefano; Florian, Daniel de; Grazzini, Massimiliano
  • Journal of High Energy Physics, Vol. 2003, Issue 07
  • DOI: 10.1088/1126-6708/2003/07/028

Phenomenology of event shapes at hadron colliders
journal, June 2010

  • Banfi, Andrea; Salam, Gavin P.; Zanderighi, Giulia
  • Journal of High Energy Physics, Vol. 2010, Issue 6
  • DOI: 10.1007/JHEP06(2010)038

Deep inelastic scattering as x 1 using soft-collinear effective theory
journal, December 2003


Exponentiation of eikonal cross sections in nonabelian gauge theories
journal, December 1983


Jet Substructure as a New Higgs-Search Channel at the Large Hadron Collider
journal, June 2008


Soft gluons away from jets: distribution and correlation
journal, June 2009


Infrared factorization, Wilson lines and the heavy quark limit
journal, April 1992


The soft-gluon current at one-loop order
journal, December 2000


Small- x F 2 structure function of a nucleus including multiple Pomeron exchanges
journal, June 1999


Soft drop
journal, May 2014

  • Larkoski, Andrew J.; Marzani, Simone; Soyez, Gregory
  • Journal of High Energy Physics, Vol. 2014, Issue 5
  • DOI: 10.1007/JHEP05(2014)146

On the QCD analysis of jet broadening
journal, January 1998


Jet substructure at the Tevatron and LHC: new results, new tools, new benchmarks
journal, May 2012


Resummation of non-global QCD observables
journal, July 2001


Non-global structure of the $ \mathcal{O}\left( {\alpha_s^2} \right) $ dijet soft function
journal, August 2011

  • Hornig, Andrew; Lee, Christopher; Stewart, Iain W.
  • Journal of High Energy Physics, Vol. 2011, Issue 8
  • DOI: 10.1007/JHEP08(2011)054

The zero-bin and mode factorization in quantum field theory
journal, October 2007


Partonic distributions for large x and renormalization of Wilson loop
journal, September 1993


Jet broadening measures in e+e− annihilation
journal, December 1992


Event generation from effective field theory
journal, October 2007


Event shape–energy flow correlations
journal, July 2003


Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
journal, March 2009


Resummation of double-differential cross sections and fully-unintegrated parton distribution functions
journal, February 2015

  • Procura, Massimiliano; Waalewijn, Wouter J.; Zeune, Lisa
  • Journal of High Energy Physics, Vol. 2015, Issue 2
  • DOI: 10.1007/JHEP02(2015)117

Abelian non-global logarithms from soft gluon clustering
journal, September 2012

  • Kelley, Randall; Walsh, Jonathan R.; Zuberi, Saba
  • Journal of High Energy Physics, Vol. 2012, Issue 9
  • DOI: 10.1007/JHEP09(2012)117

Non linear gluon evolution in path-integral form
journal, January 2003


Resummation of thrust distributions in DIS
journal, February 2000


General properties of multiparton webs: proofs from combinatorics
journal, March 2011


Single and double BFKL pomeron exchange and a dipole picture of high energy hard processes
journal, August 1994


Jet substructure with analytical methods
journal, November 2013


Towards an understanding of jet substructure
journal, September 2013

  • Dasgupta, Mrinal; Fregoso, Alessandro; Marzani, Simone
  • Journal of High Energy Physics, Vol. 2013, Issue 9
  • DOI: 10.1007/JHEP09(2013)029

Multiple soft gluon radiation in parton processes
journal, February 1989


Non-abelian eikonal exponentiation
journal, November 1984


A general method for the resummation of event-shape distributions in e + e − annihilation
journal, May 2015

  • Banfi, Andrea; McAslan, Heather; Monni, Pier Francesco
  • Journal of High Energy Physics, Vol. 2015, Issue 5
  • DOI: 10.1007/JHEP05(2015)102

Resummed event shapes at hadron-hadron colliders
journal, August 2004


Soft-collinear factorization in effective field theory
journal, February 2002


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    journal, March 2019

    • Lustermans, Gillian; Michel, Johannes K. L.; Tackmann, Frank J.
    • Journal of High Energy Physics, Vol. 2019, Issue 3
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    Jet veto resummation with jet rapidity cuts
    journal, April 2019

    • Michel, Johannes K. L.; Pietrulewicz, Piotr; Tackmann, Frank J.
    • Journal of High Energy Physics, Vol. 2019, Issue 4
    • DOI: 10.1007/jhep04(2019)142

    Measurements of the differential jet cross section as a function of the jet mass in dijet events from proton-proton collisions at s = 13 $$ \sqrt{s}=13 $$ TeV
    journal, November 2018

    • Sirunyan, A. M.; Tumasyan, A.; Adam, W.
    • Journal of High Energy Physics, Vol. 2018, Issue 11
    • DOI: 10.1007/jhep11(2018)113

    Joint two-dimensional resummation in qT and 0-jettiness at NNLL
    journal, March 2019

    • Lustermans, Gillian; Michel, Johannes K. L.; Tackmann, Frank J.
    • Journal of High Energy Physics, Vol. 2019, Issue 3
    • DOI: 10.1007/jhep03(2019)124

    Jet veto resummation with jet rapidity cuts
    journal, April 2019

    • Michel, Johannes K. L.; Pietrulewicz, Piotr; Tackmann, Frank J.
    • Journal of High Energy Physics, Vol. 2019, Issue 4
    • DOI: 10.1007/jhep04(2019)142

    How much information is in a jet?
    journal, June 2017


    Measurements of the differential jet cross section as a function of the jet mass in dijet events from proton-proton collisions at s = 13 $$ \sqrt{s}=13 $$ TeV
    journal, November 2018

    • Sirunyan, A. M.; Tumasyan, A.; Adam, W.
    • Journal of High Energy Physics, Vol. 2018, Issue 11
    • DOI: 10.1007/jhep11(2018)113

    Jet veto resummation with jet rapidity cuts
    text, January 2019

    • Michel, Johannes K. L.; Pietrulewicz, Piotr; Tackmann, Frank J.
    • Deutsches Elektronen-Synchrotron, DESY, Hamburg
    • DOI: 10.3204/pubdb-2019-02283