Two-Loop Five-Point Amplitude in N = 4 Super-Yang-Mills Theory

Abreu, Samuel; Dixon, Lance J.; Herrmann, Enrico; Page, Ben; Zeng, Mao

doi:10.1103/PhysRevLett.122.121603

Title: Two-Loop Five-Point Amplitude in $N = 4$ Super-Yang-Mills Theory

Abstract

We compute the symbol of the two-loop five-point scattering amplitude in $N = 4$ supersymmetric Yang-Mills theory, including its full color dependence. This requires constructing the symbol of all two-loop five-point nonplanar massless master integrals, for which we give explicit results.

Authors:: Abreu, Samuel; Dixon, Lance J.; Herrmann, Enrico; Page, Ben; Zeng, Mao

Publication Date:: 2019-03-29

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

Sponsoring Org.:: USDOE

OSTI Identifier:: 1504281

Alternate Identifier(s):: OSTI ID: 1526470

Report Number(s):: SLAC–PUB-17369
Journal ID: ISSN 0031-9007; PRLTAO; 121603

Grant/Contract Number:: AC02-76SF00515; SNF200021179016; 341344; ANR17CE31000101

Resource Type:: Published Article

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Name: Physical Review Letters Journal Volume: 122 Journal Issue: 12; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Abreu, Samuel, Dixon, Lance J., Herrmann, Enrico, Page, Ben, and Zeng, Mao. Two-Loop Five-Point Amplitude in N = 4 Super-Yang-Mills Theory.  United States: N. p., 2019. 
        Web.  doi:10.1103/PhysRevLett.122.121603.

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                    Abreu, Samuel, Dixon, Lance J., Herrmann, Enrico, Page, Ben, & Zeng, Mao. Two-Loop Five-Point Amplitude in N = 4 Super-Yang-Mills Theory.  United States.  doi:https://doi.org/10.1103/PhysRevLett.122.121603

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                    Abreu, Samuel, Dixon, Lance J., Herrmann, Enrico, Page, Ben, and Zeng, Mao. Fri .  
        "Two-Loop Five-Point Amplitude in N = 4 Super-Yang-Mills Theory".  United States.  doi:https://doi.org/10.1103/PhysRevLett.122.121603.

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@article{osti_1504281,

  title        = {Two-Loop Five-Point Amplitude in N = 4 Super-Yang-Mills Theory},

  author       = {Abreu, Samuel and Dixon, Lance J. and Herrmann, Enrico and Page, Ben and Zeng, Mao},

  abstractNote = {We compute the symbol of the two-loop five-point scattering amplitude in N=4 supersymmetric Yang-Mills theory, including its full color dependence. This requires constructing the symbol of all two-loop five-point nonplanar massless master integrals, for which we give explicit results.},

  doi          = {10.1103/PhysRevLett.122.121603},

  journal      = {Physical Review Letters},

  number       = 12,

  volume       = 122,

  place        = {United States},

  year         = {2019},

  month        = {3}

}

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DOI: https://doi.org/10.1103/PhysRevLett.122.121603

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Cited by: 20 works

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Figures / Tables:

FIG. 1: Diagram topologies entering the local representation of the two-loop five-point integrand of N = 4 sYM. Each diagram has an associated color structure and numerator which we suppress.

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Works referenced in this record:

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Title: Two-Loop Five-Point Amplitude in N = 4 Super-Yang-Mills Theory

Abstract

Citation Formats

Figures / Tables:

Integration-by-parts reductions from unitarity cuts and algebraic geometry journal, February 2016

Analytic Form of the Two-Loop Planar Five-Gluon All-Plus-Helicity Amplitude in QCD journal, February 2016

Integration by parts: The algorithm to calculate β-functions in 4 loops journal, November 1981

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

The Galois coaction on $\phi^4$ periods journal, January 2017

Dual Conformal Structure Beyond the Planar Limit journal, September 2018

Four-Gluon Scattering at Three Loops, Infrared Structure, and the Regge Limit journal, October 2016

SU(N) group-theory constraints on color-ordered five-point amplitudes at all loop orders journal, May 2012

Multiloop Integrals in Dimensional Regularization Made Simple journal, June 2013

Two-loop four-gluon amplitudes in N = 4 super-Yang-Mills journal, May 1997

Analytical result for dimensionally regularized massless on-shell double box journal, August 1999

Differential equations from unitarity cuts: nonplanar hexa-box integrals journal, January 2019

Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes journal, August 2012

Evidence for a nonplanar amplituhedron journal, June 2016

Connection between Feynman integrals having different values of the space-time dimension journal, November 1996

Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections journal, September 2018

On-shell structures of MHV amplitudes beyond the planar limit journal, June 2015

High-Precision Calculation of Multiloop Feynman Integrals by Difference Equations journal, December 2000

Perturbative Quantum Gravity as a Double Copy of Gauge Theory journal, August 2010

Bootstrapping the three-loop hexagon journal, November 2011

The pentabox Master Integrals with the Simplified Differential Equations approach journal, April 2016

Infrared singularities of QCD scattering amplitudes in the Regge limit to all orders journal, March 2018

Eliminating spurious poles from gauge-theoretic amplitudes journal, May 2013

Towards a basis for planar two-loop integrals journal, February 2011

Two-Loop Iteration of Five-Point N = 4 Super-Yang-Mills Amplitudes journal, November 2006

The high energy limit of QCD at two loops journal, October 2001

Two-loop integrand decomposition into master integrals and surface terms journal, December 2016

Multigluon cross sections and 5-jet production at hadron colliders journal, January 1989

Planar two-loop five-parton amplitudes from numerical unitarity journal, November 2018

Planar two-loop five-gluon amplitudes from numerical unitarity journal, June 2018

Space–time dimensionality as complex variable: Calculating loop integrals using dimensional recurrence relation and analytical properties with respect to journal, May 2010

Pentagon functions for massless planar scattering amplitudes journal, October 2018

Two-loop master integrals for jets: the non-planar topologies journal, May 2001

Bootstrapping pentagon functions journal, May 2018

Scattering amplitudes — Wilson loops duality for the first non-planar correction journal, August 2018

The singular behaviour of QCD amplitudes at two-loop order journal, May 1998

Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case journal, January 2019

Two-Loop g gg Splitting Amplitudes in QCD journal, August 2004

Two-loop soft anomalous dimension matrix and resummation at next-to-next-to-leading poles journal, October 2006

A theorem on analytical calculability of 4-loop renormalization group functions journal, March 1981

One-loop n-point gauge theory amplitudes, unitarity and collinear limits journal, August 1994

Non-planar massless two-loop Feynman diagrams with four on-shell legs journal, December 1999

A novel approach to integration by parts reduction journal, May 2015

Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals journal, March 2015

Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case journal, December 2017

Dimensionally regulated one-loop integrals journal, March 1993

First Look at Two-Loop Five-Gluon Scattering in QCD journal, March 2018

Amplitude for n -Gluon Scattering journal, June 1986

Scattering amplitudes over finite fields and multivariate functional reconstruction journal, December 2016

A current algebra for some gauge theory amplitudes journal, November 1988

Classical Polylogarithms for Amplitudes and Wilson Loops journal, October 2010

Differential equations for two-loop four-point functions journal, July 2000

Pulling the straps of polygons journal, December 2011

A two-loop five-gluon helicity amplitude in QCD journal, December 2013

From polygons and symbols to polylogarithmic functions journal, October 2012

Five-point amplitudes in N = 4 super-Yang-Mills theory and N = 8 supergravity journal, January 2012

One-loop self-dual and N = 4 super Yang-Mills journal, February 1997

One-loop corrections to five-gluon amplitudes journal, May 1993

On the highest transcendentality in SUSY journal, May 2007

Dimensionally-regulated pentagon integrals journal, January 1994

Algebraic Structure of Cut Feynman Integrals and the Diagrammatic Coaction journal, July 2017

Erratum: Analytic Form of the Two-Loop Planar Five-Gluon All-Plus-Helicity Amplitude in QCD [Phys. Rev. Lett. 116 , 062001 (2016)] journal, May 2016

Connection between Feynman integrals having different values of the space-time dimension text, January 1996

Two-loop scattering amplitudes: double-forward limit and colour-kinematics duality journal, December 2019

Physical projectors for multi-leg helicity amplitudes journal, July 2019

A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons journal, September 2019

Multi-quark colour decompositions from unitarity journal, October 2019

Prescriptive unitarity for non-planar six-particle amplitudes at two loops journal, December 2019

Two-loop N -jettiness soft function for p p → 2 j production journal, June 2019

Analytic Result for a Two-Loop Five-Particle Amplitude journal, March 2019

All Master Integrals for Three-Jet Production at Next-to-Next-to-Leading Order journal, July 2019

Precision QCD Event Shapes at Hadron Colliders: The Transverse Energy-Energy Correlator in the Back-to-Back Limit journal, August 2019

Analytic Form of the Full Two-Loop Five-Gluon All-Plus Helicity Amplitude journal, August 2019

Full-Color Two-Loop Four-Gluon Amplitude in N = 2 Supersymmetric QCD journal, December 2019

All-Multiplicity Nonplanar Amplitude Integrands in Maximally Supersymmetric Yang-Mills Theory at Two Loops journal, March 2020

Title: Two-Loop Five-Point Amplitude in $N = 4$ Super-Yang-Mills Theory

Integration-by-parts reductions from unitarity cuts and algebraic geometry
journal, February 2016

Analytic Form of the Two-Loop Planar Five-Gluon All-Plus-Helicity Amplitude in QCD
journal, February 2016

Integration by parts: The algorithm to calculate β-functions in 4 loops
journal, November 1981

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

The Galois coaction on $\phi^4$ periods
journal, January 2017

Dual Conformal Structure Beyond the Planar Limit
journal, September 2018

Four-Gluon Scattering at Three Loops, Infrared Structure, and the Regge Limit
journal, October 2016

SU(N) group-theory constraints on color-ordered five-point amplitudes at all loop orders
journal, May 2012

Multiloop Integrals in Dimensional Regularization Made Simple
journal, June 2013

Two-loop four-gluon amplitudes in N = 4 super-Yang-Mills
journal, May 1997

Analytical result for dimensionally regularized massless on-shell double box
journal, August 1999

Differential equations from unitarity cuts: nonplanar hexa-box integrals
journal, January 2019

Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes
journal, August 2012

Evidence for a nonplanar amplituhedron
journal, June 2016

Connection between Feynman integrals having different values of the space-time dimension
journal, November 1996

Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections
journal, September 2018

On-shell structures of MHV amplitudes beyond the planar limit
journal, June 2015

High-Precision Calculation of Multiloop Feynman Integrals by Difference Equations
journal, December 2000

Perturbative Quantum Gravity as a Double Copy of Gauge Theory
journal, August 2010

Bootstrapping the three-loop hexagon
journal, November 2011

The pentabox Master Integrals with the Simplified Differential Equations approach
journal, April 2016

Infrared singularities of QCD scattering amplitudes in the Regge limit to all orders
journal, March 2018

Eliminating spurious poles from gauge-theoretic amplitudes
journal, May 2013

Towards a basis for planar two-loop integrals
journal, February 2011

Two-Loop Iteration of Five-Point $N = 4$ Super-Yang-Mills Amplitudes
journal, November 2006

The high energy limit of QCD at two loops
journal, October 2001

Two-loop integrand decomposition into master integrals and surface terms
journal, December 2016

Multigluon cross sections and 5-jet production at hadron colliders
journal, January 1989

Planar two-loop five-parton amplitudes from numerical unitarity
journal, November 2018

Planar two-loop five-gluon amplitudes from numerical unitarity
journal, June 2018

Space–time dimensionality as complex variable: Calculating loop integrals using dimensional recurrence relation and analytical properties with respect to
journal, May 2010

Pentagon functions for massless planar scattering amplitudes
journal, October 2018

Two-loop master integrals for jets: the non-planar topologies
journal, May 2001

Bootstrapping pentagon functions
journal, May 2018

Scattering amplitudes — Wilson loops duality for the first non-planar correction
journal, August 2018

The singular behaviour of QCD amplitudes at two-loop order
journal, May 1998

Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case
journal, January 2019

Two-Loop g gg Splitting Amplitudes in QCD
journal, August 2004

Two-loop soft anomalous dimension matrix and resummation at next-to-next-to-leading poles
journal, October 2006

A theorem on analytical calculability of 4-loop renormalization group functions
journal, March 1981

One-loop n-point gauge theory amplitudes, unitarity and collinear limits
journal, August 1994

Non-planar massless two-loop Feynman diagrams with four on-shell legs
journal, December 1999

A novel approach to integration by parts reduction
journal, May 2015

Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
journal, March 2015

Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case
journal, December 2017

Dimensionally regulated one-loop integrals
journal, March 1993

First Look at Two-Loop Five-Gluon Scattering in QCD
journal, March 2018

Amplitude for $n$ -Gluon Scattering
journal, June 1986

Scattering amplitudes over finite fields and multivariate functional reconstruction
journal, December 2016

A current algebra for some gauge theory amplitudes
journal, November 1988

Classical Polylogarithms for Amplitudes and Wilson Loops
journal, October 2010

Differential equations for two-loop four-point functions
journal, July 2000

Pulling the straps of polygons
journal, December 2011

A two-loop five-gluon helicity amplitude in QCD
journal, December 2013

From polygons and symbols to polylogarithmic functions
journal, October 2012

Five-point amplitudes in $N = 4$ super-Yang-Mills theory and $N = 8$ supergravity
journal, January 2012

One-loop self-dual and N = 4 super Yang-Mills
journal, February 1997

One-loop corrections to five-gluon amplitudes
journal, May 1993

On the highest transcendentality in SUSY
journal, May 2007

Dimensionally-regulated pentagon integrals
journal, January 1994

Algebraic Structure of Cut Feynman Integrals and the Diagrammatic Coaction
journal, July 2017

Erratum: Analytic Form of the Two-Loop Planar Five-Gluon All-Plus-Helicity Amplitude in QCD [Phys. Rev. Lett. 116 , 062001 (2016)]
journal, May 2016

Connection between Feynman integrals having different values of the space-time dimension
text, January 1996

Two-loop scattering amplitudes: double-forward limit and colour-kinematics duality
journal, December 2019

Physical projectors for multi-leg helicity amplitudes
journal, July 2019

A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons
journal, September 2019

Multi-quark colour decompositions from unitarity
journal, October 2019

Prescriptive unitarity for non-planar six-particle amplitudes at two loops
journal, December 2019

Two-loop $N$ -jettiness soft function for $p p \to 2 j$ production
journal, June 2019

Analytic Result for a Two-Loop Five-Particle Amplitude
journal, March 2019

All Master Integrals for Three-Jet Production at Next-to-Next-to-Leading Order
journal, July 2019

Precision QCD Event Shapes at Hadron Colliders: The Transverse Energy-Energy Correlator in the Back-to-Back Limit
journal, August 2019

Analytic Form of the Full Two-Loop Five-Gluon All-Plus Helicity Amplitude
journal, August 2019

Full-Color Two-Loop Four-Gluon Amplitude in $N = 2$ Supersymmetric QCD
journal, December 2019

All-Multiplicity Nonplanar Amplitude Integrands in Maximally Supersymmetric Yang-Mills Theory at Two Loops
journal, March 2020