Bootstrapping a five-loop amplitude using Steinmann relations

Caron-Huot, Simon; Dixon, Lance J.; McLeod, Andrew; von Hippel, Matt

doi:10.1103/PhysRevLett.117.241601

Title: Bootstrapping a five-loop amplitude using Steinmann relations

Abstract

Here, the analytic structure of scattering amplitudes is restricted by Steinmann relations, which enforce the vanishing of certain discontinuities of discontinuities. We show that these relations dramatically simplify the function space for the hexagon function bootstrap in planar maximally supersymmetric Yang-Mills theory. Armed with this simplification, along with the constraints of dual conformal symmetry and Regge exponentiation, we obtain the complete five-loop six-particle amplitude.

Authors:

Caron-Huot, Simon ^[1]; Dixon, Lance J. ^[2]; McLeod, Andrew ^[3]; von Hippel, Matt ^[4]

Univ. of Copenhagen, Copenhagen (Denmark); McGill Univ., Montreal, QC (Canada)
SLAC National Accelerator Lab., Menlo Park, CA (United States); Univ. of California, Santa Barbara, CA (United States)
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)

Publication Date:: Mon Dec 05 00:00:00 EST 2016

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

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

OSTI Identifier:: 1327480

Alternate Identifier(s):: OSTI ID: 1334356

Report Number(s):: SLAC-PUB-16811
Journal ID: ISSN 0031-9007; PRLTAO; arXiv:1609.00669

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

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Volume: 117; Journal Issue: 24; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; phenomenology-HEP; theory-HEP; HEPPH; HEPTH

Citation Formats


                    Caron-Huot, Simon, Dixon, Lance J., McLeod, Andrew, and von Hippel, Matt. Bootstrapping a five-loop amplitude using Steinmann relations.  United States: N. p., 2016. 
Web.  doi:10.1103/PhysRevLett.117.241601.

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                    Caron-Huot, Simon, Dixon, Lance J., McLeod, Andrew, & von Hippel, Matt. Bootstrapping a five-loop amplitude using Steinmann relations.  United States.  https://doi.org/10.1103/PhysRevLett.117.241601

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                    Caron-Huot, Simon, Dixon, Lance J., McLeod, Andrew, and von Hippel, Matt. Mon .  
"Bootstrapping a five-loop amplitude using Steinmann relations".  United States.  https://doi.org/10.1103/PhysRevLett.117.241601.  https://www.osti.gov/servlets/purl/1327480.

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@article{osti_1327480,

  title        = {Bootstrapping a five-loop amplitude using Steinmann relations},

  author       = {Caron-Huot, Simon and Dixon, Lance J. and McLeod, Andrew and von Hippel, Matt},

  abstractNote = {Here, the analytic structure of scattering amplitudes is restricted by Steinmann relations, which enforce the vanishing of certain discontinuities of discontinuities. We show that these relations dramatically simplify the function space for the hexagon function bootstrap in planar maximally supersymmetric Yang-Mills theory. Armed with this simplification, along with the constraints of dual conformal symmetry and Regge exponentiation, we obtain the complete five-loop six-particle amplitude.},

  doi          = {10.1103/PhysRevLett.117.241601},

  journal      = {Physical Review Letters},

  number       = 24,

  volume       = 117,

  place        = {United States},

  year         = {Mon Dec 05 00:00:00 EST 2016},

  month        = {Mon Dec 05 00:00:00 EST 2016}

}

Copy to clipboard

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Drummond, James; Foster, Jack; Gürdoğan, Ömer
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DOI: 10.48550/arxiv.1812.04640

Analytic result for a two-loop five-particle amplitude
text, January 2018

Chicherin, D.; Gehrmann, T.; Henn, J. M.
arXiv
DOI: 10.48550/arxiv.1812.11057

The two-loop five-point amplitude in $\mathcal N=8$ supergravity
text, January 2019

Abreu, Samuel; Dixon, Lance J.; Herrmann, Enrico
arXiv
DOI: 10.48550/arxiv.1901.08563

Elliptic polylogarithms and Feynman parameter integrals
text, January 2019

Broedel, Johannes; Duhr, Claude; Dulat, Falko
arXiv
DOI: 10.48550/arxiv.1902.09971

The Sklyanin Bracket and Cluster Adjacency at All Multiplicity
text, January 2019

Golden, John; McLeod, Andrew J.; Spradlin, Marcus
arXiv
DOI: 10.48550/arxiv.1902.11286

PolyLogTools - Polylogs for the masses
text, January 2019

Duhr, Claude; Dulat, Falko
arXiv
DOI: 10.48550/arxiv.1904.07279

The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N} = 4$ SYM Amplitudes
text, January 2019

Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko
arXiv
DOI: 10.48550/arxiv.1906.07116

Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
text, January 2019

Bourjaily, Jacob L.; Herrmann, Enrico; Langer, Cameron
arXiv
DOI: 10.48550/arxiv.1909.09131

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Similar Records

Title: Bootstrapping a five-loop amplitude using Steinmann relations

Abstract

Citation Formats

The Multi-Regge limit of NMHV amplitudes in N=4 SYM theory journal, January 2013

Dual superconformal symmetry of scattering amplitudes in super-Yang–Mills theory journal, March 2010

Space-time S-matrix and flux-tube S-matrix III. The two-particle contributions journal, August 2014

Space-time S-matrix and flux tube S-matrix II. Extracting and matching data journal, January 2014

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

Bootstrapping an NMHV amplitude through three loops journal, October 2014

N=4 supersymmetric Yang–Mills scattering amplitudes at high energies: the Regge cut contribution journal, December 2009

Hexagon functions and the three-loop remainder function journal, December 2013

The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in $ \mathcal{N} = 4 $ SYM journal, June 2011

Analytic result for the two-loop six-point NMHV amplitude in $ \mathcal{N} = {4} $ super Yang-Mills theory journal, January 2012

Does one need the O ( ε ) - and O ( ε 2 ) -terms of one-loop amplitudes in a next-to-next-to-leading order calculation ? journal, October 2011

Harmonic Polylogarithms journal, February 2000

Adjoint BFKL at finite coupling: a short-cut from the collinear limit journal, January 2015

Optical theorems and steinmann relations journal, April 1975

BFKL Pomeron, Reggeized gluons, and Bern-Dixon-Smirnov amplitudes journal, August 2009

Two-loop six-gluon maximally helicity violating amplitude in maximally supersymmetric Yang-Mills theory journal, August 2008

Thermodynamic bubble ansatz journal, September 2011

Hedgehog bases for A n cluster polylogarithms and an application to six-point amplitudes journal, November 2015

Magic identities for conformal four-point integrals journal, January 2007

Hexagon OPE resummation and multi-Regge kinematics journal, February 2016

Classical Polylogarithms for Amplitudes and Wilson Loops journal, October 2010

Pulling the straps of polygons journal, December 2011

Hexagonal Wilson loops in planar ${ \mathcal N }=4$ SYM theory at finite coupling journal, September 2016

Evaluating the six-point remainder function near the collinear limit journal, October 2014

The four-loop six-gluon NMHV ratio function journal, January 2016

Über den Zusammenhang zwischen den Wightmanfunktionen und den retardierten Kommutatoren text, January 1960

Singularities and Discontinuities of Feynman Amplitudes journal, September 1960

Bootstrapping the three-loop hexagon journal, November 2011

Nonsinglet pentagons and NMHV amplitudes journal, July 2015

Hexagon Wilson loop = six-gluon MHV amplitude journal, July 2009

Spacetime and Flux Tube S -Matrices at Finite Coupling for N = 4 Supersymmetric Yang-Mills Theory journal, August 2013

Wightman-Funktionen und retardierte Kommutatoren. II text, January 1960

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

Transcendentality and crossing journal, January 2007

Jumpstarting the all-loop S-matrix of planar $ \mathcal{N} = {4} $ super Yang-Mills journal, July 2012

Hexagon Wilson loop OPE and harmonic polylogarithms journal, November 2013

BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes text, January 2008

Hexagon Wilson loop = six-gluon MHV amplitude text, January 2008

N=4 supersymmetric Yang Mills scattering amplitudes at high energies: the Regge cut contribution text, January 2008

Eliminating spurious poles from gauge-theoretic amplitudes preprint, January 2009

Classical Polylogarithms for Amplitudes and Wilson Loops text, January 2010

Pulling the straps of polygons text, January 2011

The massless hexagon integral in D = 6 dimensions text, January 2011

The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM text, January 2011

Bootstrapping the three-loop hexagon text, January 2011

Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory text, January 2011

The Multi-Regge limit of NMHV Amplitudes in N=4 SYM Theory text, January 2012

Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data text, January 2013

Hexagon Wilson Loop OPE and Harmonic Polylogarithms text, January 2013

Nonsinglet pentagons and NMHV amplitudes text, January 2014

Adjoint BFKL at finite coupling: a short-cut from the collinear limit text, January 2014

Bootstrapping an NMHV amplitude through three loops text, January 2014

Hexagonal Wilson Loops in Planar $\mathcal{N}=4$ SYM Theory at Finite Coupling text, January 2015

Harmonic Polylogarithms text, January 1999

Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond text, January 2005

Transcendentality and Crossing text, January 2006

Amplitudes from anomalous superconformal symmetry journal, January 2019

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

Elliptic polylogarithms and Feynman parameter integrals journal, May 2019

The multi-Regge limit of the eight-particle amplitude beyond leading logarithmic accuracy journal, July 2019

Yangian invariants and cluster adjacency in $$ \mathcal{N} $$ = 4 Yang-Mills journal, October 2019

Analytic Two-Loop Higgs Amplitudes in Effective Field Theory and the Maximal Transcendentality Principle journal, September 2018

Origin of the Six-Gluon Amplitude in Planar N = 4 Supersymmetric Yang-Mills Theory journal, April 2020

The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy text, January 2018

The cosmic Galois group and extended Steinmann relations for planar N $$ \mathcal{N} $$ = 4 SYM amplitudes text, January 2019

Heptagons from the Steinmann Cluster Bootstrap text, January 2017

The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy text, January 2018

Cluster adjacency and the four-loop NMHV heptagon text, January 2019

Analytic Result for a Two-Loop Five-Particle Amplitude text, January 2019

All-order amplitudes at any multiplicity in the multi-Regge limit text, January 2020

Cluster adjacency and the four-loop NMHV heptagon text, January 2018

The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N} = 4$ SYM Amplitudes text, January 2019

All-order amplitudes at any multiplicity in the multi-Regge limit text, January 2019

The double pentaladder integral to all ordersC text, January 2018

All-Order Amplitudes at any Multiplicity in the Multi-Regge Limit text, January 2020

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

Heptagons from the Steinmann Cluster Bootstrap text, January 2016

The Multi-Regge limit of NMHV amplitudes in N=4 SYM theory
journal, January 2013

Dual superconformal symmetry of scattering amplitudes in super-Yang–Mills theory
journal, March 2010

Space-time S-matrix and flux-tube S-matrix III. The two-particle contributions
journal, August 2014

Space-time S-matrix and flux tube S-matrix II. Extracting and matching data
journal, January 2014

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

Bootstrapping an NMHV amplitude through three loops
journal, October 2014

N=4 supersymmetric Yang–Mills scattering amplitudes at high energies: the Regge cut contribution
journal, December 2009

Hexagon functions and the three-loop remainder function
journal, December 2013

The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in $ \mathcal{N} = 4 $ SYM
journal, June 2011

Analytic result for the two-loop six-point NMHV amplitude in $ \mathcal{N} = {4} $ super Yang-Mills theory
journal, January 2012

Does one need the $O (ε)$ - and $O (ε^{2})$ -terms of one-loop amplitudes in a next-to-next-to-leading order calculation ?
journal, October 2011

Harmonic Polylogarithms
journal, February 2000

Adjoint BFKL at finite coupling: a short-cut from the collinear limit
journal, January 2015

Optical theorems and steinmann relations
journal, April 1975

BFKL Pomeron, Reggeized gluons, and Bern-Dixon-Smirnov amplitudes
journal, August 2009

Two-loop six-gluon maximally helicity violating amplitude in maximally supersymmetric Yang-Mills theory
journal, August 2008

Thermodynamic bubble ansatz
journal, September 2011

Hedgehog bases for A n cluster polylogarithms and an application to six-point amplitudes
journal, November 2015

Magic identities for conformal four-point integrals
journal, January 2007

Hexagon OPE resummation and multi-Regge kinematics
journal, February 2016

Classical Polylogarithms for Amplitudes and Wilson Loops
journal, October 2010

Pulling the straps of polygons
journal, December 2011

Hexagonal Wilson loops in planar ${ \mathcal N }=4$ SYM theory at finite coupling
journal, September 2016

Evaluating the six-point remainder function near the collinear limit
journal, October 2014

The four-loop six-gluon NMHV ratio function
journal, January 2016

Über den Zusammenhang zwischen den Wightmanfunktionen und den retardierten Kommutatoren
text, January 1960

Singularities and Discontinuities of Feynman Amplitudes
journal, September 1960

Bootstrapping the three-loop hexagon
journal, November 2011

Nonsinglet pentagons and NMHV amplitudes
journal, July 2015

Hexagon Wilson loop = six-gluon MHV amplitude
journal, July 2009

Spacetime and Flux Tube $S$ -Matrices at Finite Coupling for $N = 4$ Supersymmetric Yang-Mills Theory
journal, August 2013

Wightman-Funktionen und retardierte Kommutatoren. II
text, January 1960

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

Transcendentality and crossing
journal, January 2007

Jumpstarting the all-loop S-matrix of planar $ \mathcal{N} = {4} $ super Yang-Mills
journal, July 2012

Hexagon Wilson loop OPE and harmonic polylogarithms
journal, November 2013

BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
text, January 2008

Hexagon Wilson loop = six-gluon MHV amplitude
text, January 2008

N=4 supersymmetric Yang Mills scattering amplitudes at high energies: the Regge cut contribution
text, January 2008

Eliminating spurious poles from gauge-theoretic amplitudes
preprint, January 2009

Classical Polylogarithms for Amplitudes and Wilson Loops
text, January 2010

Pulling the straps of polygons
text, January 2011

The massless hexagon integral in D = 6 dimensions
text, January 2011

The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM
text, January 2011

Bootstrapping the three-loop hexagon
text, January 2011

Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
text, January 2011

The Multi-Regge limit of NMHV Amplitudes in N=4 SYM Theory
text, January 2012

Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
text, January 2013

Hexagon Wilson Loop OPE and Harmonic Polylogarithms
text, January 2013

Nonsinglet pentagons and NMHV amplitudes
text, January 2014

Adjoint BFKL at finite coupling: a short-cut from the collinear limit
text, January 2014

Bootstrapping an NMHV amplitude through three loops
text, January 2014

Hexagonal Wilson Loops in Planar $\mathcal{N}=4$ SYM Theory at Finite Coupling
text, January 2015

Harmonic Polylogarithms
text, January 1999

Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
text, January 2005

Transcendentality and Crossing
text, January 2006

Amplitudes from anomalous superconformal symmetry
journal, January 2019

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

Elliptic polylogarithms and Feynman parameter integrals
journal, May 2019

The multi-Regge limit of the eight-particle amplitude beyond leading logarithmic accuracy
journal, July 2019

Yangian invariants and cluster adjacency in $$ \mathcal{N} $$ = 4 Yang-Mills
journal, October 2019

Analytic Two-Loop Higgs Amplitudes in Effective Field Theory and the Maximal Transcendentality Principle
journal, September 2018

Origin of the Six-Gluon Amplitude in Planar $N = 4$ Supersymmetric Yang-Mills Theory
journal, April 2020

The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
text, January 2018

The cosmic Galois group and extended Steinmann relations for planar N $$ \mathcal{N} $$ = 4 SYM amplitudes
text, January 2019

Heptagons from the Steinmann Cluster Bootstrap
text, January 2017

The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
text, January 2018

Cluster adjacency and the four-loop NMHV heptagon
text, January 2019

Analytic Result for a Two-Loop Five-Particle Amplitude
text, January 2019

All-order amplitudes at any multiplicity in the multi-Regge limit
text, January 2020

Cluster adjacency and the four-loop NMHV heptagon
text, January 2018

The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N} = 4$ SYM Amplitudes
text, January 2019

All-order amplitudes at any multiplicity in the multi-Regge limit
text, January 2019

The double pentaladder integral to all ordersC
text, January 2018

All-Order Amplitudes at any Multiplicity in the Multi-Regge Limit
text, January 2020

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

Heptagons from the Steinmann Cluster Bootstrap
text, January 2016

The algebraic structure of cut Feynman integrals and the diagrammatic coaction
text, January 2017

Prescriptive Unitarity
text, January 2017

Bootstrapping the QCD soft anomalous dimension
text, January 2017