Prescriptive unitarity for non-planar six-particle amplitudes at two loops

Bourjaily, Jacob L.; Herrmann, Enrico; Langer, Cameron; McLeod, Andrew J.; Trnka, Jaroslav

doi:10.1007/JHEP12(2019)073

Title: Prescriptive unitarity for non-planar six-particle amplitudes at two loops

Abstract

We extend the applications of prescriptive unitarity beyond the planar limit to provide local, polylogarithmic, integrand-level representations of six-particle MHV scattering amplitudes in both maximally supersymmetric Yang-Mills theory and gravity. The integrand basis we construct is diagonalized on a spanning set of non-vanishing leading singularities that ensures the manifest matching of all soft-collinear singularities in both theories. As a consequence, this integrand basis naturally splits into infrared-finite and infrared-divergent parts, with hints toward an integrand-level exponentiation of infrared divergences. Importantly, we use the same basis of integrands for both theories, so that the presence or absence of residues at infinite loop momentum becomes a feature detectable by inspecting the cuts of the theory. Complete details of our results are provided as sup- plementary material.

Authors:

Bourjaily, Jacob L. ^[1];

^[2];

^[3]; McLeod, Andrew J. ^[4]; Trnka, Jaroslav ^[3]

Univ. of Copenhagen (Denmark). The Niels Bohr Inst.; Harvard Univ., Cambridge, MA (United States). Jefferson Physical Lab.
Stanford Univ., CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP)
Univ. of Copenhagen (Denmark). The Niels Bohr Inst

Publication Date:: Tue Dec 10 00:00:00 EST 2019

Research Org.:: Univ. of California, Davis, CA (United States); Stanford Univ., CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); Simons Foundation

Contributing Org.:: Aspen Center for Physics

OSTI Identifier:: 1600516

Grant/Contract Number:: SC0009999; PHY-1607611; AC02-76SF00515

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: 2019; Journal Issue: 12; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Extended Supersymmetry; Scattering Amplitudes; Supergravity Models

Citation Formats


                    Bourjaily, Jacob L., Herrmann, Enrico, Langer, Cameron, McLeod, Andrew J., and Trnka, Jaroslav. Prescriptive unitarity for non-planar six-particle amplitudes at two loops.  United States: N. p., 2019. 
Web.  doi:10.1007/JHEP12(2019)073.

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                    Bourjaily, Jacob L., Herrmann, Enrico, Langer, Cameron, McLeod, Andrew J., & Trnka, Jaroslav. Prescriptive unitarity for non-planar six-particle amplitudes at two loops.  United States.  https://doi.org/10.1007/JHEP12(2019)073

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                    Bourjaily, Jacob L., Herrmann, Enrico, Langer, Cameron, McLeod, Andrew J., and Trnka, Jaroslav. Tue .  
"Prescriptive unitarity for non-planar six-particle amplitudes at two loops".  United States.  https://doi.org/10.1007/JHEP12(2019)073.  https://www.osti.gov/servlets/purl/1600516.

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@article{osti_1600516,

  title        = {Prescriptive unitarity for non-planar six-particle amplitudes at two loops},

  author       = {Bourjaily, Jacob L. and Herrmann, Enrico and Langer, Cameron and McLeod, Andrew J. and Trnka, Jaroslav},

  abstractNote = {We extend the applications of prescriptive unitarity beyond the planar limit to provide local, polylogarithmic, integrand-level representations of six-particle MHV scattering amplitudes in both maximally supersymmetric Yang-Mills theory and gravity. The integrand basis we construct is diagonalized on a spanning set of non-vanishing leading singularities that ensures the manifest matching of all soft-collinear singularities in both theories. As a consequence, this integrand basis naturally splits into infrared-finite and infrared-divergent parts, with hints toward an integrand-level exponentiation of infrared divergences. Importantly, we use the same basis of integrands for both theories, so that the presence or absence of residues at infinite loop momentum becomes a feature detectable by inspecting the cuts of the theory. Complete details of our results are provided as sup- plementary material.},

  doi          = {10.1007/JHEP12(2019)073},

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

  number       = 12,

  volume       = 2019,

  place        = {United States},

  year         = {Tue Dec 10 00:00:00 EST 2019},

  month        = {Tue Dec 10 00:00:00 EST 2019}

}

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DOI: 10.1016/S0550-3213(99)00809-3

All Master Integrals for Three-Jet Production at Next-to-Next-to-Leading Order
text, January 2019

Chicherin, D.; Gehrmann, Thomas; Henn, J. M.
American Physical Society
DOI: 10.5167/uzh-176008

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

Drummond, James; Foster, Jack; Gürdoğan, Ömer
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2018-05809

Six-Gluon Amplitudes in Planar ${\cal N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
text, January 2019

Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2019-01783

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
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2019-02565

The double pentaladder integral to all ordersC
text, January 2018

Caron-Huot, Simon; Dixon, Lance J.; Von Hippel, Matt
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2018-05437

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

Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2019-03749

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

Badger, Simon; Brønnum-Hansen, Christian; Hartanto, Heribertus Bayu
Springer
DOI: 10.5167/uzh-172597

What is the Simplest Quantum Field Theory?
text, January 2008

Arkani-Hamed, Nima; Cachazo, Freddy; Kaplan, Jared
arXiv
DOI: 10.48550/arxiv.0808.1446

Inclusive Heavy Flavor Hadroproduction in NLO QCD: the Exact Analytic Result
text, January 2008

Czakon, M.; Mitov, A.
arXiv
DOI: 10.48550/arxiv.0811.4119

Local Spacetime Physics from the Grassmannian
text, January 2009

Arkani-Hamed, Nima; Bourjaily, Jacob; Cachazo, Freddy
arXiv
DOI: 10.48550/arxiv.0912.3249

Unification of Residues and Grassmannian Dualities
text, January 2009

Arkani-Hamed, Nima; Bourjaily, Jacob; Cachazo, Freddy
arXiv
DOI: 10.48550/arxiv.0912.4912

Classical Polylogarithms for Amplitudes and Wilson Loops
text, January 2010

Goncharov, Alexander B.; Spradlin, Marcus; Vergu, C.
arXiv
DOI: 10.48550/arxiv.1006.5703

All tree-level amplitudes in massless QCD
text, January 2010

Dixon, Lance J.; Henn, Johannes M.; Plefka, Jan
arXiv
DOI: 10.48550/arxiv.1010.3991

Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills
text, January 2011

Caron-Huot, Simon
arXiv
DOI: 10.48550/arxiv.1105.5606

New expressions for gravitational scattering amplitudes
preprint, January 2011

Hodges, Andrew
arXiv
DOI: 10.48550/arxiv.1108.2227

Uniqueness of two-loop master contours
text, January 2012

Caron-Huot, Simon; Larsen, Kasper J.
arXiv
DOI: 10.48550/arxiv.1205.0801

Multiloop integrals in dimensional regularization made simple
text, January 2013

Henn, Johannes M.
arXiv
DOI: 10.48550/arxiv.1304.1806

A Two-Loop Five-Gluon Helicity Amplitude in QCD
text, January 2013

Badger, Simon; Frellesvig, Hjalte; Zhang, Yang
arXiv
DOI: 10.48550/arxiv.1310.1051

A Feynman integral via higher normal functions
text, January 2014

Bloch, Spencer; Kerr, Matt; Vanhove, Pierre
arXiv
DOI: 10.48550/arxiv.1406.2664

Logarithmic Singularities and Maximally Supersymmetric Amplitudes
preprint, January 2014

Bern, Zvi; Herrmann, Enrico; Litsey, Sean
arXiv
DOI: 10.48550/arxiv.1412.8584

Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM
text, January 2015

Bourjaily, Jacob L.; Trnka, Jaroslav
arXiv
DOI: 10.48550/arxiv.1505.05886

A Complete Two-Loop, Five-Gluon Helicity Amplitude in Yang-Mills Theory
text, January 2015

Badger, Simon; Mogull, Gustav; Ochirov, Alexander
arXiv
DOI: 10.48550/arxiv.1507.08797

Evidence for a Nonplanar Amplituhedron
text, January 2015

Bern, Zvi; Herrmann, Enrico; Litsey, Sean
arXiv
DOI: 10.48550/arxiv.1512.08591

Local mirror symmetry and the sunset Feynman integral
preprint, January 2016

Bloch, Spencer; Kerr, Matt; Vanhove, Pierre
arXiv
DOI: 10.48550/arxiv.1601.08181

Gravity On-shell Diagrams
text, January 2016

Herrmann, Enrico; Trnka, Jaroslav
arXiv
DOI: 10.48550/arxiv.1604.03479

Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
text, January 2016

Caron-Huot, Simon; Dixon, Lance J.; McLeod, Andrew
arXiv
DOI: 10.48550/arxiv.1609.00669

Full Colour for Loop Amplitudes in Yang-Mills Theory
text, January 2016

Ochirov, Alexander; Page, Ben
arXiv
DOI: 10.48550/arxiv.1612.04366

Heptagons from the Steinmann Cluster Bootstrap
text, January 2016

Dixon, Lance J.; Drummond, James; Harrington, Thomas
arXiv
DOI: 10.48550/arxiv.1612.08976

Prescriptive Unitarity
text, January 2017

Bourjaily, Jacob L.; Herrmann, Enrico; Trnka, Jaroslav
arXiv
DOI: 10.48550/arxiv.1704.05460

Bootstrapping the QCD soft anomalous dimension
text, January 2017

Almelid, Øyvind; Duhr, Claude; Gardi, Einan
arXiv
DOI: 10.48550/arxiv.1706.10162

A first look at two-loop five-gluon scattering in QCD
text, January 2017

Badger, Simon; Brønnum-Hansen, Christian; Hartanto, Heribertus Bayu
arXiv
DOI: 10.48550/arxiv.1712.02229

The planar double box integral for top pair production with a closed top loop to all orders in the dimensional regularisation parameter
text, January 2018

Adams, Luise; Chaubey, Ekta; Weinzierl, Stefan
arXiv
DOI: 10.48550/arxiv.1804.11144

The Double Pentaladder Integral to All Orders
text, January 2018

Caron-Huot, Simon; Dixon, Lance J.; von Hippel, Matt
arXiv
DOI: 10.48550/arxiv.1806.01361

Implications of nonplanar dual conformal symmetry
text, January 2018

Chicherin, Dmitry; Henn, Johannes M.; Sokatchev, Emery
arXiv
DOI: 10.48550/arxiv.1807.06321

Planar Two-Loop Five-Parton Amplitudes from Numerical Unitarity
text, January 2018

Abreu, S.; Cordero, F. Febres; Ita, H.
arXiv
DOI: 10.48550/arxiv.1809.09067

Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case
text, January 2018

Badger, Simon; Brønnum-Hansen, Christian; Hartanto, Heribertus Bayu
arXiv
DOI: 10.48550/arxiv.1811.11699

Removing infrared divergences from two-loop integrals
text, January 2018

Anastasiou, Charalampos; Sterman, George
arXiv
DOI: 10.48550/arxiv.1812.03753

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

Drummond, James; Foster, Jack; Gürdoğan, Ömer
arXiv
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-particle amplitude in $\mathcal{N}=8$ supergravity
text, January 2019

Chicherin, D.; Gehrmann, T.; Henn, J. M.
arXiv
DOI: 10.48550/arxiv.1901.05932

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 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

Multi-Quark Colour Decompositions from Unitarity
text, January 2019

Ochirov, Alexander; Page, Ben
arXiv
DOI: 10.48550/arxiv.1908.02695

One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
text, January 1994

Bern, Z.; Dixon, L.; Dunbar, D. C.
arXiv
DOI: 10.48550/arxiv.hep-ph/9403226

Progress in One-Loop QCD Computations
text, January 1996

Bern, Z.; Dixon, L.; Kosower, D. A.
arXiv
DOI: 10.48550/arxiv.hep-ph/9602280

New Recursion Relations for Tree Amplitudes of Gluons
text, January 2004

Britto, Ruth; Cachazo, Freddy; Feng, Bo
arXiv
DOI: 10.48550/arxiv.hep-th/0412308

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Title: Prescriptive unitarity for non-planar six-particle amplitudes at two loops

Abstract

Citation Formats

Heptagons from the Steinmann cluster bootstrap journal, February 2017

A cluster bootstrap for two-loop MHV amplitudes journal, February 2015

New recursion relations for tree amplitudes of gluons journal, May 2005

Scattering of Massless Particles in Arbitrary Dimensions journal, October 2014

Bounded Collection of Feynman Integral Calabi-Yau Geometries journal, January 2019

Multiloop Integrals in Dimensional Regularization Made Simple journal, June 2013

The Amplituhedron journal, October 2014

The double pentaladder integral to all orders journal, July 2018

All orders structure and efficient computation of linearly reducible elliptic Feynman integrals text, January 2019

Local integrand representations of all two-loop amplitudes in planar SYM journal, August 2015

Grassmannian Geometry of Scattering Amplitudes book, May 2016

Scattering of massless particles: scalars, gluons and gravitons journal, July 2014

Local spacetime physics from the Grassmannian journal, January 2011

Evidence for a nonplanar amplituhedron journal, June 2016

Grassmannians for scattering amplitudes in 4d N = 4 $$ \mathcal{N}=4 $$ SYM and 3d ABJM journal, December 2014

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

Bootstrapping two-loop Feynman integrals for planar N = 4 $$ \mathcal{N}=4 $$ sYM journal, October 2018

A Feynman integral via higher normal functions journal, August 2015

Perturbation Theory at Eight Loops: Novel Structures and the Breakdown of Manifest Conformality in N = 4 Supersymmetric Yang-Mills Theory journal, May 2016

New expressions for gravitational scattering amplitudes journal, July 2013

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

Generalized unitarity and one-loop amplitudes in super-Yang–Mills journal, October 2005

Local integrands for two-loop all-plus Yang-Mills amplitudes journal, August 2016

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

Implications of nonplanar dual conformal symmetry journal, September 2018

Bootstrapping pentagon functions journal, May 2018

Progress in One-Loop qcd Computations journal, December 1996

Dual-conformal regularization of infrared loop divergences and the chiral box expansion journal, January 2015

Stratifying on-shell cluster varieties: the geometry of non-planar on-shell diagrams journal, October 2016

Traintracks through Calabi-Yau Manifolds: Scattering Amplitudes beyond Elliptic Polylogarithms journal, August 2018

Amplitude for n -Gluon Scattering journal, June 1986

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

Removing infrared divergences from two-loop integrals text, January 2019

Prescriptive unitarity journal, June 2017

Uniqueness of two-loop master contours journal, October 2012

The two-loop sunrise graph with arbitrary masses journal, May 2013

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

Direct Proof of the Tree-Level Scattering Amplitude Recursion Relation in Yang-Mills Theory journal, May 2005

Singularity Structure of Maximally Supersymmetric Scattering Amplitudes journal, December 2014

Scattering in three dimensions from rational maps journal, October 2013

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

Two-Loop Five-Point Amplitude in N = 4 Super-Yang-Mills Theory journal, March 2019

Dual Conformal Structure Beyond the Planar Limit journal, September 2018

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

Inclusive heavy flavor hadroproduction in NLO QCD: The exact analytic result journal, January 2010

The two-loop five-particle amplitude in N $$ \mathcal{N} $$ = 8 supergravity journal, March 2019

Fourth order spectral functions for the electron propagator journal, May 1962

Bootstrapping a Five-Loop Amplitude Using Steinmann Relations journal, December 2016

Removing infrared divergences from two-loop integrals journal, July 2019

Bootstrapping the QCD soft anomalous dimension journal, September 2017

Elliptic Double-Box Integrals: Massless Scattering Amplitudes beyond Polylogarithms journal, March 2018

Amplitudes and correlators to ten loops using simple, graphical bootstraps journal, November 2016

Multi-quark colour decompositions from unitarity text, January 2019

Gluon scattering amplitudes at strong coupling journal, June 2007

The kite integral to all orders in terms of elliptic polylogarithms journal, December 2016

A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon journal, March 2015

Cluster adjacency and the four-loop NMHV heptagon journal, March 2019

The two-loop five-point amplitude in N $$ \mathcal{N} $$ = 8 supergravity journal, March 2019

New Representations of the Perturbative S Matrix journal, February 2016

Simple loop integrals and amplitudes in $ \mathcal{N} = 4 $ SYM journal, May 2011

Singularities and Discontinuities of Feynman Amplitudes journal, September 1960

Multi-quark colour decompositions from unitarity journal, October 2019

What is the simplest quantum field theory? journal, September 2010

All tree-level amplitudes in massless QCD journal, January 2011

Two-loop amplitudes of gluons and octa-cuts in Script N = 4 super Yang-Mills journal, November 2005

Superconformal symmetry and two-loop amplitudes in planar N = 4 super Yang-Mills journal, December 2011

Yangian symmetry of scattering amplitudes in 𝒩 = 4 super Yang-Mills theory journal, May 2009

Five-Loop Four-Point Amplitude of N = 4 Super-Yang-Mills Theory journal, December 2012

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

Logarithmic singularities and maximally supersymmetric amplitudes journal, June 2015

Local mirror symmetry and the sunset Feynman integral journal, January 2017

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

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

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

A note on polytopes for scattering amplitudes journal, April 2012

The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM journal, January 2011

A duality for the S matrix journal, March 2010

Heptagons from the Steinmann cluster bootstrap
journal, February 2017

A cluster bootstrap for two-loop MHV amplitudes
journal, February 2015

New recursion relations for tree amplitudes of gluons
journal, May 2005

Scattering of Massless Particles in Arbitrary Dimensions
journal, October 2014

Bounded Collection of Feynman Integral Calabi-Yau Geometries
journal, January 2019

Multiloop Integrals in Dimensional Regularization Made Simple
journal, June 2013

The Amplituhedron
journal, October 2014

The double pentaladder integral to all orders
journal, July 2018

All orders structure and efficient computation of linearly reducible elliptic Feynman integrals
text, January 2019

Local integrand representations of all two-loop amplitudes in planar SYM
journal, August 2015

Grassmannian Geometry of Scattering Amplitudes
book, May 2016

Scattering of massless particles: scalars, gluons and gravitons
journal, July 2014

Local spacetime physics from the Grassmannian
journal, January 2011

Evidence for a nonplanar amplituhedron
journal, June 2016

Grassmannians for scattering amplitudes in 4d N = 4 $$ \mathcal{N}=4 $$ SYM and 3d ABJM
journal, December 2014

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

Bootstrapping two-loop Feynman integrals for planar N = 4 $$ \mathcal{N}=4 $$ sYM
journal, October 2018

A Feynman integral via higher normal functions
journal, August 2015

Perturbation Theory at Eight Loops: Novel Structures and the Breakdown of Manifest Conformality in $N = 4$ Supersymmetric Yang-Mills Theory
journal, May 2016

New expressions for gravitational scattering amplitudes
journal, July 2013

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

Generalized unitarity and one-loop amplitudes in super-Yang–Mills
journal, October 2005

Local integrands for two-loop all-plus Yang-Mills amplitudes
journal, August 2016

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

Implications of nonplanar dual conformal symmetry
journal, September 2018

Bootstrapping pentagon functions
journal, May 2018

Progress in One-Loop qcd Computations
journal, December 1996

Dual-conformal regularization of infrared loop divergences and the chiral box expansion
journal, January 2015

Stratifying on-shell cluster varieties: the geometry of non-planar on-shell diagrams
journal, October 2016

Traintracks through Calabi-Yau Manifolds: Scattering Amplitudes beyond Elliptic Polylogarithms
journal, August 2018

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

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

Removing infrared divergences from two-loop integrals
text, January 2019

Prescriptive unitarity
journal, June 2017

Uniqueness of two-loop master contours
journal, October 2012

The two-loop sunrise graph with arbitrary masses
journal, May 2013

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

Direct Proof of the Tree-Level Scattering Amplitude Recursion Relation in Yang-Mills Theory
journal, May 2005

Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
journal, December 2014

Scattering in three dimensions from rational maps
journal, October 2013

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

Two-Loop Five-Point Amplitude in $N = 4$ Super-Yang-Mills Theory
journal, March 2019

Dual Conformal Structure Beyond the Planar Limit
journal, September 2018

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

Inclusive heavy flavor hadroproduction in NLO QCD: The exact analytic result
journal, January 2010

The two-loop five-particle amplitude in N $$ \mathcal{N} $$ = 8 supergravity
journal, March 2019

Fourth order spectral functions for the electron propagator
journal, May 1962

Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
journal, December 2016

Removing infrared divergences from two-loop integrals
journal, July 2019

Bootstrapping the QCD soft anomalous dimension
journal, September 2017

Elliptic Double-Box Integrals: Massless Scattering Amplitudes beyond Polylogarithms
journal, March 2018

Amplitudes and correlators to ten loops using simple, graphical bootstraps
journal, November 2016

Multi-quark colour decompositions from unitarity
text, January 2019

Gluon scattering amplitudes at strong coupling
journal, June 2007

The kite integral to all orders in terms of elliptic polylogarithms
journal, December 2016

A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon
journal, March 2015

Cluster adjacency and the four-loop NMHV heptagon
journal, March 2019

The two-loop five-point amplitude in N $$ \mathcal{N} $$ = 8 supergravity
journal, March 2019

New Representations of the Perturbative $S$ Matrix
journal, February 2016

Simple loop integrals and amplitudes in $ \mathcal{N} = 4 $ SYM
journal, May 2011

Singularities and Discontinuities of Feynman Amplitudes
journal, September 1960

Multi-quark colour decompositions from unitarity
journal, October 2019

What is the simplest quantum field theory?
journal, September 2010

All tree-level amplitudes in massless QCD
journal, January 2011

Two-loop amplitudes of gluons and octa-cuts in Script N = 4 super Yang-Mills
journal, November 2005

Superconformal symmetry and two-loop amplitudes in planar N = 4 super Yang-Mills
journal, December 2011

Yangian symmetry of scattering amplitudes in 𝒩 = 4 super Yang-Mills theory
journal, May 2009

Five-Loop Four-Point Amplitude of $N = 4$ Super-Yang-Mills Theory
journal, December 2012

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

Logarithmic singularities and maximally supersymmetric amplitudes
journal, June 2015

Local mirror symmetry and the sunset Feynman integral
journal, January 2017

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

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

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

A note on polytopes for scattering amplitudes
journal, April 2012

The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM
journal, January 2011

A duality for the S matrix
journal, March 2010

The soft-collinear bootstrap: $ \mathcal{N} = {4} $ Yang-Mills amplitudes at six- and seven-loops
journal, March 2012

Full colour for loop amplitudes in Yang-Mills theory
journal, February 2017

Unification of residues and Grassmannian dualities
journal, January 2011