Landau singularities from the amplituhedron

Dennen, T.; Prlina, I.; Spradlin, M.; Stanojevic, S.; Volovich, A.

doi:10.1007/JHEP06(2017)152

Title: Landau singularities from the amplituhedron

Abstract

We propose a simple geometric algorithm for determining the complete set of branch points of amplitudes in planar N = 4 super-Yang-Mills theory directly from the amplituhedron, without resorting to any particular representation in terms of local Feynman integrals. This represents a step towards translating integrands directly into integrals. In particular, the algorithm provides information about the symbol alphabets of general amplitudes. We illustrate the algorithm applied to the one- and two-loop MHV amplitudes.

Authors:

Dennen, T. ^[1]; Prlina, I. ^[2]; Spradlin, M. ^[2]; Stanojevic, S. ^[2]; Volovich, A. ^[2]

Brown Univ., Providence, RI (United States); Google Inc., Mountain View, CA (United States)
Brown Univ., Providence, RI (United States)

Publication Date:: Wed Jun 28 00:00:00 EDT 2017

Research Org.:: Brown Univ., Providence, RI (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Fusion Energy Sciences (FES)

OSTI Identifier:: 1424013

Grant/Contract Number:: sc0010010

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: 2017; Journal Issue: 6; 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

Citation Formats


                    Dennen, T., Prlina, I., Spradlin, M., Stanojevic, S., and Volovich, A. Landau singularities from the amplituhedron.  United States: N. p., 2017. 
Web.  doi:10.1007/JHEP06(2017)152.

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                    Dennen, T., Prlina, I., Spradlin, M., Stanojevic, S., & Volovich, A. Landau singularities from the amplituhedron.  United States.  https://doi.org/10.1007/JHEP06(2017)152

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                    Dennen, T., Prlina, I., Spradlin, M., Stanojevic, S., and Volovich, A. Wed .  
"Landau singularities from the amplituhedron".  United States.  https://doi.org/10.1007/JHEP06(2017)152.  https://www.osti.gov/servlets/purl/1424013.

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@article{osti_1424013,

  title        = {Landau singularities from the amplituhedron},

  author       = {Dennen, T. and Prlina, I. and Spradlin, M. and Stanojevic, S. and Volovich, A.},

  abstractNote = {We propose a simple geometric algorithm for determining the complete set of branch points of amplitudes in planar N = 4 super-Yang-Mills theory directly from the amplituhedron, without resorting to any particular representation in terms of local Feynman integrals. This represents a step towards translating integrands directly into integrals. In particular, the algorithm provides information about the symbol alphabets of general amplitudes. We illustrate the algorithm applied to the one- and two-loop MHV amplitudes.},

  doi          = {10.1007/JHEP06(2017)152},

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

  number       = 6,

  volume       = 2017,

  place        = {United States},

  year         = {Wed Jun 28 00:00:00 EDT 2017},

  month        = {Wed Jun 28 00:00:00 EDT 2017}

}

Copy to clipboard

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Works referenced in this record:

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Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills
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Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM
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Works referencing / citing this record:

Causality, unitarity thresholds, anomalous thresholds and infrared singularities from the loop-tree duality at higher orders
journal, December 2019

Aguilera-Verdugo, J. Jesús; Driencourt-Mangin, Félix; Plenter, Judith
Journal of High Energy Physics, Vol. 2019, Issue 12
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All-Helicity Symbol Alphabets from Unwound Amplituhedra
text, January 2017

Prlina, Igor; Spradlin, Marcus; Stankowicz, James
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Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops
text, January 2017

Prlina, Igor; Spradlin, Marcus; Stankowicz, James
arXiv
DOI: 10.48550/arxiv.1712.08049

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Title: Landau singularities from the amplituhedron

Abstract

Citation Formats

Fusing gauge theory tree amplitudes into loop amplitudes journal, February 1995

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

On analytic properties of vertex parts in quantum field theory journal, October 1959

Singularities in the physical region journal, July 1965

Bootstrapping an NMHV amplitude through three loops journal, October 2014

From d logs to dilogs; the super Yang-Mills MHV amplitude revisited journal, January 2014

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

Cuts and coproducts of massive triangle diagrams journal, July 2015

From multiple unitarity cuts to the coproduct of Feynman integrals journal, October 2014

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

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

Supersymmetric Yang-Mills theories journal, March 1977

The Amplituhedron journal, October 2014

Determination of the Pion-Nucleon Scattering Amplitude from Dispersion Relations and Unitarity. General Theory journal, November 1958

Analytic Properties of Transition Amplitudes in Perturbation Theory journal, September 1959

Progress in One-Loop qcd Computations journal, December 1996

Motivic amplitudes and cluster coordinates journal, January 2014

Towards the amplituhedron volume journal, March 2016

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

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

Looking for a bulk point journal, January 2017

Singularities of the Second Type journal, July 1962

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

Evidence for a nonplanar amplituhedron journal, June 2016

Amplitude for n -Gluon Scattering journal, June 1986

Into the amplituhedron journal, December 2014

Positive amplitudes in the amplituhedron journal, August 2015

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

Iterated path integrals journal, January 1977

Classical Polylogarithms for Amplitudes and Wilson Loops journal, October 2010

Amplituhedron Cells and Stanley Symmetric Functions journal, March 2016

Pulling the straps of polygons journal, December 2011

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

Singularities and Discontinuities of Feynman Amplitudes journal, September 1960

Bootstrapping the three-loop hexagon journal, November 2011

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

Landau singularities and symbology: one- and two-loop MHV amplitudes in SYM theory journal, March 2016

Local integrals for planar scattering amplitudes journal, June 2012

The four-loop remainder function and multi-Regge behavior at NNLLA in planar $ \mathcal{N} $ = 4 super-Yang-Mills theory journal, June 2014

Physical sheet properties of second type singularities journal, November 1962

Bootstrapping six-gluon scattering in planar N=4 super-Yang-Mills theory conference, August 2014

On Analytic Properties of Vertex Parts in Quantum Field Theory book, January 1965

Analytic Properties of Transition Amplitudes in Perturbation Theory book, August 2017

Motivic amplitudes and cluster coordinates text, January 2014

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

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

Bootstrapping the three-loop hexagon text, January 2011

From multiple unitarity cuts to the coproduct of Feynman integrals text, January 2014

The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory text, January 2014

Bootstrapping six-gluon scattering in planar ${\cal N}=4$ super-Yang-Mills theory preprint, January 2014

Bootstrapping an NMHV amplitude through three loops text, January 2014

Anatomy of the Amplituhedron preprint, January 2014

Amplituhedron cells and Stanley symmetric functions preprint, January 2014

Positive Amplitudes In The Amplituhedron text, January 2014

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

Landau Singularities and Symbology: One- and Two-loop MHV Amplitudes in SYM Theory text, January 2015

Evidence for a Nonplanar Amplituhedron text, January 2015

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

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

Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes text, January 1994

Progress in One-Loop QCD Computations text, January 1996

Causality, unitarity thresholds, anomalous thresholds and infrared singularities from the loop-tree duality at higher orders journal, December 2019

All-Helicity Symbol Alphabets from Unwound Amplituhedra text, January 2017

Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops text, January 2017

Fusing gauge theory tree amplitudes into loop amplitudes
journal, February 1995

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

On analytic properties of vertex parts in quantum field theory
journal, October 1959

Singularities in the physical region
journal, July 1965

Bootstrapping an NMHV amplitude through three loops
journal, October 2014

From d logs to dilogs; the super Yang-Mills MHV amplitude revisited
journal, January 2014

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

Cuts and coproducts of massive triangle diagrams
journal, July 2015

From multiple unitarity cuts to the coproduct of Feynman integrals
journal, October 2014

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

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

Supersymmetric Yang-Mills theories
journal, March 1977

The Amplituhedron
journal, October 2014

Determination of the Pion-Nucleon Scattering Amplitude from Dispersion Relations and Unitarity. General Theory
journal, November 1958

Analytic Properties of Transition Amplitudes in Perturbation Theory
journal, September 1959

Progress in One-Loop qcd Computations
journal, December 1996

Motivic amplitudes and cluster coordinates
journal, January 2014

Towards the amplituhedron volume
journal, March 2016

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

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

Looking for a bulk point
journal, January 2017

Singularities of the Second Type
journal, July 1962

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

Evidence for a nonplanar amplituhedron
journal, June 2016

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

Into the amplituhedron
journal, December 2014

Positive amplitudes in the amplituhedron
journal, August 2015

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

Iterated path integrals
journal, January 1977

Classical Polylogarithms for Amplitudes and Wilson Loops
journal, October 2010

Amplituhedron Cells and Stanley Symmetric Functions
journal, March 2016

Pulling the straps of polygons
journal, December 2011

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

Singularities and Discontinuities of Feynman Amplitudes
journal, September 1960

Bootstrapping the three-loop hexagon
journal, November 2011

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

Landau singularities and symbology: one- and two-loop MHV amplitudes in SYM theory
journal, March 2016

Local integrals for planar scattering amplitudes
journal, June 2012

The four-loop remainder function and multi-Regge behavior at NNLLA in planar $ \mathcal{N} $ = 4 super-Yang-Mills theory
journal, June 2014

Physical sheet properties of second type singularities
journal, November 1962

Bootstrapping six-gluon scattering in planar N=4 super-Yang-Mills theory
conference, August 2014

On Analytic Properties of Vertex Parts in Quantum Field Theory
book, January 1965

Analytic Properties of Transition Amplitudes in Perturbation Theory
book, August 2017

Motivic amplitudes and cluster coordinates
text, January 2014

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

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

Bootstrapping the three-loop hexagon
text, January 2011

From multiple unitarity cuts to the coproduct of Feynman integrals
text, January 2014

The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory
text, January 2014

Bootstrapping six-gluon scattering in planar ${\cal N}=4$ super-Yang-Mills theory
preprint, January 2014

Bootstrapping an NMHV amplitude through three loops
text, January 2014

Anatomy of the Amplituhedron
preprint, January 2014

Amplituhedron cells and Stanley symmetric functions
preprint, January 2014

Positive Amplitudes In The Amplituhedron
text, January 2014

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

Landau Singularities and Symbology: One- and Two-loop MHV Amplitudes in SYM Theory
text, January 2015

Evidence for a Nonplanar Amplituhedron
text, January 2015

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

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

Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
text, January 1994

Progress in One-Loop QCD Computations
text, January 1996

Causality, unitarity thresholds, anomalous thresholds and infrared singularities from the loop-tree duality at higher orders
journal, December 2019

All-Helicity Symbol Alphabets from Unwound Amplituhedra
text, January 2017

Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops
text, January 2017