All two-loop MHV remainder functions in multi-Regge kinematics

Del Duca, Vittorio; Duhr, Claude; Dulat, Falko; Penante, Brenda

doi:10.1007/jhep01(2019)162

Title: All two-loop MHV remainder functions in multi-Regge kinematics

Abstract

We introduce a method to extract the symbol of the coefficient of (2πi)² of MHV remainder functions in planar N = 4 Super Yang-Mills in multi-Regge kinematics region directly from the symbol in full kinematics. At two loops this symbol can be uplifted to the full function in a unique way, without any beyond-the-symbol ambiguities. We can therefore determine all two-loop MHV amplitudes at function level in all kinematic regions with different energy signs in multi-Regge kinematics. We analyse our results and we observe that they are consistent with the hypothesis of a contribution from the exchange of a three-Reggeon composite state starting from two loops and eight points in certain kinematic regions.

Authors:

Del Duca, Vittorio ^[1]; Duhr, Claude ^[2]; Dulat, Falko ^[3]; Penante, Brenda ^[4]

Federal Inst. of Technology, Zurich (Switzerland). Inst. for Theoretical Physics
European Organization for Nuclear Research (CERN), Geneva (Switzerland). Theoretical Physics Dept.; Univ. Catholique de Louvain, Louvain-la-Neuve (Belgium). Center for Cosmology, Particle Physics and Phenomenology (CP3)
SLAC National Accelerator Lab., Menlo Park, CA (United States)
European Organization for Nuclear Research (CERN), Geneva (Switzerland). Theoretical Physics Dept.

Publication Date:: Mon Jan 21 00:00:00 EST 2019

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

Sponsoring Org.:: USDOE

OSTI Identifier:: 1503549

Report Number(s):: SLAC-PUB-17357
Journal ID: ISSN 1029-8479

Grant/Contract Number:: 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: 1; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Scattering Amplitudes; Gauge Symmetry; Supersymmetric Gauge Theory

Citation Formats


                    Del Duca, Vittorio, Duhr, Claude, Dulat, Falko, and Penante, Brenda. All two-loop MHV remainder functions in multi-Regge kinematics.  United States: N. p., 2019. 
Web.  doi:10.1007/jhep01(2019)162.

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                    Del Duca, Vittorio, Duhr, Claude, Dulat, Falko, & Penante, Brenda. All two-loop MHV remainder functions in multi-Regge kinematics.  United States.  https://doi.org/10.1007/jhep01(2019)162

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                    Del Duca, Vittorio, Duhr, Claude, Dulat, Falko, and Penante, Brenda. Mon .  
"All two-loop MHV remainder functions in multi-Regge kinematics".  United States.  https://doi.org/10.1007/jhep01(2019)162.  https://www.osti.gov/servlets/purl/1503549.

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@article{osti_1503549,

  title        = {All two-loop MHV remainder functions in multi-Regge kinematics},

  author       = {Del Duca, Vittorio and Duhr, Claude and Dulat, Falko and Penante, Brenda},

  abstractNote = {We introduce a method to extract the symbol of the coefficient of (2πi)2 of MHV remainder functions in planar N = 4 Super Yang-Mills in multi-Regge kinematics region directly from the symbol in full kinematics. At two loops this symbol can be uplifted to the full function in a unique way, without any beyond-the-symbol ambiguities. We can therefore determine all two-loop MHV amplitudes at function level in all kinematic regions with different energy signs in multi-Regge kinematics. We analyse our results and we observe that they are consistent with the hypothesis of a contribution from the exchange of a three-Reggeon composite state starting from two loops and eight points in certain kinematic regions.},

  doi          = {10.1007/jhep01(2019)162},

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

  number       = 1,

  volume       = 2019,

  place        = {United States},

  year         = {Mon Jan 21 00:00:00 EST 2019},

  month        = {Mon Jan 21 00:00:00 EST 2019}

}

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Figure 1: Simplicial MRK coordinates parametrising the transverse space for the scattering of N particles in MRK.

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Journal Article Bargheer, Till ; Papathanasiou, Georgios ; Schomerus, Volker - Journal of High Energy Physics (Online)

Here, we study the symbol of the two-loop n-gluon MHV amplitude for all Mandelstam regions in multi-Regge kinematics in N=4 super Yang-Mills theory. While the number of distinct Mandelstam regions grows exponentially with n, the increase of independent symbols turns out to be merely quadratic. We uncover how to construct the symbols for any number of external gluons from just two building blocks which are naturally associated with the six- and seven-gluon amplitude, respectively. The second building block is entirely new, and in addition to its symbol, we also construct a prototype function that correctly reproduces all terms of maximalmore » functional transcendentality.« less
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https://doi.org/10.1007/JHEP05(2016)012

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Bootstrapping the Three-Loop Hexagon

Journal Article Dixon, Lance J ; /CERN /SLAC ; Drummond, James M ; ... - JHEP 1111:023,2011

We consider the hexagonal Wilson loop dual to the six-point MHV amplitude in planar N = 4 super Yang-Mills theory. We apply constraints from the operator product expansion in the near-collinear limit to the symbol of the remainder function at three loops. Using these constraints, and assuming a natural ansatz for the symbol's entries, we determine the symbol up to just two undetermined constants. In the multi-Regge limit, both constants drop out from the symbol, enabling us to make a non-trivial confirmation of the BFKL prediction for the leading-log approximation. This result provides a strong consistency check of both ourmore »« less
https://doi.org/10.1007/JHEP11(2011)023

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Hexagon functions and the three-loop remainder function

Journal Article Dixon, Lance J. ; Drummond, James M. ; von Hippel, Matt ; ... - Journal of High Energy Physics (Online)

We present the three-loop remainder function, which describes the scattering of six gluons in the maximally-helicity-violating configuration in planar NN = 4 super-Yang-Mills theory, as a function of the three dual conformal cross ratios. The result can be expressed in terms of multiple Goncharov polylogarithms. We also employ a more restricted class of hexagon functions which have the correct branch cuts and certain other restrictions on their symbols. We classify all the hexagon functions through transcendental weight five, using the coproduct for their Hopf algebra iteratively, which amounts to a set of first-order differential equations. The three-loop remainder function ismore »« less
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The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy

Journal Article Del Duca, Vittorio ; Druc, Stefan ; Drummond, James ; ... - Journal of High Energy Physics (Online)

We present an all-loop dispersion integral, well-defined to arbitrary logarithmic accuracy, describing the multi-Regge limit of the 2 → 5 amplitude in planar N = 4 super Yang-Mills theory. It follows from factorization, dual conformal symmetry and consistency with soft limits, and specifically holds in the region where the energies of all produced particles have been analytically continued. After promoting the known symbol of the 2-loop N -particle MHV amplitude in this region to a function, we specialize to N = 7, and extract from it the next-to-leading order (NLO) correction to the BFKL central emission vertex, namely the buildingmore »« less
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https://doi.org/10.1007/jhep06(2018)116

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

Journal Article - Journal of High Energy Physics (Online)

We present the four-loop remainder function for six-gluon scattering with maximal helicity violation in planar NN = 4 super-Yang-Mills theory, as an analytic function of three dual-conformal cross ratios. The function is constructed entirely from its analytic properties, without ever inspecting any multi-loop integrand. We employ the same approach used at three loops, writing an ansatz in terms of hexagon functions, and fixing coefficients in the ansatz using the multi-Regge limit and the operator product expansion in the near-collinear limit. We express the result in terms of multiple polylogarithms, and in terms of the coproduct for the associated Hopf algebra.more »« less
https://doi.org/10.1007/JHEP06(2014)116

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Title: All two-loop MHV remainder functions in multi-Regge kinematics

Abstract

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Polylogarithmes multiples uniformes en une variable journal, April 2004

Automated computation of one-loop integrals in massless theories journal, June 2005

Notes on the scattering amplitude — Wilson loop duality journal, July 2011

Heptagons from the Steinmann cluster bootstrap journal, February 2017

Collinear Limit of Scattering Amplitudes at Strong Coupling journal, December 2014

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

Conformal properties of four-gluon planar amplitudes and Wilson loops journal, May 2008

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

Notes on motivic periods journal, January 2017

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

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

The two-loop symbol of all multi-Regge regions journal, May 2016

On planar gluon amplitudes/Wilson loops duality journal, May 2008

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

Analyticity for multi-Regge limits of the Bern–Dixon–Smirnov amplitudes journal, November 2009

MHV amplitudes in super-Yang–Mills and Wilson Loops journal, May 2008

High-energy evolution to three loops journal, February 2018

Multi-Regge limit of the n-gluon bubble ansatz journal, November 2012

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

BFKL pomeron in the next-to-leading approximation journal, June 1998

Implications of multi-Regge limits for the Bern–Dixon–Smirnov conjecture journal, June 2009

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

Iterated amplitudes in the high-energy limit journal, December 2008

Bootstrapping null polygon Wilson loops journal, March 2011

Irreducible part of the next-to-leading BFKL kernel journal, October 1997

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

Gluon scattering amplitudes at strong coupling journal, June 2007

An analytic result for the two-loop seven-point MHV amplitude in N $$ \mathcal{N} $$ = 4 SYM journal, August 2014

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

Iterated path integrals journal, January 1977

Comments on gluon scattering amplitudes via AdS/CFT journal, November 2007

An analytic result for the two-loop hexagon Wilson loop in $ \mathcal{N} = 4 $ SYM journal, March 2010

Energy scale(s) and next-to-leading BFKL equation journal, July 1998

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

Bootstrapping the three-loop hexagon journal, November 2011

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

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

Systematics of the multi-Regge three-loop symbol journal, November 2017

The complete planar S-matrix of $ \mathcal{N} = 4 $ SYM as a Wilson loop in twistor space journal, December 2010

Dual superconformal symmetry, and the amplitude/Wilson loop connection journal, September 2008

The Bethe roots of Regge cuts in strongly coupled N = 4 $$ \mathcal{N}=4 $$ SYM theory journal, July 2015

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

The two-loop hexagon Wilson loop in $ \mathcal{N} = 4 $ SYM journal, May 2010

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

OPE for super loops journal, November 2011

Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes journal, February 2010

Cluster functions and scattering amplitudes for six and seven points journal, July 2017

Multi-Regge kinematics and the moduli space of Riemann spheres with marked points journal, August 2016

An operator product expansion for polygonal null Wilson loops journal, April 2011

Cluster Adjacency Properties of Scattering Amplitudes in N = 4 Supersymmetric Yang-Mills Theory journal, April 2018

Multiple zeta values and periods of moduli spaces $\overline{\mathfrak{M}}_{0,n}$ journal, January 2009

Optical theorems and steinmann relations journal, April 1975

The differential of all two-loop MHV amplitudes in $ \mathcal{N}=4 $ Yang-Mills theory journal, September 2013

OPE for all helicity amplitudes journal, August 2015

Exciting the GKP string at any coupling journal, April 2012

Classical Polylogarithms for Amplitudes and Wilson Loops journal, October 2010

Pulling the straps of polygons journal, December 2011

Single-valued harmonic polylogarithms and the multi-Regge limit journal, October 2012

Dimensionally regulated one-loop box scalar integrals with massless internal lines journal, April 2001

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

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

Cluster algebras and the subalgebra constructibility of the seven-particle remainder function journal, January 2019

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

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 IV. Gluons and fusion journal, September 2014

OPE for all helicity amplitudes II. Form factors and data analysis journal, December 2015

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

Motivic amplitudes and cluster coordinates journal, January 2014

The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy journal, June 2018

Optical theorems and steinmann relations journal, April 1975

Analyticity for multi-Regge limits of the Bern–Dixon–Smirnov amplitudes journal, November 2009

Iterated amplitudes in the high-energy limit journal, December 2008

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

Integrability of scattering amplitudes in N=4 SUSY text, January 2009

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

Polylogarithmes multiples uniformes en une variable
journal, April 2004

Automated computation of one-loop integrals in massless theories
journal, June 2005

Notes on the scattering amplitude — Wilson loop duality
journal, July 2011

Heptagons from the Steinmann cluster bootstrap
journal, February 2017

Collinear Limit of Scattering Amplitudes at Strong Coupling
journal, December 2014

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

Conformal properties of four-gluon planar amplitudes and Wilson loops
journal, May 2008

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

Notes on motivic periods
journal, January 2017

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

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

The two-loop symbol of all multi-Regge regions
journal, May 2016

On planar gluon amplitudes/Wilson loops duality
journal, May 2008

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

Analyticity for multi-Regge limits of the Bern–Dixon–Smirnov amplitudes
journal, November 2009

MHV amplitudes in super-Yang–Mills and Wilson Loops
journal, May 2008

High-energy evolution to three loops
journal, February 2018

Multi-Regge limit of the n-gluon bubble ansatz
journal, November 2012

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

BFKL pomeron in the next-to-leading approximation
journal, June 1998

Implications of multi-Regge limits for the Bern–Dixon–Smirnov conjecture
journal, June 2009

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

Iterated amplitudes in the high-energy limit
journal, December 2008

Bootstrapping null polygon Wilson loops
journal, March 2011

Irreducible part of the next-to-leading BFKL kernel
journal, October 1997

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

Gluon scattering amplitudes at strong coupling
journal, June 2007

An analytic result for the two-loop seven-point MHV amplitude in N $$ \mathcal{N} $$ = 4 SYM
journal, August 2014

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

Iterated path integrals
journal, January 1977

Comments on gluon scattering amplitudes via AdS/CFT
journal, November 2007

An analytic result for the two-loop hexagon Wilson loop in $ \mathcal{N} = 4 $ SYM
journal, March 2010

Energy scale(s) and next-to-leading BFKL equation
journal, July 1998

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

Bootstrapping the three-loop hexagon
journal, November 2011

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

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

Systematics of the multi-Regge three-loop symbol
journal, November 2017

The complete planar S-matrix of $ \mathcal{N} = 4 $ SYM as a Wilson loop in twistor space
journal, December 2010

Dual superconformal symmetry, and the amplitude/Wilson loop connection
journal, September 2008

The Bethe roots of Regge cuts in strongly coupled N = 4 $$ \mathcal{N}=4 $$ SYM theory
journal, July 2015

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

The two-loop hexagon Wilson loop in $ \mathcal{N} = 4 $ SYM
journal, May 2010

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

OPE for super loops
journal, November 2011

Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
journal, February 2010

Cluster functions and scattering amplitudes for six and seven points
journal, July 2017

Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
journal, August 2016

An operator product expansion for polygonal null Wilson loops
journal, April 2011

Cluster Adjacency Properties of Scattering Amplitudes in $N = 4$ Supersymmetric Yang-Mills Theory
journal, April 2018

Multiple zeta values and periods of moduli spaces $\overline{\mathfrak{M}}_{0,n}$
journal, January 2009

Optical theorems and steinmann relations
journal, April 1975

The differential of all two-loop MHV amplitudes in $ \mathcal{N}=4 $ Yang-Mills theory
journal, September 2013

OPE for all helicity amplitudes
journal, August 2015

Exciting the GKP string at any coupling
journal, April 2012

Classical Polylogarithms for Amplitudes and Wilson Loops
journal, October 2010

Pulling the straps of polygons
journal, December 2011

Single-valued harmonic polylogarithms and the multi-Regge limit
journal, October 2012

Dimensionally regulated one-loop box scalar integrals with massless internal lines
journal, April 2001

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

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

Cluster algebras and the subalgebra constructibility of the seven-particle remainder function
journal, January 2019

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

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 IV. Gluons and fusion
journal, September 2014

OPE for all helicity amplitudes II. Form factors and data analysis
journal, December 2015

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

Motivic amplitudes and cluster coordinates
journal, January 2014

The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
journal, June 2018

Optical theorems and steinmann relations
journal, April 1975

Analyticity for multi-Regge limits of the Bern–Dixon–Smirnov amplitudes
journal, November 2009

Iterated amplitudes in the high-energy limit
journal, December 2008

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

Integrability of scattering amplitudes in N=4 SUSY
text, January 2009

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

An analytic result for the two-loop seven-point MHV amplitude in N=4 SYM
text, January 2014

Analytic structure of the $n = 7$ scattering amplitude in $\mathcal{N}=4$ SYM theory in multi-Regge kinematics: Conformal Regge cut contribution
text, January 2014

Systematics of the Multi-Regge Three-Loop Symbol
text, January 2016

Dimensionally regulated one-loop box scalar integrals with massless internal lines
text, January 2000