Heptagon functions and seven-gluon amplitudes in multi-Regge kinematics
Abstract
We compute all 2 → 5 gluon scattering amplitudes in planar $$\mathscr{N}$$ = 4 super-Yang-Mills theory in the multi-Regge limit that is sensitive to the non-trivial (“long”) Regge cut. We provide the amplitudes through four loops and to all logarithmic accuracy at leading power, in terms of single-valued multiple polylogarithms of two variables. To obtain these results, we leverage the function-level results for the amplitudes in the Steinmann cluster bootstrap. To high powers in the series expansion in the two variables, our results agree with the recently conjectured all-order central emission vertex used in the Fourier-Mellin representation of amplitudes in multi-Regge kinematics. Our results therefore provide a resummation of the Fourier-Mellin residues into single-valued polylogarithms, and constitute an important cross-check between the bootstrap approach and the all-orders multi-Regge proposal.
- Authors:
-
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Humboldt Univ. of Berlin (Germany). Inst. for Physics; Max Planck Inst. for Physics, Munich (Germany)
- Publication Date:
- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP); USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1847098
- Alternate Identifier(s):
- OSTI ID: 1865163
- Report Number(s):
- SLAC–PUB–17630
Journal ID: ISSN 1029-8479; TRN: US2303074
- 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: 2021; Journal Issue: 12; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Nature
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 1/N expansion; duality in gauge field theories; scattering amplitudes
Citation Formats
Dixon, Lance J., Liu, Yu-Ting, and Miczajka, Julian. Heptagon functions and seven-gluon amplitudes in multi-Regge kinematics. United States: N. p., 2021.
Web. doi:10.1007/jhep12(2021)218.
Dixon, Lance J., Liu, Yu-Ting, & Miczajka, Julian. Heptagon functions and seven-gluon amplitudes in multi-Regge kinematics. United States. https://doi.org/10.1007/jhep12(2021)218
Dixon, Lance J., Liu, Yu-Ting, and Miczajka, Julian. Fri .
"Heptagon functions and seven-gluon amplitudes in multi-Regge kinematics". United States. https://doi.org/10.1007/jhep12(2021)218. https://www.osti.gov/servlets/purl/1847098.
@article{osti_1847098,
title = {Heptagon functions and seven-gluon amplitudes in multi-Regge kinematics},
author = {Dixon, Lance J. and Liu, Yu-Ting and Miczajka, Julian},
abstractNote = {We compute all 2 → 5 gluon scattering amplitudes in planar $\mathscr{N}$ = 4 super-Yang-Mills theory in the multi-Regge limit that is sensitive to the non-trivial (“long”) Regge cut. We provide the amplitudes through four loops and to all logarithmic accuracy at leading power, in terms of single-valued multiple polylogarithms of two variables. To obtain these results, we leverage the function-level results for the amplitudes in the Steinmann cluster bootstrap. To high powers in the series expansion in the two variables, our results agree with the recently conjectured all-order central emission vertex used in the Fourier-Mellin representation of amplitudes in multi-Regge kinematics. Our results therefore provide a resummation of the Fourier-Mellin residues into single-valued polylogarithms, and constitute an important cross-check between the bootstrap approach and the all-orders multi-Regge proposal.},
doi = {10.1007/jhep12(2021)218},
journal = {Journal of High Energy Physics (Online)},
number = 12,
volume = 2021,
place = {United States},
year = {Fri Dec 31 00:00:00 EST 2021},
month = {Fri Dec 31 00:00:00 EST 2021}
}
Works referenced in this record:
The Massless Higher-Loop Two-Point Function
journal, February 2009
- Brown, Francis
- Communications in Mathematical Physics, Vol. 287, Issue 3
The Multi-Regge limit of NMHV amplitudes in N=4 SYM theory
journal, January 2013
- Lipatov, Lev; Prygarin, Alexander; Schnitzer, Howard J.
- Journal of High Energy Physics, Vol. 2013, Issue 1
Heptagons from the Steinmann cluster bootstrap
journal, February 2017
- Dixon, Lance J.; Drummond, James; Harrington, Thomas
- Journal of High Energy Physics, Vol. 2017, Issue 2
BFKL approach and six-particle maximally helicity violating amplitude in super Yang-Mills theory
journal, June 2011
- Lipatov, L. N.; Prygarin, A.
- Physical Review D, Vol. 83, Issue 12
Bootstrapping an NMHV amplitude through three loops
journal, October 2014
- Dixon, Lance J.; von Hippel, Matt
- Journal of High Energy Physics, Vol. 2014, Issue 10
Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond
journal, October 2005
- Bern, Zvi; Dixon, Lance J.; Smirnov, Vladimir A.
- Physical Review D, Vol. 72, Issue 8
N=4 supersymmetric Yang–Mills scattering amplitudes at high energies: the Regge cut contribution
journal, December 2009
- Bartels, J.; Lipatov, L. N.; Sabio Vera, A.
- The European Physical Journal C, Vol. 65, Issue 3-4
Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
journal, December 2016
- Caron-Huot, Simon; Dixon, Lance J.; McLeod, Andrew
- Physical Review Letters, Vol. 117, Issue 24
Erratum to: All orders results for self-crossing Wilson loops mimicking double parton scattering
journal, August 2016
- Dixon, Lance J.; Esterlis, Ilya
- Journal of High Energy Physics, Vol. 2016, Issue 8
Six-Gluon amplitudes in planar N$$ \mathcal{N} $$ = 4 super-Yang-Mills theory at six and seven loops
journal, August 2019
- Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko
- Journal of High Energy Physics, Vol. 2019, Issue 8
PolyLogTools — polylogs for the masses
journal, August 2019
- Duhr, Claude; Dulat, Falko
- Journal of High Energy Physics, Vol. 2019, Issue 8
Adjoint BFKL at finite coupling: a short-cut from the collinear limit
journal, January 2015
- Basso, Benjamin; Caron-Huot, Simon; Sever, Amit
- Journal of High Energy Physics, Vol. 2015, Issue 1
BFKL Pomeron, Reggeized gluons, and Bern-Dixon-Smirnov amplitudes
journal, August 2009
- Bartels, J.; Lipatov, L. N.; Vera, A. Sabio
- Physical Review D, Vol. 80, Issue 4
Analytic properties of high-energy production amplitudes in N=4 susy
journal, February 2012
- Lipatov, L. N.
- Theoretical and Mathematical Physics, Vol. 170, Issue 2
Cluster adjacency beyond MHV
journal, March 2019
- Drummond, James; Foster, Jack; Gürdoğan, Ömer
- Journal of High Energy Physics, Vol. 2019, Issue 3
A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon
journal, March 2015
- Drummond, J. M.; Papathanasiou, G.; Spradlin, M.
- Journal of High Energy Physics, Vol. 2015, Issue 3
Cluster adjacency and the four-loop NMHV heptagon
journal, March 2019
- Drummond, James; Foster, Jack; Gürdoğn, Ömer
- Journal of High Energy Physics, Vol. 2019, Issue 3
BFKL equation for the adjoint representation of the gauge group in the next-to-leading approximation at <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math> SUSY
journal, January 2012
- Fadin, V. S.; Lipatov, L. N.
- Physics Letters B, Vol. 706, Issue 4-5
Integrability of scattering amplitudes in N = 4 SUSY
journal, July 2009
- Lipatov, L. N.
- Journal of Physics A: Mathematical and Theoretical, Vol. 42, Issue 30
The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
journal, June 2018
- Del Duca, Vittorio; Druc, Stefan; Drummond, James
- Journal of High Energy Physics, Vol. 2018, Issue 6
Analytic structure of the scattering amplitude in SYM theory in the multi-Regge kinematics: Conformal Regge pole contribution
journal, March 2014
- Bartels, Jochen; Kormilitzin, Andrey; Lipatov, Lev N.
- Physical Review D, Vol. 89, Issue 6
BFKL approach and maximally helicity violating amplitude in super-Yang-Mills theory
journal, September 2012
- Bartels, J.; Kormilitzin, A.; Lipatov, L. N.
- Physical Review D, Vol. 86, Issue 6
Eliminating spurious poles from gauge-theoretic amplitudes
journal, May 2013
- Hodges, Andrew
- Journal of High Energy Physics, Vol. 2013, Issue 5
Lifting heptagon symbols to functions
journal, October 2020
- Dixon, Lance J.; Liu, Yu-Ting
- Journal of High Energy Physics, Vol. 2020, Issue 10
Space-time S-matrix and flux tube S-matrix II. Extracting and matching data
journal, January 2014
- Basso, Benjamin; Sever, Amit; Vieira, Pedro
- Journal of High Energy Physics, Vol. 2014, Issue 1
Dual superconformal invariance, momentum twistors and Grassmannians
journal, November 2009
- Mason, Lionel; Skinner, David
- Journal of High Energy Physics, Vol. 2009, Issue 11
Superconformal symmetry and two-loop amplitudes in planar N = 4 super Yang-Mills
journal, December 2011
- Caron-Huot, S.
- Journal of High Energy Physics, Vol. 2011, Issue 12
Origin of the Six-Gluon Amplitude in Planar Supersymmetric Yang-Mills Theory
journal, April 2020
- Basso, Benjamin; Dixon, Lance J.; Papathanasiou, Georgios
- Physical Review Letters, Vol. 124, Issue 16
Virtual next-to-leading corrections to the Lipatov vertex
journal, February 1999
- Del Duca, Vittorio; Schmidt, Carl R.
- Physical Review D, Vol. 59, Issue 7
Mandelstam cuts and lightlike Wilson loops in supersymmetry
journal, February 2011
- Lipatov, L. N.; Prygarin, A.
- Physical Review D, Vol. 83, Issue 4
Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
journal, August 2016
- Del Duca, Vittorio; Druc, Stefan; Drummond, James
- Journal of High Energy Physics, Vol. 2016, Issue 8
Harmonic Polylogarithms
journal, February 2000
- Remiddi, E.; Vermaseren, J. A. M.
- International Journal of Modern Physics A, Vol. 15, Issue 05
The cosmic Galois group and extended Steinmann relations for planar N$$ \mathcal{N} $$ = 4 SYM amplitudes
journal, September 2019
- Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko
- Journal of High Energy Physics, Vol. 2019, Issue 9
Motivic amplitudes and cluster coordinates
journal, January 2014
- Golden, J. K.; Goncharov, A. B.; Spradlin, M.
- Journal of High Energy Physics, Vol. 2014, Issue 1
Analytic structure of the scattering amplitude in SYM theory in multi-Regge kinematics: Conformal Regge cut contribution
journal, February 2015
- Bartels, Jochen; Kormilitzin, Andrey; Lipatov, Lev N.
- Physical Review D, Vol. 91, Issue 4
Cluster Adjacency Properties of Scattering Amplitudes in Supersymmetric Yang-Mills Theory
journal, April 2018
- Drummond, James; Foster, Jack; Gürdoğan, Ömer
- Physical Review Letters, Vol. 120, Issue 16
Multiple zeta values and periods of moduli spaces $\overline{\mathfrak{M}}_{0,n}$
journal, January 2009
- Brown, Francis C. S.
- Annales scientifiques de l'École normale supérieure, Vol. 42, Issue 3
Multiple polylogarithms, cyclotomy and modular complexes
journal, January 1998
- Goncharov, A. B.
- Mathematical Research Letters, Vol. 5, Issue 4
One-loop n-point gauge theory amplitudes, unitarity and collinear limits
journal, August 1994
- Bern, Zvi; Dixon, Lance; Dunbar, David C.
- Nuclear Physics B, Vol. 425, Issue 1-2
Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
journal, March 2015
- Panzer, Erik
- Computer Physics Communications, Vol. 188
Mathematical Aspects of Scattering Amplitudes
conference, November 2015
- Duhr, Claude
- 2014 Theoretical Advanced Study Institute in Elementary Particle Physics, Journeys Through the Precision Frontier: Amplitudes for Colliders
Reggeization of Elementary Particles in Renormalizable Gauge Theories: Vectors and Spinors
journal, December 1973
- Grisaru, Marcus T.; Schnitzer, Howard J.; Tsao, Hung-Sheng
- Physical Review D, Vol. 8, Issue 12
Reggeization of Yang-Mills Gauge Mesons in Theories with a Spontaneously Broken Symmetry
journal, April 1973
- Grisaru, Marcus T.; Schnitzer, Howard J.; Tsao, Hung-Sheng
- Physical Review Letters, Vol. 30, Issue 17
Thermodynamic bubble ansatz
journal, September 2011
- Alday, Luis F.; Gaiotto, Davide; Maldacena, Juan
- Journal of High Energy Physics, Vol. 2011, Issue 9
Classical Polylogarithms for Amplitudes and Wilson Loops
journal, October 2010
- Goncharov, A. B.; Spradlin, M.; Vergu, C.
- Physical Review Letters, Vol. 105, Issue 15
Single-valued harmonic polylogarithms and the multi-Regge limit
journal, October 2012
- Dixon, Lance J.; Duhr, Claude; Pennington, Jeffrey
- Journal of High Energy Physics, Vol. 2012, Issue 10
On the pomeranchuk singularity in asymptotically free theories
journal, December 1975
- Fadin, V. S.; Kuraev, E. A.; Lipatov, L. N.
- Physics Letters B, Vol. 60, Issue 1