skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Planar two-loop five-gluon amplitudes from numerical unitarity

Abstract

We present a calculation of the planar two-loop five-gluon amplitudes. The amplitudes are obtained in a variant of the generalized unitarity approach suitable for numerical computations, which we extend for use with finite field arithmetics. Employing a new method for the generation of unitarity-compatible integration-by-parts identities, all helicity amplitudes are reduced to a linear combination of master integrals for the first time. The approach allows us to compute exact values for the integral coefficients at rational phase-space points. All required master integrals are known analytically, and we obtain arbitrary-precision values for the amplitudes.

Authors:
; ; ; ;
Publication Date:
Research Org.:
Univ. of California, Los Angeles, CA (United States); Univ. of Freiburg (Germany)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); Alexander von Humboldt Foundation (Germany); German Federal Ministry of Education and Research (BMBF)
OSTI Identifier:
1455090
Alternate Identifier(s):
OSTI ID: 1498880
Grant/Contract Number:  
[SC0009937]
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
[Journal Name: Physical Review D Journal Volume: 97 Journal Issue: 11]; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; perturbative QCD; scattering amplitudes

Citation Formats

Abreu, S., Febres Cordero, F., Ita, H., Page, B., and Zeng, M. Planar two-loop five-gluon amplitudes from numerical unitarity. United States: N. p., 2018. Web. doi:10.1103/PhysRevD.97.116014.
Abreu, S., Febres Cordero, F., Ita, H., Page, B., & Zeng, M. Planar two-loop five-gluon amplitudes from numerical unitarity. United States. doi:10.1103/PhysRevD.97.116014.
Abreu, S., Febres Cordero, F., Ita, H., Page, B., and Zeng, M. Wed . "Planar two-loop five-gluon amplitudes from numerical unitarity". United States. doi:10.1103/PhysRevD.97.116014.
@article{osti_1455090,
title = {Planar two-loop five-gluon amplitudes from numerical unitarity},
author = {Abreu, S. and Febres Cordero, F. and Ita, H. and Page, B. and Zeng, M.},
abstractNote = {We present a calculation of the planar two-loop five-gluon amplitudes. The amplitudes are obtained in a variant of the generalized unitarity approach suitable for numerical computations, which we extend for use with finite field arithmetics. Employing a new method for the generation of unitarity-compatible integration-by-parts identities, all helicity amplitudes are reduced to a linear combination of master integrals for the first time. The approach allows us to compute exact values for the integral coefficients at rational phase-space points. All required master integrals are known analytically, and we obtain arbitrary-precision values for the amplitudes.},
doi = {10.1103/PhysRevD.97.116014},
journal = {Physical Review D},
number = [11],
volume = [97],
place = {United States},
year = {2018},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevD.97.116014

Citation Metrics:
Cited by: 19 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Integration-by-parts reductions from unitarity cuts and algebraic geometry
journal, February 2016


Analytic Form of the Two-Loop Planar Five-Gluon All-Plus-Helicity Amplitude in QCD
journal, February 2016


Integration by parts: The algorithm to calculate β-functions in 4 loops
journal, November 1981


Automatic Feynman Graph Generation
journal, April 1993


One-loop amplitudes for e+e− to four partons
journal, March 1998


Integrand-level reduction of loop amplitudes by computational algebraic geometry methods
journal, September 2012


A complete two-loop, five-gluon helicity amplitude in Yang-Mills theory
journal, October 2015

  • Badger, Simon; Mogull, Gustav; Ochirov, Alexander
  • Journal of High Energy Physics, Vol. 2015, Issue 10
  • DOI: 10.1007/JHEP10(2015)064

Two-Loop Four-Gluon Amplitudes from Numerical Unitarity
journal, October 2017


Recursive calculations for processes with n gluons
journal, September 1988


Automatic Integral Reduction for Higher Order Perturbative Calculations
journal, July 2004


On the integrand-reduction method for two-loop scattering amplitudes
journal, November 2011

  • Mastrolia, Pierpaolo; Ossola, Giovanni
  • Journal of High Energy Physics, Vol. 2011, Issue 11
  • DOI: 10.1007/JHEP11(2011)014

FIESTA4: Optimized Feynman integral calculations with GPU support
journal, July 2016


Scattering amplitudes from multivariate polynomial division
journal, November 2012


Subleading poles in the numerical unitarity method at two loops
journal, May 2017


Erratum: Infrared Singularities of Scattering Amplitudes in Perturbative QCD [Phys. Rev. Lett. 102 , 162001 (2009)]
journal, November 2013


A new algorithm for the generation of unitarity-compatible integration by parts relations
journal, January 2012


Infrared Singularities of Scattering Amplitudes in Perturbative QCD
journal, April 2009


Hepta-cuts of two-loop scattering amplitudes
journal, April 2012

  • Badger, Simon; Frellesvig, Hjalte; Zhang, Yang
  • Journal of High Energy Physics, Vol. 2012, Issue 4
  • DOI: 10.1007/JHEP04(2012)055

High-Precision Calculation of Multiloop Feynman Integrals by Difference Equations
journal, December 2000


The pentabox Master Integrals with the Simplified Differential Equations approach
journal, April 2016

  • Papadopoulos, Costas G.; Tommasini, Damiano; Wever, Christopher
  • Journal of High Energy Physics, Vol. 2016, Issue 4
  • DOI: 10.1007/JHEP04(2016)078

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


One-loop calculations in quantum field theory: From Feynman diagrams to unitarity cuts
journal, September 2012


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


Towards a basis for planar two-loop integrals
journal, February 2011


Azurite : An algebraic geometry based package for finding bases of loop integrals
journal, December 2017

  • Georgoudis, Alessandro; Larsen, Kasper J.; Zhang, Yang
  • Computer Physics Communications, Vol. 221
  • DOI: 10.1016/j.cpc.2017.08.013

Kira—A Feynman integral reduction program
journal, September 2018


Two-loop integrand decomposition into master integrals and surface terms
journal, December 2016


The computation of loop amplitudes in gauge theories
journal, July 1992


Two-loop five-point all-plus helicity Yang-Mills amplitude
journal, April 2016


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


Analytic all-plus-helicity gluon amplitudes in QCD
journal, December 2017


Full one-loop amplitudes from tree amplitudes
journal, April 2008


Supersymmetric regularization, two-loop QCD amplitudes, and coupling shifts
journal, October 2002


Reduze – Feynman integral reduction in C++
journal, July 2010


Towards a numerical unitarity approach for two-loop amplitudes in QCD
conference, October 2016

  • Ita, Harald
  • Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2016)
  • DOI: 10.22323/1.260.0080

The singular behaviour of QCD amplitudes at two-loop order
journal, May 1998


FORM version 4.0
journal, May 2013

  • Kuipers, J.; Ueda, T.; Vermaseren, J. A. M.
  • Computer Physics Communications, Vol. 184, Issue 5
  • DOI: 10.1016/j.cpc.2012.12.028

Numerical evaluation of multiple polylogarithms
journal, May 2005


Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
journal, March 2009


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


A novel approach to integration by parts reduction
journal, May 2015


Regularization and renormalization of gauge fields
journal, July 1972


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


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


The analytical value of the electron (g − 2) at order α3 in QED
journal, June 1996


Algorithm FIRE—Feynman Integral REduction
journal, October 2008


Automated implementation of on-shell methods for one-loop amplitudes
journal, August 2008


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


Multi-loop amplitudes and resummation
journal, January 2003


Scattering amplitudes over finite fields and multivariate functional reconstruction
journal, December 2016


Slimgb: Gröbner bases with slim polynomials
journal, December 2009


Dual conformal symmetry, integration-by-parts reduction, differential equations, and the nonplanar sector
journal, November 2017


Two-Loop Six Gluon All-Plus Helicity Amplitude
journal, August 2016


A two-loop five-gluon helicity amplitude in QCD
journal, December 2013

  • Badger, Simon; Frellesvig, Hjalte; Zhang, Yang
  • Journal of High Energy Physics, Vol. 2013, Issue 12
  • DOI: 10.1007/JHEP12(2013)045

LiteRed 1.4: a powerful tool for reduction of multiloop integrals
journal, June 2014


Reducing full one-loop amplitudes to scalar integrals at the integrand level
journal, February 2007


FIRE5: A C++ implementation of Feynman Integral REduction
journal, April 2015


A numerical unitarity formalism for evaluating one-loop amplitudes
journal, March 2008


Erratum: Analytic Form of the Two-Loop Planar Five-Gluon All-Plus-Helicity Amplitude in QCD [Phys. Rev. Lett. 116 , 062001 (2016)]
journal, May 2016