Extracting analytical one-loop amplitudes from numerical evaluations

Abstract

In this article we present a method to generate analytic expressions for the integral coefficients of loop amplitudes using numerical evaluations only. We use high-precision arithmetic to explore the singularity structure of the coefficients and decompose them into parts of manageable complexity. To illustrate the usability of our method we provide analytical expressions for all helicity configurations of the colour-ordered six-point gluon amplitudes at one loop with a gluon in the loop.

16 pages, 1 figure, fixed typo in Eq. 4.8

References in corpus (20)

• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
• Scattering amplitudes over finite fields and multivariate functional reconstruction
• Bootstrapping One-Loop QCD Amplitudes with General Helicities
• The two-loop five-point amplitude in $\mathcal{N}=4$ super-Yang-Mills theory
• Analytic Form of the Planar Two-Loop Five-Parton Scattering Amplitudes in QCD
• Analytic Form of the Planar Two-Loop Five-Gluon Scattering Amplitudes in QCD
• Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity
• A first look at two-loop five-gluon scattering in QCD
• S@M, a Mathematica Implementation of the Spinor-Helicity Formalism
• Planar Two-Loop Five-Parton Amplitudes from Numerical Unitarity
• Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case
• Matter dependence of the four-loop cusp anomalous dimension
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• All One-loop Maximally Helicity Violating Gluonic Amplitudes in QCD
• Quark and gluon form factors to four loop order in QCD: the $N_f^3$ contributions
• Determine Arbitrary Feynman Integrals by Vacuum Integrals
• The two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity
• The one-loop amplitude for six-gluon scattering
• Analytic Structure of Three-Mass Triangle Coefficients
• The rational parts of one-loop QCD amplitudes III: The six-gluon case

Cited by in corpus (15)

• Interpolation of Dense and Sparse Rational Functions and other Improvements in $\text{FireFly}$
• Les Houches 2021: Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• Two-Loop QCD Corrections for Three-Photon Production at Hadron Colliders
• Ansätze for Scattering Amplitudes from $p$-adic Numbers and Algebraic Geometry
• The one-loop amplitudes for Higgs + 4 partons with full mass effects
• Two-Loop Five-Parton Leading-Colour Finite Remainders in the Spinor-Helicity Formalism
• One-loop hexagon integral to higher orders in the dimensional regulator
• Computational challenges for multi-loop collider phenomenology
• The $pp\to W(\to l\nu )+\gamma$ process at next-to-next-to-leading order
• p-adic reconstruction of rational functions in multi-loop amplitudes
• Vector boson pair production at one loop: analytic results for the process $q\bar{q}\ell \bar{\ell }{\ell }^{\prime }{\bar{\ell }}^{\prime }g$
• Analytical amplitudes from numerical solutions of the scattering equations
• Learning the Simplicity of Scattering Amplitudes
• Analytic results for scalar-mediated Higgs boson production in association with two jets
• Two-loop leading-color QCD corrections for Higgs plus two-jet production in the heavy-top limit