Two-loop Feynman integrals involve Riemann spheres, elliptic curves, hyperelliptic curves of genus 2 and 3, K3 surfaces, and a rationalizable Del Pezzo surface of degree 2.
Canonical reference
Towards a Basis for Planar Two-Loop Integrals
Canonical reference. 100% of citing Pith papers cite this work as background.
7
Pith papers citing it
Background
100% of classified citations
abstract
The existence of a finite basis of algebraically independent one-loop integrals has underpinned important developments in the computation of one-loop amplitudes in field theories and gauge theories in particular. We give an explicit construction reducing integrals to a finite basis for planar integrals at two loops, both to all orders in the dimensional regulator e, and also when all integrals are truncated to O(e). We show how to reorganize integration-by-parts equations to obtain elements of the first basis efficiently, and how to use Gram determinants to obtain additional linear relations reducing this all-orders basis to the second one. The techniques we present should apply to non-planar integrals, to integrals with massive propagators, and beyond two loops as well.
citation-role summary
background 5
citation-polarity summary
roles
background 5polarities
background 5representative citing papers
Two-loop all-plus helicity amplitudes for self-dual Higgs plus gluons are obtained via four-dimensional unitarity cuts into one-loop and tree amplitudes plus finite-field tensor reduction.
Leading-colour two-loop virtual amplitudes for ttbar+jet are extracted analytically via finite-field evaluations and differential equations, then packaged in a C++ library with new numerical integration techniques.
Kira 2.0 implements finite-field coefficient reconstruction for IBP reductions and improved user-equation handling, yielding lower memory use and faster performance on state-of-the-art problems.
First numerical evaluation of planar two-loop helicity amplitudes for W-boson plus four partons using finite-field reduction and sector decomposition on a subset of master integrals.
Analytic expressions for the finite remainders of two-loop leading-color helicity amplitudes in Higgs plus two-jet production are obtained in the heavy-top effective theory using numerical unitarity and a new partial-fraction algorithm.
A closed formula computes static post-Newtonian corrections at arbitrary odd orders in gravity, yielding the explicit seventh post-Newtonian potential that matches an independent diagrammatic method.
citing papers explorer
-
The spectrum of Feynman-integral geometries at two loops
Two-loop Feynman integrals involve Riemann spheres, elliptic curves, hyperelliptic curves of genus 2 and 3, K3 surfaces, and a rationalizable Del Pezzo surface of degree 2.
-
Two-loop all-plus helicity amplitudes for self-dual Higgs boson with gluons via unitarity cut constraints
Two-loop all-plus helicity amplitudes for self-dual Higgs plus gluons are obtained via four-dimensional unitarity cuts into one-loop and tree amplitudes plus finite-field tensor reduction.
-
Double virtual QCD corrections to $t\bar{t}+$jet production at the LHC
Leading-colour two-loop virtual amplitudes for ttbar+jet are extracted analytically via finite-field evaluations and differential equations, then packaged in a C++ library with new numerical integration techniques.
-
Integral Reduction with Kira 2.0 and Finite Field Methods
Kira 2.0 implements finite-field coefficient reconstruction for IBP reductions and improved user-equation handling, yielding lower memory use and faster performance on state-of-the-art problems.
-
A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons
First numerical evaluation of planar two-loop helicity amplitudes for W-boson plus four partons using finite-field reduction and sector decomposition on a subset of master integrals.
-
Two-loop leading-color QCD corrections for Higgs plus two-jet production in the heavy-top limit
Analytic expressions for the finite remainders of two-loop leading-color helicity amplitudes in Higgs plus two-jet production are obtained in the heavy-top effective theory using numerical unitarity and a new partial-fraction algorithm.
-
All-order structure of static gravitational interactions and the seventh post-Newtonian potential
A closed formula computes static post-Newtonian corrections at arbitrary odd orders in gravity, yielding the explicit seventh post-Newtonian potential that matches an independent diagrammatic method.