Two-loop integral reduction from elliptic and hyperelliptic curves
From MaRDI portal
Publication:2636285
DOI10.1007/JHEP12(2015)086zbMath1388.81391arXiv1507.06310MaRDI QIDQ2636285
Alessandro Georgoudis, Yang Zhang
Publication date: 31 May 2018
Published in: Journal of High Energy Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1507.06310
Feynman diagrams (81T18) Relationships between surfaces, higher-dimensional varieties, and physics (14J81)
Related Items (8)
f-ALGEBRAS THAT ARE EMBEDDABLE IN UNITAL f-ALGEBRAS ⋮ \(\varepsilon\)-factorized differential equations for two-loop non-planar triangle Feynman integrals with elliptic curves ⋮ Feynman integrals in dimensional regularization and extensions of Calabi-Yau motives ⋮ Elliptic Feynman integrals and pure functions ⋮ Differential equations on unitarity cut surfaces ⋮ Prescriptive unitarity for non-planar six-particle amplitudes at two loops ⋮ Positive semidefinite forms over totally ordered domains ⋮ Integration by parts identities in integer numbers of dimensions. A criterion for decoupling systems of differential equations
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The classification of two-loop integrand basis in pure four-dimension
- On genera of curves from high-loop generalized unitarity cuts
- FIRE4, LiteRed and accompanying tools to solve integration by parts relations
- Algorithm FIRE-Feynman integral reduction
- The elliptic dilogarithm for the sunset graph
- \texttt{Reduze} -- Feynman integral reduction in \texttt{C++}
- BOKASUN: A fast and precise numerical program to calculate the master integrals of the two-loop sunrise diagrams
- Precise numerical evaluation of the two loop sunrise graph master integrals in the equal mass case
- Global residues and two-loop hepta-cuts
- Critical points and number of master integrals
- Multivariate residues and maximal unitarity
- Analytic treatment of the two loop equal mass sunrise graph
- New recursion relations for tree amplitudes of gluons
- Generalized unitarity and one-loop amplitudes in \(\mathcal N=1\) super-Yang-Mills
- Two-loop sunset diagrams with three massive lines
- Reducing full one-loop amplitudes to scalar integrals at the integrand level
- Towards all-order Laurent expansion of generalised hypergeometric functions about rational values of parameters
- On the evaluation of sunset-type Feynman diagrams
- Numerical evaluation of the general massive 2-loop sunrise self-mass master integrals from differential equations
- Global structure of curves from generalized unitarity cut of three-loop diagrams
- An integrand reconstruction method for three-loop amplitudes
- Integrand-level reduction of loop amplitudes by computational algebraic geometry methods
- One-loop \(n\)-point gauge theory amplitudes, unitarity and collinear limits.
- On the integrand-reduction method for two-loop scattering amplitudes
- A new algorithm for the generation of unitarity-compatible integration by parts relations
- On the evaluation of a certain class of Feynman diagrams in \(x\)-space: sunrise-type topologies at any loop order
- A second-order differential equation for the two-loop sunrise graph with arbitrary masses
- Schouten identities for Feynman graph amplitudes: The Master Integrals for the two-loop massive sunrise graph
- A novel approach to integration by parts reduction
- HIGH-PRECISION CALCULATION OF MULTILOOP FEYNMAN INTEGRALS BY DIFFERENCE EQUATIONS
- The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms
- Elliptic integral evaluations of Bessel moments and applications
- The two-loop sunrise graph with arbitrary masses
- The two-loop sunrise integral around four space-time dimensions and generalisations of the Clausen and Glaisher functions towards the elliptic case
- Multiloop integrand reduction for dimensionally regulated amplitudes
This page was built for publication: Two-loop integral reduction from elliptic and hyperelliptic curves
