Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph
By A. Primo, L. Tancredi. 2017
146 citations recorded by the source corpus.
Abstract We consider the calculation of the master integrals of the three-loop massive banana graph. In the case of equal internal masses, the graph is reduced to three master integrals which satisfy an irreducible system of three coupled linear differential equations. The solution of the system requires finding a 3 × 3 matrix of homogeneous solutions. We show how the maximal cut can be used to determine all entries of this matrix in terms of products of elliptic integrals of first and second kind of suitable arguments. All independent solutions are found by performing the integration which defines the maximal cut on different contours. Once the homogeneous solution is known, the inhomogeneous solution can be obtained by use of Euler's variation of constants.
Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/2c0dc70e0f56ff306e25a0aec69c75685b4da139
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In Nuclear and High Energy Physics
- Hjalte Frellesvig
- Bernhard Mistlberger
- Costas G. Papadopoulos
- Gudrun Heinrich
- Claude Duhr
- Valentin Hirschi
- Olivier Mattelaer
- Cms Collaboration
In Statistical and Nonlinear Physics
Citations in the corpus
- Higgs boson production at hadron colliders at N3LO in QCD (2018, background): “[75, 76] it was demonstrated how one can find a solution for a coupled homogeneous part of a system differential equations for Feynman integrals.”
- Cuts of Feynman Integrals in Baikov representation (2017, background): “4For related work see [72, 73, 74, 75, 76, 77] 5A Mathematica script, Baikov.”