Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations
arXiv:1607.06427 · doi:10.1007/JHEP10(2016)115
Abstract
We evaluate a four-loop conformal integral, i.e. an integral over four four-dimensional coordinates, by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master integrals. To solve these linear differential equations we follow the strategy suggested by Henn and switch to a uniformly transcendental basis of master integrals. We find a solution to these equations up to weight eight in terms of multiple polylogarithms. Further, we present an analytical result for the given four-loop conformal integral considered in four-dimensional space-time in terms of single-valued harmonic polylogarithms. As a by-product, we obtain analytical results for all the other 212 master integrals within dimensional regularization, i.e. considered in D dimensions.
10 pages, 2 figures
References in corpus (6)
- Algorithm FIRE -- Feynman Integral REduction
- FIRE5: a C++ implementation of Feynman Integral REduction
- Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
- The massless higher-loop two-point function
- Iterative structure of finite loop integrals
- Non-planar master integrals for the production of two off-shell vector bosons in collisions of massless partons