Analytic Epsilon Expansions of Master Integrals Corresponding to Massless Three-Loop Form Factors and Three-Loop g-2 up to Four-Loop Transcendentality Weight
arXiv:1010.1334 · doi:10.1007/JHEP02(2011)102
Abstract
We evaluate analytically higher terms of the epsilon-expansion of the three-loop master integrals corresponding to three-loop quark and gluon form factors and to the three-loop master integrals contributing to the electron g-2 in QED up to the transcendentality weight typical to four-loop calculations, i.e. eight and seven, respectively. The calculation is based on a combination of a method recently suggested by one of the authors (R.L.) with other techniques: sector decomposition implemented in FIESTA, the method of Mellin--Barnes representation, and the PSLQ algorithm.
28 pages,4 figures
References in corpus (14)
- Algorithm FIRE -- Feynman Integral REduction
- Quark and gluon form factors to three loops
- HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters
- Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA)
- Sector Decomposition
- Resolution of singularities for multi-loop integrals
- On the Resolution of Singularities of Multiple Mellin-Barnes Integrals
- Revised value of the eighth-order electron g-2
- Group structure of the integration-by-part identities and its application to the reduction of multiloop integrals
- Nine-Propagator Master Integrals for Massless Three-Loop Form Factors
- Master Integrals for Fermionic Contributions to Massless Three-Loop Form Factors
- Calculating multiloop integrals using dimensional recurrence relation and D-analyticity
- Tenth-order lepton g-2: Contribution of some fourth-order radiative corrections to the sixth-order g-2 containing light-by-light-scattering subdiagrams
- Blowing up Feynman integrals