Contraction and decomposition matrices for vacuum diagrams

Abstract

Tensor reduction of vacuum diagrams uses contraction and decomposition matrices. We present general recurrence relations for the calculation of those matrices and an explicit formula for the 3-loop decomposition matrix and its determinant.

10 pages

References in corpus (3)

• The four-loop beta-function in Quantum Chromodynamics
• The 4-loop quark mass anomalous dimension and the invariant quark mass
• Beta functions and anomalous dimensions up to three loops