Efficient GPU Integration for Multi-loop Feynman Diagrams with Massless Internal Lines

Abstract

We compute Feynman loop integrals or expansion coefficients for sets of self-energy diagrams with massless internal lines and which give rise to either finite integral values or UV-divergences. In case of UV-divergence, dimensional regularization can be implemented using a linear extrapolation as the dimensional regularization parameter tends to zero. The numerical integration is performed with lattice and composite lattice rules combined with a transformation to alleviate boundary singularities, and implemented in CUDA C. The GPU results are accurate and efficient in execution time compared to other numerical methods and architectures.