Numerical Regularization for 4-loop Self-Energy Feynman Diagrams

In recent work we computed 4-loop integrals for self-energy diagrams with 11 massive internal lines. Presently we perform numerical integration and regularization for diagrams with 8 to 11 lines, while considering massive and massless cases. For dimensional regularization, a sequence of integrals is computed depending on a parameter ( ε ) that is incorporated via the space-time dimension, and approaches zero. We consider diagrams where the leading term in the expansion is in 1/ ε 2 or in 1/ ε or finite. The numerical integration methods include non-adaptive – double exponential, and Quasi-Monte Carlo methods with composite lattice rules implemented in CUDA C for acceleration on GPUs. The leading term coefficients in the integral expansion are obtained via linear or nonlinear extrapolation as ε tends to zero.