Transformed Lattice Rules for Feynman Loop Integrals on GPUs

Abstract

We focus on the application of rank-1 lattice rules with tanh and sinm type transformations for the integration of functions which may have singularities on the boundaries of the integration domain. Using this technique we compute Feynman loop integrals for classes of 2-loop box and 3-loop self-energy Feynman diagrams that have up to eight internal lines with masses. The d-dimensional rule approximation with n points relies on a generator vector of length d with integer components, which is computed once and for all using the Component-by-Component method by Nuyens and Cools (2006). The generator vector is incorporated in the (CUDA) integration program that implements the lattice integration for fast execution on GPUs. Results are obtained efficiently and without special attention to specific problem characteristics.