Numerical Approach to Two-loop Three Point Functions with Masses

The calculation of loop integrals is essential to obtain the precise theoretical prediction for high-energy reactions. Loop integrals for oneloop diagrams can be expressed by logarithms and dilogarithms. For a class of higher order diagrams, compact analytic expressions are obtained. For instance, some two-loop two point functions with single mass(m) are given by functions of x = s/m. As two-loop diagrams in the electro-weak theory include complicated mass combinations, an analytic formula seems not available. In general, for the case with more than two independent dimensionless variables, it seems to be impossible to obtain a compact analytic formula by polylogarithms and so forth. In scattering processes, we have two or more invariants and in the electroweak theory we encounter diagrams with many different