Seminarium "Teoria cząstek elementarnych i kosmologia"

The method of differential equations has become the standard avenue in the evaluation of multi-loop Feynman integrals. However for problems where so-called elliptic sectors appear, a general algorithm for solving analytically the differential equations has not been established yet. A numerical solution may be attempted nevertheless for Feynman integrals depending on few kinematic parameters. In this seminar I will review methods recently developed to numerically compute multi-loop integrals depending on one dimensionless scale. Such numerical approaches provide results well suited for fast numerical evaluation and sufficiently precise for phenomenological studies. I will discuss the application to the calculation of the higher order QCD corrections to B-meson decays.