Evaluating Feynman integrals by differential equations
by
Vladimir A. Smirnov(SINP, Moscow State University)
→
Europe/Berlin
313
313
Description
Differential equations are used to evaluate master integrals for families of Feynman integrals. The strategy based on a transition to a uniformly transcendental basis of master integrals is applied. A four-loop conformal integral, i.e. an integral over four
four-dimensional coordinates, is evaluated by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master integrals. A solution to these equations up to weight eight is found in terms of multiple
polylogarithms. An analytical result for the given four-loop conformal integral is obtained in terms of single-valued harmonic polylogarithms. The three-loop Feynman integral which was the last missing ingredient for the analytical evaluation of the three-loop quark static potential is evaluated with differential equations by introducing an auxiliary parameter $y$, which corresponds to the residual energy in some of the HQET propagators. Differential equations for the corresponding 109 master integrals are solved by turning to a uniformly transcendental basis, and boundary conditions are found from the asymptotic behaviour in the limit of large y. The original integral is recovered at y=0.
