ИСТИНА

Differential equations are used to evaluate master integrals for several families of Feynman integrals. Analytical results are obtained for all the master integrals of two families of massless Feynman integrals with two external momenta on the light cone associated with three-point four-loop non-planar graphs. Using these results, the four-loop contributions to the photon quark and Higgs quark form factors involving two closed fermion loops are analytically evaluated. 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. An analytical result is obtained also for a three-loop coordinate-space integral which place the central role in the three-loop computation of the conformal four-point correlation function in the so-called bi-scalar CFT, an integrable four-dimensional theory obtained in a special limit of twisted N=4 SYM.