A short review of recent renormalization group analyses of the self-consistence of the Standard Model is presented.
Results of our recent re-analysis of the electroweak contribution to the relation between pole and running masses of top-quark within the Standard Model is reviewed. We argue, that if vacuum of SM is stable, then there exists an optimal value of reno
rmalization group scale (IR-point), at which the radiative corrections to the matching condition between parameters of Higgs sector and pole masses is minimal or equal to zero. Within the available accuracy, we find the IR-point to lie in an interval between value of Z-boson mass and twice the value of W-boson mass. The value of scale is relevant for extraction of Higgs self-coupling from cross-section as well as for construction of effective Lagrangian.
In this talk, we discuss the algorithm for the construction of analytical coefficients of higher order epsilon expansion of some Horn type hypergeometric functions of two variables around rational values of parameters.
We briefly discuss the transcendental constants generated through the epsilon-expansion of generalized hypergeometric functions and their interrelation with the sixth root of unity.
The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such functions with parameters whose values differ from the original ones by integers, is discussed
in the context of evaluating Feynman diagrams. Where this is possible, we compare our results with those obtained using standard techniques. It is shown that the criterion of reducibility of multiloop Feynman integrals can be reformulated in terms of the criterion of reducibility of hypergeometric functions. The relation between the numbers of master integrals obtained by differential reduction and integration by parts is discussed.
