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.
We briefly sketch a proof concerning the structure of the all-order epsilon-expansions of generalized hypergeometric functions with special sets of parameters.
We prove the following theorems: 1) The Laurent expansions in epsilon of the Gauss hypergeometric functions 2F1(I_1+a*epsilon, I_2+b*epsilon; I_3+p/q + c epsilon; z), 2F1(I_1+p/q+a*epsilon, I_2+p/q+b*epsilon; I_3+ p/q+c*epsilon;z), 2F1(I_1+p/
q+a*epsilon, I_2+b*epsilon; I_3+p/q+c*epsilon;z), where I_1,I_2,I_3,p,q are arbitrary integers, a,b,c are arbitrary numbers and epsilon is an infinitesimal parameter, are expressible in terms of multiple polylogarithms of q-roots of unity with coefficients that are ratios of polynomials; 2) The Laurent expansion of the Gauss hypergeometric function 2F1(I_1+p/q+a*epsilon, I_2+b*epsilon; I_3+c*epsilon;z) is expressible in terms of multiple polylogarithms of q-roots of unity times powers of logarithm with coefficients that are ratios of polynomials; 3) The multiple inverse rational sums (see Eq. (2)) and the multiple rational sums (see Eq. (3)) are expressible in terms of multiple polylogarithms; 4) The generalized hypergeometric functions (see Eq. (4)) are expressible in terms of multiple polylogarithms with coefficients that are ratios of polynomials.
