We discuss the lower Higgs boson mass bounds which come from the absolute stability of the Standard Model (SM) vacuum and from the Higgs inflation, as well as the prediction of the Higgs boson mass coming from asymptotic safety of the SM. We account for the 3-loop renormalization group evolution of the couplings of the Standard Model and for a part of two-loop corrections that involve the QCD coupling alpha_s to initial conditions for their running. This is one step above the current state of the art procedure ("one-loop matching--two-loop running"). This results in reduction of the theoretical uncertainties in the Higgs boson mass bounds and predictions, associated with the Standard Model physics, to 1-2 GeV. We find that with the account of existing experimental uncertainties in the mass of the top quark and alpha_s (taken at 2sigma level) the bound reads M_H>=M_min (equality corresponds to the asymptotic safety prediction), where M_min=129+-6 GeV. We argue that the discovery of the SM Higgs boson in this range would be in agreement with the hypothesis of the absence of new energy scales between the Fermi and Planck scales, whereas the coincidence of M_H with M_min would suggest that the electroweak scale is determined by Planck physics. In order to clarify the relation between the Fermi and Planck scale a construction of an electron-positron or muon collider with a center of mass energy ~200+200 GeV (Higgs and t-quark factory) would be needed.Comment: Version accepted in JHEP, including note added regarding theoretical end experimental results that appeared since the original version of the paper. Additional computer code can be found at http://www.inr.ac.ru/~fedor/SM

When calculating higher terms of the epsilon-expansion of massive Feynman diagrams, one needs to evaluate particular cases of multiple inverse binomial sums. These sums are related to the derivatives of certain hypergeometric functions with respect to their parameters. Exploring this connection and using it together with an approach based on generating functions, we analytically calculate a number of such infinite sums, for an arbitrary value of the argument which corresponds to an arbitrary value of the off-shell external momentum. In such a way, we find a number of new results for physically important Feynman diagrams. Considered examples include two-loop two- and three-point diagrams, as well as three-loop vacuum diagrams with two different masses. The results are presented in terms of generalized polylogarithmic functions. As a physical example, higher-order terms of the epsilon-expansion of the polarization function of the neutral gauge bosons are constructed.Comment: 54 pages, LaTeX, 2 eps figures; v4: some typos corrected; notations in Eqs.(C.7),(D.9), (E.3) improve

For certain dimensionally-regulated one-, two-and three-loop diagrams, problems of constructing the ε-expansion and the analytic continuation of the results are studied. In some examples, an arbitrary term of the ε-expansion can be calculated. For more complicated cases, only a few higher terms in ε are obtained. Apart from the oneloop two-and three-point diagrams, the examples include two-loop (mainly on-shell) propagator-type diagrams and three-loop vacuum diagrams. As a by-product, some new relations involving Clausen function, generalized log-sine integrals and certain Euler-Zagier sums are established, and some useful results for the hypergeometric functions of argument 1 4 are presented.

We have calculated the fermion contributions to the shift of the position of the poles of the massive gauge boson propagators at two-loop order in the Standard Model. Together with the bosonic contributions calculated previously the full two-loop corrections are available. This allows us to investigate the full correction in the relationship between MS and pole masses of the vector bosons Z and W . Two-loop renormalization and the corresponding renormalization group equations are discussed. Analytical results for the master-integrals appearing in the massless fermion contributions are given. A new approach of summing multiple binomial sums has been developed.1 real for arbitrary values of the Higgs-boson mass. In contrast, since the W -and Z-bosons decay, at leading order, into light fermion pairs, the light (massless) fermion corrections give rise to a non-zero imaginary part at the one loop level already. The problem of gauge (in)dependence of the complex pole has been extensively discussed in literature [2]. Only recently, two important results have been proven to all orders in perturbation theory: i) the position of the complex pole is a gauge independent quantity [3]; ii) the branching ratios and partial widths associated with the pole residues are gauge independent [4]. Moreover, it has been shown that the pole mass of the W-boson is an infrared finite quantity with respect to massless photonic corrections. An alternative proof of the infrared finiteness of the two-loop bosonic contributions to the pole of the gauge bosons was presented in I by explicite calculation. It is based on the fact that within dimensional regularization [5], in d = 4 − 2ε space-time dimensions, the singular 1/ε terms, which regularize both ultraviolet (UV) and infrared (IR) singularities, are absent after UV renormalization of the position of the pole in the propagators.In the present paper, besides from completing our previous calculation by including the missing fermion contributions, we will discuss in some detail general features and technical problems which are specifically related to these contributions.The paper is organized as follows. In Section 2 we briefly reconsider the definition of the pole-mass of the massive gauge-bosons within the SM and remind the reader of some notation given in I. The required analytical results for the massless fermion two-loop masterintegrals are presented in Section 3. In Section 4 we discuss the UV renormalization of the pole mass and the interrelation between our results and the one's familiar from the standard renormalization group approach. In particular, we performed several cross-checks of the singular 1/ε 2 -and 1/ε-terms. General aspects as well as numerical results for the finite parts are discussed in Section 5. Some technical details and a number of our analytical results will be presented in Appendices. In Appendix A we present a set of non-standard binomial sums which are needed for the ε-expansion of some of the hypergeometric functions entering the master-integrals. The one-loo...

The relationship between MS and pole masses of the vector bosons Z and W is calculated at the two-loop level in the Standard Model. We only consider the purely bosonic contributions which represent a gauge invariant subclass of diagrams. All calculations were performed in the linear R ξ gauge with three arbitrary gauge parameters utilizing the method of asymptotic expansions. The results are presented in analytic form as series in the small parameters sin 2 θ W and the mass ratio m 2 Z /m 2 H . We also present the corresponding on-shell mass counter-terms for the massive gauge bosons, which will be needed for the calculation of observables at two-loops in the on-shell renormalization scheme.