  The main aim of this work is to study the conditions of absolute vacuum
stability within the Standard Model (SM) by the knowledge of the behaviour of
the Higgs quartic coupling up to high energy scales and using the new data on
the Higgs mass given by ATLAS and CMS as an input parameter. The Higgs mass
value observed by ATLAS and CMS leads to a negative value of the quartic
coupling, making metastable the vacuum of the Standard Model, as it is seen by
the renormalization group improved (RGI) effective potential. The stability
status of SM crucially depends upon the precise values of the top and Higgs
masses, a more precision determination of those masses and related
uncertainties can modify drastically our conclusions about the SM stability
properties. For this reason, we have computed the vacuum bubbles and the Higgs
tadpole diagrams, at two-loop level of accuracy, in a renormalization scheme
proposed by A. Sirlin and R. Zucchini, where the input parameters are obtained
in terms of physical observables related with muon decay, and where the
threshold effects are included. In particular, we focus on the analytic
computation of the Higgs tadpoles contributions by two different methods. From
one side we have computed the sum of the tadpoles as the first derivative of
the two-loop Higgs 1PI effective potential in the Sirlin-Zucchini scheme, on
the other side we have checked the obtained result toward the direct
diagrammatic two- loop computation, by proposing a way of automatization of our
procedure based on the generation of Feynman diagrams, reduction of their
integrands and evaluation of scalar integrals and sum of all contributions in a
non-redundant way. We used the code TARCER that implements the Tarasov method
to reduce two-loop tensorial integrals.
