The Higgs Boson at LHC and the Vacuum Stability of the Standard Model

Abstract

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.