Implications of the discovery of a Higgs boson with a mass of 125 GeV

The discovery of a Higgs-like particle by the ATLAS and CMS experiments at the LHC has been a major event for particle physics. The rather precise knowledge of the mass of the Higgs boson and of its couplings to the other Standard Model elds has important consequences for the physical phenomena taking place at the Fermi scale of electroweak symmetry breaking. We will analyze some of these implications in the most motivated frameworks for physics at that scale { supersymmetry, models of a composite Higgs boson, and the Standard Model itself. At the same time, precision experiments in avour physics require a highly non-generic structure of avour and CP transitions. This is relevant to any model of electroweak symmetry breaking with a relatively low scale of new phenomena, motivated by naturalness, where some mechanism has to be found in order to keep unwanted avour e ects under control. We will discuss in particular the consequences of the approximate U(2)3 symmetry exhibited by the quarks of the Standard Model. The combined analysis of the indirect constraints from avour, Higgs and electroweak physics will allow us to outline a picture of some most natural models of physics at the Fermi scale. This is particularly interesting in view of the forthcoming improvements in the direct experimental investigation of the phenomena at that energies. Although non trivially, a few models emerge that look capable of accommodating a 125 GeV Higgs boson, consistently with all the other constraints, with new particles in an interesting mass range for discovery at the LHC, as well as associated avour signals. Finally, the measurement of the last parameter of the Standard Model { the Higgs quartic coupling { has important consequences even if no new physics is present close to the Fermi scale: its near-critical value, which puts the electroweak vacuum in a metastable state close to a phase transition, may have an interesting connection with Planck-scale physics. We derive the bound for vacuum stability with full two-loop precision and use it to explore some possible scenarios of near-criticality.