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In Veltman's original view, the Higgs particle mass Mh was naturally large thus marking a second threshold in weak interactions, as with the W mass and the non-renormalizable 4-fermion V--A theory. Besides, with a large Mh, Spontaneous Symmetry Breaking (SSB) would essentially be determined by the pure scalar sector regardless of the other sectors of the theory. Surprisingly, this picture is not completely ruled out. In fact, if SSB in -4 theories is a weak first-order phase transition, as indicated by most recent lattice simulations, in addition to the known resonance with mass Mh ~ 125 GeV, there might be a heavier excitation with mass M² h ~ m² h ln(s=Mh), where Λs is the ultraviolet cutoff of the scalar sector. The larger Mh controls vacuum stability and, differently from Mh, would remain finite in units of the weak scale h-i ~ 246:2 GeV when Λs ! 1. Lattice simulations of the propagator performed in the 4D Ising limit of the theory are consistent with this two-mass structure and lead to the estimate Mh ~ 700 GeV. In spite of its large mass, however, the heavier state would couple to longitudinal vector bosons with the same typical strength of the low-mass state and would thus represent a relatively narrow resonance. In this way, such hypothetical resonance would naturally fit with some excess of 4-lepton events observed by ATLAS around 680 GeV. Analogous data from CMS are needed to confirm or disprove this interpretation. Finally, the effect of a two-mass structure on radiative corrections is discussed in connection with the value of αs(MZ) from e+e- → hadrons. [ABSTRACT FROM AUTHOR]

As in boiling super-heated liquid, first-order phase transitions in QFT arise from an abrupt decay of an excited state of false vacuum into an energetically more favorable minimum of energy through bubble nucleation. We review an efficient semi-analytical approach to compute such a tunneling decay rate with any number of scalar fields and space-time dimensions. It is based on exact analytical solutions of piece-wise linear potentials with an arbitrary number of segments that describe any given potential up to the desired precision. Contributions beyond the linear order as well as the generalization to more fields are considered and computed through analytical linear expansions within a few iterations. Thereby, this approach provides a fast and robust method for evaluating tunneling decay in theories with multiple scalar fields. [ABSTRACT FROM AUTHOR]