Higgs vacuum decay and implications for the Standard Model

Abstract

The confirmed discovery of the Higgs boson in 2012 raises some intriguing cosmological questions about the fate of the false vacuum and what this means for the Standard Model. Quantum field theory allows for the existence of metastable fields where a potential develops a lower energy state, or true vacuum, at large field values where the energy is lower than its local minimum, or false vacuum, value. The most recent measurements of the Higgs and top masses suggest this is the case for the Higgs potential. A phase transition may occur through the process of quantum tunnelling, resulting in the nucleation of a rapidly expanding true vacuum bubble on a false vacuum background. Such a bubble may have devastating consequences for the universe if it expands to cover all of space. The fact that this has clearly not yet happened allows us to put constraints on our model for vacuum decay and provides insight into Beyond Standard Model physics. Using methods from Euclidean field theory, we find the tunnelling rates of toy model potentials as well as a close approximation to the Higgs in various spacetimes. We first investigate tunnelling in asymptotically at space before applying a similar method to false vacuum decay in de Sitter space, also incorporating the effects of back reaction. Two different potentials are considered to investigate vacuum decay in a Randall-Sundrum braneworld: a quartic potential with two well defined vacua, and a Higgs-like potential closely approximating the Higgs at high energies. Vacuum decay is studied for fields living on a 4-dimensional brane in RS2, and the presence of a fifth dimension is found to have little infuence on the decay rate. We further use these potentials to look at the case of vacuum decay seeded by the presence of a black hole in five dimensions. By comparing the tunnelling rate with the Hawking evaporation, it is found that small black holes at high energy scales can catalyse vacuum decay. The energy scales needed to form such black holes may potentially be reached in the most energetic of cosmic ray collisions. Finally, we look at the negative modes of O(4) and black hole instantons and find that instantons seeded by a black hole characteristically have a single negative mode. For O(4) instantons at energies close to the Planck scale, an infinite stack of negative modes arises, raising the question of how this is to be interpreted.