On the metastability of the Standard Model

Sammanfattning: With the discovery of a particle consistent with the Standard Model (SM) Higgs at the Large Hadron Collider (LHC) at CERN in 2012, the final ingredient of the SM has been found. The SM provides us with a powerful description of the physics of fundamental particles, holding up at all energy scales we can probe with accelerator based experiments. However, astrophysics and cosmology show us that the SM is not the final answer, but e.g. fails to describe dark matter and massive neutrinos. Like any non-trivial quantum field theory, the SM must be subject to a so-called renormalization procedure in order to extrapolate the model between different energy scales. In this context, new problems of more theoretical nature arise, e.g. the famous hierarchy problem of the Higgs mass. Renormalization also leads to what is known as the metastability problem of the SM: assuming the particle found at the LHC is the SM Higgs boson, the potential develops a second minimum deeper than the electroweak one in which we live, at energy scales below the Planck scale. Absolute stability all the way up to the Planck scale is excluded at a confidence level of about 98 %. For the central experimental SM values the instability occurs at scales larger than ~ 10¹⁰ GeV. One can take two viewpoints regarding this instability: assuming validity of the SM all the way up to the Planck scale, the problem does not necessarily lead to an inconsistency of our existence. If we assume our universe to have ended up in the electroweak minimum after the Big Bang, the probability that it would have transitioned to its true minimum during the lifetime of the universe is spectacularly small.  If we on the other hand demand absolute stability, new physics must modify the SM at or below the instability scale of ~ 10¹⁰ GeV, and we can explore which hints the instability might provide us with on this new physics. In this work, the metastability problem of the SM and possible implications are revisited. We give an introduction to the technique of renormalization and apply this to the SM. We then discuss the stability of the SM potential and the hints this might provide us with on new physics at large scales.