Higher-order scalar interactions and SM vacuum stability

Abstract

Investigation of the structure of the Standard Model effective potential at very large field strengths opens a window towards new phenomena and can reveal properties of the UV completion of the SM. The map of the lifetimes of the vacua of the SM enhanced by nonrenormalizable scalar couplings has been compiled to show how new interactions modify stability of the electroweak vacuum. Whereas it is possible to stabilize the SM by adding Planck scale suppressed interactions and taking into account running of the new couplings, the generic effect is shortening the lifetime and hence further destabilisation of the SM electroweak vacuum. These findings have been illustrated with phase diagrams of modified SM-like models. It has been demonstrated that stabilisation can be achieved by lowering the suppression scale of higher order operators while picking up such combinations of new couplings, which do not deepen the new minima of the potential. Our results show the dependence of the lifetime of the electroweak minimum on the magnitude of the new couplings, including cases with very small couplings (which means very large effective suppression scale) and couplings vastly different in magnitude (which corresponds to two different suppression scales).

The fate of the Higgs vacuum

“…We adopt the 'effective field theory' approach, and add extra polynomial terms to the potential which contain the mass scale of new physics, in this case the Planck mass [37][38][39] …”

The Higgs mass and the scale of new physics

“…In this appendix we briefly discuss estimates for the tunneling rates in the presence of a ∼ λ 6 ϕ 6 -term [64][65][66][67]. The tunnelling rate can be calculated by determining the Euclidean action of bubbles S E [ϕ bounce ], where ϕ bounce is the bounce solution of the Euclidean equations of motion for a real scalar field…”

Stability of the effective potential of the gauge-less top-Higgs model in curved spacetime

“…The issue of the stability of the Higgs potential in a flat spacetime (often under the assumption of no new physics up to the Planck scale) has been considered in many papers, see for example [1][2][3][4][5][6][7] and the references therein. However, the instability may affect cosmological evolution of the Universe and to take it into account one should couple the Standard Model (SM) Lagrangian to gravitational background.…”