Large-Field Vacuum Decay in General Multi-Scalar Theories

Abstract

Many theories beyond the standard model exhibit multiple scalar particles. Such multi-scalar theories can in principle host lower-energy vacua, and thus predict that our universe has a finite lifetime due to false vacuum decay. This scenario cannot be ruled out a priori as even the standard model's electroweak vacuum has been shown to be metastable; however, for theoretical consistency, we still require that the model does not predict a lifetime much smaller than the age of the universe. The calculation of these tunneling rates at leading order for multi-scalar theories typically includes numerical approaches, or approximations which are frequently not analytically controlled. In this article we show that, in the large-field regime, a one-dimensional radial bounce always produces the exact dominant contribution to the leading order tunneling rate, with corrections being exponentially suppressed. This allows us to write simple analytical expressions to calculate the tunneling rate in multi-scalar theories, in terms of an effective quartic coupling $λ_\text{eff}$. For theories with biquadratic scalar potentials, we also derive straightforward analytical expressions for $λ_\text{eff}$ in terms of the original theory's couplings. Finally, we provide example applications of our results to study the vacuum stability of the 2HDM+a model and the 3-3-1 model.