Abstract
We present a fast and efficient method for studying vacuum stability constraints in multi-scalar theories beyond the Standard Model. This method is designed for a reliable use in large scale parameter scans. The minimization of the scalar potential is done with the well-known polynomial homotopy continuation, and the decay rate of a false vacuum in a multi-scalar theory is estimated by an exact solution of the bounce action in the one-field case. We compare to more precise calculations of the tunnelling path at the tree- and one-loop level and find good agreement for the resulting constraints on the parameter space. Numerical stability, runtime and reliability are significantly improved compared to approaches existing in the literature. This procedure is applied to several phenomenologically interesting benchmark scenarios defined in the Minimal Supersymmetric Standard Model. We utilize our efficient approach to study the impact of simultaneously varying multiple fields and illustrate the importance of correctly identifying the most dangerous minimum among the minima that are deeper than the electroweak vacuum.
Highlights
Instability occurs at scales 1010 GeV with a lifetime that is significantly larger than the age of the universe
We present a fast and efficient method for studying vacuum stability constraints in multi-scalar theories beyond the Standard Model
In this paper we present an approach that provides a highly efficient and reliable evaluation of the constraints from vacuum stability such that they can be incorporated into beyond the SM (BSM) parameter scans, which typically run over a large number of points in a multi-dimensional parameter space
Summary
The vacuum state of a (quantum) field theory is determined by the state of lowest potential energy. The totally symmetric coefficient tensors λabcd, Aabc, m2ab and ta as well as the constant c contain all possible real coefficients with non-negative mass dimension This potential includes in general up to 3n stationary points. The second minimum exists as soon as (A(φ))2 > 32 m2(φ)λ(φ) 9 and is deeper than the minimum at the origin if (2.7) This discussion implies that large cubic terms A compared to the mass parameters and self-couplings are potentially dangerous for the stability of the initial vacuum at the origin. Another subtlety is that PHC only finds point-like, isolated solutions This is especially important in the physically interesting cases of gauge theories where any vacuum is only unique up to gauge transformations. For the case of at least one Higgs doublet this can be achieved by setting the charged and imaginary components of one Higgs doublet to zero without loss of generality
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