Geometric minimization of highly symmetric potentials

Abstract

In non-minimal Higgs mechanisms, one often needs to minimize highly symmetric Higgs potentials. Here we propose a geometric way of doing it, which, surprisingly, is often much more efficient than the usual method. By construction, it gives the global minimum for any set of free parameters of the potential, thus offering an intuitive understanding of how they affect the vacuum expectation values. For illustration, we apply this method to the S_4 and A_4-symmetric three-Higgs-doublet models. We find that at least three recent phenomenological analyses of the A_4-symmetric model used a local, not the global minimum. We discuss coexistence of minima of different types, and comment on the mathematical origin of geometrical CP-violation and on a new symmetry linking different minima.

18 pages, 3 figures; v2: corrected comments on Ref.[7]; v3: minor modifications, matches the published version

References in corpus (4)

• A_4 model for the quark mass matrices
• Properties of the general NHDM. II. Higgs potential and its symmetries
• Three-Higgs-doublet model with $A_4$ symmetry
• Frustrated symmetries in multi-Higgs-doublet models

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