Speaker
Description
The Higgs boson discovery raised new questions about the Standard Model's mysteries, particularly the existence of three matter generations with vastly different masses. New physics might be revealed through electron-positron collider experiments at specific energy levels, as the Standard Model serves as a foundation for examining nature across all scales .
An extended scalar sector enables a sharp first-order electroweak phase transition (FOPT). While the Standard Model with 125 GeV Higgs shows only smooth crossover, introducing new light scalar degrees of freedom—such as in two-Higgs-doublet models—can create a decisive first-order transition. Arnold's classification of simple singularities (A–D–E series) is extensively used in modern critical phenomena theory.
Groebner basis calculations showed that across the physically allowed parameter space: mS = 400 GeV – TeV, |sin θ| ≤ 0.3, a₂ = 1–8, b₄ > 0, with arbitrary Z₂-breaking b₁, b₃, a₁ within LHC bounds, the Milnor number remains stably μ = 9.
The result has several important implications:
a) Searching for exceptional E₆–E₈ singularities in the scalar sector beyond the Standard Model requires significantly more complicated models (additional singlets, triplets, higher representations, or explicit breaking of global symmetries);
b) The stability of μ = 9 explains the remarkable flatness of the potential along the singlet direction (the well-known “flat direction” in the Higgs portal), with cosmological consequences (inflation, strong first-order phase transitions, etc.);
c) The algebraic technique (Groebner bases + Milnor number) proves to be a powerful and universal tool for classifying critical points in multi-parameter field theories.
Thus, in real scalar extensions of the Standard Model with a single Z₂ singlet, the electroweak vacuum is always characterized by a composite singularity with Milnor number 9, which excludes it from belonging to the exotic simple A–D–E catastrophes, in particular to the theoretically most degenerate E₈.
