#11 Can the A4 Three-Higgs doublet model kill Maxwell's equations? - Possibility of charge-breaking minima in Three-Higgs doublets with an A4 symmetry

In the Standard Model (SM) of particle physics, the conservation of electric charge (without which Electromagnetism is destroyed and Maxwell’s Equations cease to be valid) is guaranteed.

On the other hand, in Three Higgs Doublet Models (3HDM) – which can be very interesting for explanations of Dark Matter or antimatter asymmetry – charge-breaking minima can coexist with neutral minima, and this possibility must be avoided at all costs. The A4 symmetry imposed on the 3HDM substantially reduces its number of free parameters, increasing the predictivity of the model – can charge-breaking minima occur in this specific model? Can they coexist with neutral minima? If so, for what regions of parameter space does that happen?

This project consists in minimizing – analytically at first, numerically afterwards – the 3HDM A4 potential, and analyzing its possible minima, comparing their depths. If successful, it may well lead to a journal publication.

Requirements: Good dominion of numerical skills (Python or Matlab, for instance)