3HDM with softly broken $$\Delta (54)$$ and $$\Sigma (36)$$

Abstract We perform an analysis of the scalar sector of 3 Higgs Doublet Models with softly broken $$\Delta (54)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mo>(</mml:mo> <mml:mn>54</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and $$\Sigma (36)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Σ</mml:mi> <mml:mo>(</mml:mo> <mml:mn>36</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> symmetries. We consider the various vacuum expectation value alignments and consider, for each, softly broken terms that deviate the alignment. We check the evolution of the minima, present analytical and numerical results for the lifting of the degeneracies of the physical eigenstates, and describe the decays of the states considering any residual symmetries.