Imposing magic conservation, equivalent to commutativity of the initial density matrix and the T-matrix, in 2-to-2 two-Higgs-doublet scattering yields SO(8) for arbitrary initial states and SU(2)_R for definite-isospin states.
Essential to this result is the fact that the initial state is a superposition of states of differing total isospin, as seen clearly in Eq
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Emergent symmetry in a two-Higgs-doublet model from quantum information and nonstabiliserness
Imposing magic conservation, equivalent to commutativity of the initial density matrix and the T-matrix, in 2-to-2 two-Higgs-doublet scattering yields SO(8) for arbitrary initial states and SU(2)_R for definite-isospin states.