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Computable conditions for order-2 $CP$ symmetry in NHDM potentials
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abstract
We derive necessary and sufficient conditions for order-2 $CP$ ($CP2$) symmetry in $N$-Higgs-doublet potentials for $N>2$. The conditions, which are formulated as relations between vectors that transform under the adjoint representation of $\mathsf{SU}(N)$ under a change of doublet basis, are representation theoretical in nature. Making use of Lie algebra and representation theory we devise an efficient, computable algorithm which may be applied to decide whether or not a given numerical potential is $CP2$ invariant.
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Scalar Lie point symmetries of the Standard Model with one or two real gauge singlets
SM+S has four and SM+2S has eleven inequivalent maximal scalar Lie point symmetry algebras of the field equations, with parameter-based algorithms to identify them.
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