Representation-theoretical characterization of canonical custodial symmetry in NHDM potentials
Abstract
By considering the basis-covariant constituents of N-Higgs-doublet potentials, we derive necessary and sufficient conditions for canonical SO(4)_C Custodial Symmetry (CS) of potentials with N>2 doublets, based on representation-theoretical and geometrical relations. In essence, our characterization relates the presence of canonical CS to basis-covariant vectors corresponding to particular bases of the defining representation of the orthogonal Lie algebras. For N=3,4 and 5, the conditions demand little computational effort to be evaluated, and we provide practical algorithms that may be efficiently implemented in a computer program, for deciding whether or not a potential is custodial-symmetric.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.05085
- arXiv:
- arXiv:2407.05085
- Bibcode:
- 2024arXiv240705085P
- Keywords:
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- High Energy Physics - Phenomenology;
- High Energy Physics - Theory;
- Mathematical Physics
- E-Print:
- 26 pages, minor modifications, matches published version