arXiv subjects

R. Plantey

Publications and source records attributed to R. Plantey.

4 recordsLinked to original sources

arXiv2024

Representation-theoretical characterization of canonical custodial symmetry in NHDM potentials

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.

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arXiv2024

Computable conditions for order-2 $CP$ symmetry in NHDM potentials

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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arXiv2023

Weinberg's 3HDM potential with spontaneous CP violation

We study the potential of Weinberg's $\mathbb{Z}_2\times\mathbb{Z}_2$-symmetric three-Higgs-doublet model (3HDM). The potential is designed to accommodate CP violation in the scalar sector within a gauge theory, while at the same time allowing for natural flavour conservation. This framework allows for both explicit and spontaneous CP violation. CP can be explicitly violated when the coefficients of the potential are taken to be complex. With coefficients chosen to be real, CP can be spontaneously violated via complex vacuum expectation values (vevs). In the absence of the terms leading to the possibility of CP violation, either explicit or induced by complex vevs, the potential has two global U(1) symmetries. In this case, spontaneous symmetry breaking would in general give rise to massless states. In a realistic implementation, those terms must be included, thus preventing the existence of Goldstone bosons. A scan over parameters, imposing the existence of a neutral state at 125 GeV that is nearly CP-even shows that, in the absence of fine-tuning, the scalar spectrum contains one or two states with masses below 125 GeV that have a significant CP-odd component. These light states would have a low production rate via the Bjorken process and could thus have escaped detection at LEP. At the LHC the situation is less clear. While we do not here aim for a full phenomenological study of the light states, we point out that the $γγ$ decay channel would be challenging to measure because of suppressed couplings to $WW$.

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arXiv2022

Light scalars in the Weinberg 3HDM potential with spontaneous CP violation

The $\mathbb Z_2\times \mathbb Z_2$-symmetric 3HDM potential, sometimes called Weinberg's 3HDM potential, can accommodate both explicit and spontaneous CP violation as well as natural flavour conservation and is hence relevant for studies of CP violation coming from a realistic extended Higgs sector. The model has an interesting regime, controlled by a single parameter, where it acquires an approximate global $U(1) \times U(1)$ symmetry which causes CP violating effects to be small and two pseudo-Goldstone bosons to be present in the scalar spectrum. From parameter space scans, we find that, in a realistic implementation featuring an SM-like Higgs boson, this model predominantely leads to the existence of light additional Higgs bosons with a mass lower than the SM-like Higgs boson.

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