Related papers: Computable conditions for order-2 $CP$ symmetry in…
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…
Conditions for CP violation in the scalar potential sector of general N-Higgs-doublet models (NHDMs) are analyzed from a group theoretical perspective. For the simplest two-Higgs-doublet model (2HDM) potential, a minimum set of conditions…
Symmetries of the Two-Higgs-Doublet Model (2HDM) potential that can be extended to the whole Lagrangian, i.e. the CP-symmetries CP1, CP2, CP3 and the Higgs-family symmetries Z2, U(1) and SO(3) are discussed. Sufficient and necessary…
CP-odd invariants provide a basis independent way of studying the CP properties of Lagrangians. We propose powerful methods for constructing basis invariants and determining whether they are CP-odd or CP-even, then systematically construct…
We discuss the CP properties of the potential in the general Two-Higgs-Doublet Model (THDM). This is done in a concise way using real gauge invariant functions built from the scalar products of the doublet fields. The space of these…
We present a simple and transparent method to study custodial symmetry in the Two-Higgs-Doublet Model. The method allows to formulate the basis independent, sufficient and necessary, conditions for the custodial symmetry of the scalar…
When building CP-symmetric models beyond the Standard Model, one can impose CP-symmetry of higher order. This means that one needs to apply the CP-transformation more than two times to get the identity transformation, but still the model is…
In the two-Higgs-doublet model, different Higgs doublets can be viewed as components of a generic "hyperspinor". We decompose the Higgs potential of this model into irreducible representations of the SU(2) group of transformations of this…
Three-Higgs-doublet models (3HDM) allow for a novel, physically distinct form of CP invariance: CP symmetry of order 4 (CP4). Due to the large basis change freedom in 3HDM, it is imperative to recognize the presence of a possibly hidden CP4…
The scalar potential of the N-Higgs-doublet model (NHDM) is best analyzed not in the space of N complex doublets $\phi_a$ but in the $N^2$-dimensional space of real-valued bilinears constructed of $\phi_a^\dagger \phi_b$. In particular,…
We derive necessary and sufficient conditions for all global symmetries of the most general two Higgs doublet model (2HDM) scalar potential entirely in terms of reparametrization independent, i.e. basis invariant, objects. This culminates…
We discuss the three different classes of CP-symmetries that can be realized in a two-Higgs-doublet model, CP1, CP2 and CP3. We express conditions for realizing these symmetries in terms of masses and couplings of the model, thereby…
We derive basis-independent, necessary and sufficient conditions for the custodial symmetry in N-Higgs-doublet models (NHDM) for N > 2, and apply them on some 3HDM examples.
The most general Higgs potential of the two-Higgs-doublet model (2HDM) contains three squared-mass parameters and seven quartic self-coupling parameters. Among these, one squared-mass parameter and three quartic coupling parameters are…
We consider models with any number of Higgs doublets and study the conditions for decoupling. We show that, under very general circumstances, all the quadratic coefficients of the scalar potential must be present, except in special cases,…
We discuss how one can identify CP violation (and conservation) in multi-Higgs-doublet potentials. After a brief review of CP violation in the 2HDM, we refer to the fact that for NHDM with $N \geq 3$ the well known methods useful in the…
We study the conditions under which the CP violation in the quark mixing matrix can leak into the scalar potential of the real two-Higgs-doublet model (2HDM) via divergent radiative corrections, thereby spoiling the renormalizability of the…
CP-odd invariants are useful for studying the CP properties of Lagrangians in any basis. We explain how to build basis invariants for the scalar sector, and how to distinguish CP-odd invariants from CP-even invariants. Up to a certain…
In this paper, we present the novel analytical expressions for the bounded-from-below or the vacuum stability conditions of scalar potential for a general CP violating two-Higgs-doublet model by using the concepts of co-positivity and the…
In Two-Higgs-Doublet models, the conditions for CP violation can be expressed in terms of invariants under U(2) rotations among the two SU(2) Higgs doublet fields. In order to design a strategy for measuring the invariants we express them…