Viability of minimal left–right models with discrete symmetries

Abstract

We provide a systematic study of minimal left-right models that are invariant under P , C, and/or CP transformations. Due to the high amount of symmetry such models are quite predictive in the amount and pattern of CP violation they can produce or accommodate at lower energies. Using current experimental constraints some of the models can already be excluded. For this purpose we provide an overview of the experimental constraints on the different left-right symmetric models, considering bounds from colliders, meson-mixing and low-energy observables, such as beta decay and electric dipole moments. The features of the various Yukawa and Higgs sectors are discussed in detail. In particular, we give the Higgs potentials for each case, discuss the possible vacua and investigate the amount of fine-tuning present in these potentials. It turns out that all left-right models with P , C, and/or CP symmetry have a high degree of fine-tuning, unless supplemented with mechanisms to suppress certain parameters. The models that are symmetric under both P and C are not in accordance with present observations, whereas the models with either P , C, or CP symmetry cannot be excluded by data yet. To further constrain and discriminate between the models measurements of B-meson observables at LHCb and B-factories will be especially important, while measurements of the EDMs of light nuclei in particular could provide complementary tests of the LRMs.

Analysis of fine-tuning measures in models with extended Higgs sectors

“…We solve these equations for a set of parameters to obtain the values of these parameters. Then we will use the Dekens measure [5] to identify the amount of fine-tuning in these equations. When using the Dekens measure, we split the set of parameters in two groups.…”

“…This then raises the questions: is one of these ways to apply the Dekens measure more appropriate than the other? Or does one have to check all cases and find the maximum, as done in [5]? To investigate this, we will turn to a simplified case where we can easily compare all the different scenarios.…”

“…Another measure of fine-tuning inspired by the Barbieri-Guidice measure has been considered in the study of left-right symmetric models [5]. In this measure, the relations between the parameters in the scalar potential are considered in all possible variations, using the equations that determine the minimum of the potential.…”

“…In this measure, the relations between the parameters in the scalar potential are considered in all possible variations, using the equations that determine the minimum of the potential. A conclusion of [5] was that several popular left-right symmetric models display a very large amount of fine-tuning. In contrast, we will reach a different conclusion in this paper.…”

Is left–right symmetry the key?

“…LR symmetries. It is easy to verify that the only realistic discrete LR symmetries, preserving the kinetic terms, are P and C, the generalised parity and chargeconjugation respectively, supplemented by the exchange of the left and right SU (2) gauge groups (for a recent discussion and references, see [12]). …”