We study the naturalness properties of the B − L Supersymmetric Standard Model (BLSSM) with Type-I seesaw and compare them to those of the Minimal Supersymmetric Standard Model (MSSM) at both low (i.e., Large Hadron Collider) energies and high (i.e., unification) scales. By adopting standard measures of naturalness, we assess that, in presence of full unification of the additional gauge couplings and scalar/fermionic masses of the BLSSM, such a scenario reveals a somewhat higher degree of Fine-Tuning (FT) than the MSSM, when the latter is computed at the unification scale and all available theoretical and experimental constraints, but the Dark Matter (DM) ones, are taken into account. Yet, such a difference, driven primarily by the collider limits requiring a high mass for the gauge boson associated to the breaking of the additional U (1) B−L gauge group of the BLSSM in addition to the SU (3) C × SU (2) L × U (1) Y of the MSSM, should be regarded as a modest price to pay for the former in relation to the latter, if one notices that the non-minimal scenario offers a significant volume of parameter space where numerous DM solutions of different compositions can be found to the relic density constraints, unlike the case of the minimal structure, wherein only one type of solution is accessible over an ever diminishing parameter space. In fact, this different level of tension within the two SUSY models in complying with current data is well revealed when the FT measure is recomputed in terms of the low energy spectra of the two models, over their allowed regions of parameter space now in presence of all DM bounds, as it is shown that the tendency is now opposite, the BLSSM appearing more natural than the MSSM. Contents 1 Introduction 1 2 The B − L Supersymmetric Standard Model 3 3 Renormalisation Group Equations 7 4 Collider and Dark Matter Constraints 10 5 Fine-Tuning Measures 13 6 Results 15
We explore alternative descriptions of the charged lepton sector in modular invariant models of lepton masses and mixing angles. In addition to the modulus, the symmetry breaking sector of our models includes ordinary flavons. Neutrino mass terms depend only on the modulus and are tailored to minimize the number of free parameters. The charged lepton Yukawa couplings rely upon the flavons alone. We build modular invariant models at levels 4 and 5, where neutrino masses are described both in terms of the Weinberg operator or through a type I seesaw mechanism. At level 4, our models reproduce the hierarchy among electron, muon and tau masses by letting the weights play the role of Froggatt-Nielsen charges. At level 5, our setup allows the treatment of left and right handed charged leptons on the same footing. We have optimized the free parameters of our models in order to match the experimental data, obtaining a good degree of compatibility and predictions for the absolute neutrino masses and the CP violating phases. At a more fundamental level, the whole lepton sector could be correctly described by the simultaneous presence of several moduli. Our examples are meant to make a first step in this direction. arXiv:1908.11867v1 [hep-ph] 30 Aug 2019 Recently, modular invariance has been invoked as candidate flavour symmetry [10]. In its simplest implementation a unique complex field, the modulus, acts as symmetry breaking parameter, thus simplifying the vacuum alignment problem. Modular invariance, in the limit of exact supersymmetry, completely determines the Yukawa couplings, to any order of the expansion in powers of the modulus. Moreover, neutrino masses, mixing angles and phases are all related to each other and, in minimal models, depend only on a few parameters. The formalism has been extended to consistently include CP transformations [11] 1 and it can involve several moduli [16,17]. The idea that Yukawa couplings are determined by a set of moduli is clearly not new, and has been naturally realized in the context of string theory [18][19][20][21][22], in D-brane compactification [23][24][25][26][27][28][29], in magnetized extra dimensions [30][31][32], and in orbifold compactification [33][34][35][36]. Modular invariance has also been incorporated in early flavour models [37][38][39][40][41]. However, the main advantage of the recent approach is that it can be implemented in a bottom-up perspective, relying on the group transformation properties of modular forms of given weight and level. Several models of lepton masses and mixing angles have been built at level 2 [42, 43], 3 [10, 44-47], 4 [48-50] and 5 [51,52]. Extensions to quarks [53,54] and to grand unified theories [55,56] have also been proposed. In most of the existing constructions, there is a unique symmetry breaking parameter: the modulus itself. While this scenario is certainly appealing since it minimizes the symmetry breaking sector, it does not yet provide a convincing explanation of the charged lepton masses. The mass hierarchy is achieved by...
We show how quark and lepton mass hierarchies can be reproduced in the framework of modular symmetry. The mechanism is analogous to the Froggatt-Nielsen (FN) mechanism, but without requiring any Abelian symmetry to be introduced, nor any Standard Model (SM) singlet flavon to break it. The modular weights of fermion fields play the role of FN charges, and SM singlet fields with non-zero modular weight called weightons play the role of flavons. We illustrate the mechanism by analysing A4 (modular level 3) models of quark and lepton (including neutrino) masses and mixing, with a single modulus field. We discuss two examples in some detail, both numerically and analytically, showing how both fermion mass and mixing hierarchies emerge from different aspects of the modular symmetry.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.