Flavor from the double tetrahedral group without supersymmetry: Flavorful axions and neutrinos

Abstract

We extend the work of Carone, Chaurasia and Vasquez on non-supersymmetric models of flavor based on the double tetrahedral group. Three issues are addressed: (1) the sector of flavorsymmetry-breaking fields is simplified and their potential studied explicitly, (2) a flavorful axion is introduced to solve the strong CP problem and (3) the model is extended to include the neutrino sector. We show how the model can accommodate the strong hierarchies manifest in the charged fermion Yukawa matrices, while predicting a qualitatively different form for the light neutrino mass matrix that is consistent with observed neutrino mass squared differences and mixing angles.The structure of the fermion Yukawa couplings in the standard model may result from the sequential breaking of a horizontal discrete family symmetry. Long ago, Aranda, Carone and Lebed [1, 2] showed how the double tetrahedral group T ′ could be used to construct successful supersymmetric flavor models that are similar to those based on U(2) symmetry [3,4], with or without the assumption of conventional supersymmetric grand unification. For other early work on T ′ as a flavor symmetry, see Ref. [5]. Many other authors have since explored the use of T ′ symmetry in models that aim to address the flavor structure of the standard model [6].Much of the work on T ′ flavor models has assumed weak-scale supersymmetry, to stabilize the hierarchy between the weak scale and the grand unified or Planck scale. Over the past decade, however, there has been no direct evidence for superpartners at the LHC, nor indirect evidence in the form of a convincing pattern of deviations from the predictions of the standard model for some subset of its observables. While one cannot exclude the possibility that supersymmetry is present and just beyond the reach of current experiments (a statement that applies to any new physics that has a decoupling limit), the current state of affairs has motivated a greater open-mindedness towards consideration of non-supersymmetric extensions of the standard model. For example, the possibility that the standard model could arise consistently from a string theory without supersymmetry has been discussed in Ref. [7].The hierarchies between mass scales might result from dynamical mechanisms (for example, cosmic relaxation [8] or Nnaturalness [9]), or anthropic selection [10]. On the other hand, the fundamental mass scales found in nature may simply be random and fine tuned, for reasons that are obscure to us at present. In this work, we assume the absence of supersymmetry and focus on phenomenological issues, while remaining agnostic on the question of naturalness.The purpose of the present work is to further explore the possibility of nonsupersymmetric models of flavor based on T ′ symmetry, following a study by Carone, Chaurasia and Vasquez [11]. In Ref. [11], a nonsupersymmetric T ′ model was presented in which the flavor scale M F was treated as a free parameter. (There is less motivation to link the flavor scale to a grand unified scale in a frame...

Lepton Flavour Symmetries

“…Being a subgroup of SU(2) with doublet representations, T contains the necessary ingredients to account for the (2+1) quark structure along the lines of U(2) models (Aranda et al, 2000a,b). On the other hand, as T contains the representations of A 4 , it also contains the ingredients necessary to reproduce the lepton observables along the lines of A 4 models (Aranda, 2007;Aranda et al, 2010;Carone et al, 2017;Carone and Merchand, 2019;Chen and Mahanthappa, 2007;Ding, 2008;Everett and Stuart, 2011;Feruglio et al, 2007;Frampton and Kephart, 2007;Frampton and Matsuzaki, 2009) In the presence of quark and leptons, one can aim at a flavour model compatible with gauge unification. In Grand Unified Theories such as SU(5), one family of SM fermions is unified into a 5 i + 10 i of SU(5): 5 i ∼ (l i , d c i ), 10 i ∼ (e c i , q i , u c i ).…”

Quark flavor phenomenology of the QCD axion

“…While in the simplest scenario PQ and FN symmetries are identified [53][54][55], PQ could also be a subgroup of a larger flavor symmetry; see, e.g., Refs. [56][57][58][59][60][61][62][63][64][65]. Finally, flavored PQ symmetries can arise also in the context of minimal-flavor violation (MFV) [66,67] or as accidental symmetries in models with gauged flavor symmetries [68][69][70][71].…”

Looking forward to lepton-flavor-violating ALPs

“…This would leave LFV decays as the main experimental signature to hunt for. Similarly, our updated LFV sensitivities will probe the parameter space of axion or relaxion models which try to address the flavor puzzle [36][37][38][39][40].…”