Controlled flavor violation in the MSSM from a unified Δ(27)\Delta(27) flavor symmetry

We study the phenomenology of a unified supersymmetric theory with a flavor symmetry $\Delta(27)$. The model accommodates quark and lepton masses, mixing angles and CP phases. In this model, the Dirac and Majorana mass matrices have a unified texture zero structure in the $(1,1)$ entry that leads to the Gatto-Sartori-Tonin relation between the Cabibbo angle and ratios of the masses in the quark sectors, and to a natural departure from zero of the $\theta_{13}^\ell$ angle in the lepton sector. We derive the flavor structures of the trilinears and soft mass matrices, and show their general non-universality. This causes large flavor violating effects. As a consequence, the parameter space for this model is constrained, allowing it to be (dis)proven by flavor violation searches in the next decade. Although the results are model specific, we compare them to previous studies to show similar flavour effects (and associated constraints) are expected in general in supersymmetric flavor models, and may be used to distinguish them.Comment: 21 pages, 6 figure

Quasi-degenerate neutrinos and tri-bi-maximal mixing

Assuming high-energy tri-bi-maximal mixing we study the radiative running of leptonic mixing angles and obtain limits on the high-energy scale from requiring consistency with the observed mixing. We construct a model in which a non-Abelian discrete family symmetry leads both to a quasi-degenerate neutrino mass spectrum and to near tri-bi-maximal mixing.Comment: 7 pages, to appear in the proceedings of DISCRETE'0

Leptogenesis in Δ(27)\Delta(27) with a Universal Texture Zero

We investigate the possibility of viable leptogenesis in an appealing $\Delta(27)$ model with a universal texture zero in the (1,1) entry. The model accommodates the mass spectrum, mixing and CP phases for both quarks and leptons and allows for grand unification. Flavoured Boltzmann equations for the lepton asymmetries are solved numerically, taking into account both $N_1$ and $N_2$ right-handed neutrino decays. The $N_1$-dominated scenario is successful and the most natural option for the model, with $M_1 \in [10^9, 10^{12}]$ GeV, and $M_1/M_2 \in [0.002, 0.1]$, which constrains the parameter space of the underlying model and yields lower bounds on the respective Yukawa couplings. Viable leptogenesis is also possible in the $N_2$-dominated scenario, with the asymmetry in the electron flavour protected from $N_1$ washout by the texture zero. However, this occurs in a region of parameter space which has a stronger mass hierarchy $M_1/M_2 < 0.002$, and $M_2$ relatively close to $M_3$, which is not a natural expectation of the $\Delta(27)$ model.Comment: v2: 20 pages, 2 figures. Version accepted in JHE

Reactor mixing angle from hybrid neutrino masses

In terms of its eigenvector decomposition, the neutrino mass matrix (in the basis where the charged lepton mass matrix is diagonal) can be understood as originating from a tribimaximal dominant structure with small deviations, as demanded by data. If neutrino masses originate from at least two different mechanisms, referred to as "hybrid neutrino masses", the experimentally observed structure naturally emerges provided one mechanism accounts for the dominant tribimaximal structure while the other is responsible for the deviations. We demonstrate the feasibility of this picture in a fairly model-independent way by using lepton-number-violating effective operators, whose structure we assume becomes dictated by an underlying $A_4$ flavor symmetry. We show that if a second mechanism is at work, the requirement of generating a reactor angle within its experimental range always fixes the solar and atmospheric angles in agreement with data, in contrast to the case where the deviations are induced by next-to-leading order effective operators. We prove this idea is viable by constructing an $A_4$-based ultraviolet completion, where the dominant tribimaximal structure arises from the type-I seesaw while the subleading contribution is determined by either type-II or type-III seesaw driven by a non-trivial $A_4$ singlet (minimal hybrid model). After finding general criteria, we identify all the $\mathbb{Z}_N$ symmetries capable of producing such $A_4$-based minimal hybrid models.Comment: 18 pages, 5 figures. v3: section including sum rules added, accepted by JHE

Lepton Mixing and Cancellation of the Dirac Mass Hierarchy in SO(10) GUTs with Flavor Symmetries T7 and Sigma(81)

In SO(10) grand unified theories (GUTs) the hierarchy which is present in the Dirac mass term of the neutrinos is generically as strong as the one in the up-type quark mass term. We propose a mechanism to partially or completely cancel this hierarchy in the light neutrino mass matrix in the seesaw context. The two main ingredients of the cancellation mechanism are the existence of three fermionic gauge singlets and of a discrete flavor symmetry G_f which is broken at a higher scale than SO(10). Two realizations of the cancellation mechanism are presented. The realization based on the Frobenius group T7 = Z7 x Z3 leads to a partial cancellation of the hierarchy and relates maximal 2-3 lepton mixing with the geometric hierarchy of the up-quark masses. In the realization with the group Sigma(81) the cancellation is complete and tri-bimaximal lepton mixing is reproduced at the lowest order. In both cases, to fully accommodate the leptonic data we take into account additional effects such as effects of higher-dimensional operators involving more than one flavon. The heavy neutral fermion mass spectra are considered. For both realizations we analyze the flavon potential at the renormalizable level as well as ways to generate the Cabibbo angle.Comment: 31 page

Ultraviolet Completion of Flavour Models

Effective Flavour Models do not address questions related to the nature of the fundamental renormalisable theory at high energies. We study the ultraviolet completion of Flavour Models, which in general has the advantage of improving the predictivity of the effective models. In order to illustrate the important features we provide minimal completions for two known A4 models. We discuss the phenomenological implications of the explicit completions, such as lepton flavour violating contributions that arise through the exchange of messenger fields.Comment: 18 pages, 8 figure

The Messenger Sector of SUSY Flavour Models and Radiative Breaking of Flavour Universality

The flavour messenger sectors and their impact on the soft SUSY breaking terms are investigated in SUSY flavour models. In the case when the flavour scale M is below the SUSY breaking mediation scale M_S, the universality of soft terms, even if assumed at M_S, is radiatively broken. We estimate this effect in a broad class of models. In the CKM basis that effect gives flavour off-diagonal soft masses comparable to the tree-level estimate based on the flavour symmetry.Comment: 24 pages, 3 figures. v3: minor changes in the text, typos corrected, version accepted for publication in JHE

An SO(10) Grand Unified Theory of Flavor

We present a supersymmetric SO(10) grand unified theory (GUT) of flavor based on an $S_4$ family symmetry. It makes use of our recent proposal to use SO(10) with type II seesaw mechanism for neutrino masses combined with a simple ansatz that the dominant Yukawa matrix (the {\bf 10}-Higgs coupling to matter) has rank one. In this paper, we show how the rank one model can arise within some plausible assumptions as an effective field theory from vectorlike {\bf 16} dimensional matter fields with masses above the GUT scale. In order to obtain the desired fermion flavor texture we use $S_4$ flavon multiplets which acquire vevs in the ground state of the theory. By supplementing the $S_4$ theory with an additional discrete symmetry, we find that the flavon vacuum field alignments take a discrete set of values provided some of the higher dimensional couplings are small. Choosing a particular set of these vacuum alignments appears to lead to an unified understanding of observed quark-lepton flavor: (i) the lepton mixing matrix that is dominantly tri-bi-maximal with small corrections related to quark mixings; (ii) quark lepton mass relations at GUT scale: $m_b\simeq m_{\tau}$ and $m_\mu\simeq 3 m_s$ and (iii) the solar to atmospheric neutrino mass ratio $m_\odot/m_{\rm atm}\simeq \theta_{\rm Cabibbo}$ in agreement with observations. The model predicts the neutrino mixing parameter, $U_{e3} \simeq \theta_{\rm Cabibbo}/(3\sqrt2) \sim 0.05$, which should be observable in planned long baseline experiments.Comment: Final version of the paper as it will appear in JHEP