non-Abelian Discrete Flavor Symmetries Research Articles

Modular flavor models with positive modular weights: a new lepton model building

We propose an interesting assignment of positive modular weights for fields in a modular non-Abelian discrete flavor symmetry. By this assignment, we can construct inverse seesaw and linear seesaw models without any additional symmetries which possess good testability in current experiments. At first, we discuss possibilities for positive modular weights from a theoretical point of view. Then we show concrete examples of inverse seesaw and linear seesaw scenarios applying modular A4 symmetry as examples and demonstrate some predictions as well as consistency with experimental results such as neutrino masses and mixings.

Neutrino Flavor Model Building and the Origins of Flavor and CP Violation

The neutrino sector offers one of the most sensitive probes of new physics beyond the Standard Model of Particle Physics (SM). The mechanism of neutrino mass generation is still unknown. The observed suppression of neutrino masses hints at a large scale, conceivably of the order of the scale of a rand unified theory (GUT), which is a unique feature of neutrinos that is not shared by the charged fermions. The origin of neutrino masses and mixing is part of the outstanding puzzle of fermion masses and mixings, which is not explained ab initio in the SM. Flavor model building for both quark and lepton sectors is important in order to gain a better understanding of the origin of the structure of mass hierarchy and flavor mixing, which constitute the dominant fraction of the SM parameters. Recent activities in neutrino flavor model building based on non-Abelian discrete flavor symmetries and modular flavor symmetries have been shown to be a promising direction to explore. The emerging models provide a framework that has a significantly reduced number of undetermined parameters in the flavor sector. In addition, such a framework affords a novel origin of CP violation from group theory due to the intimate connection between physical CP transformation and group theoretical properties of non-Abelian discrete groups. Model building based on non-Abelian discrete flavor symmetries and their modular variants enables the particle physics community to interpret the current and anticipated upcoming data from neutrino experiments. Non-Abelian discrete flavor symmetries and their modular variants can result from compactification of a higher-dimensional theory. Pursuit of flavor model building based on such frameworks thus also provides the connection to possible UV completions: in particular, to string theory. We emphasize the importance of constructing models in which the uncertainties of theoretical predictions are smaller than, or at most compatible with, the error bars of measurements in neutrino experiments. While there exist proof-of-principle versions of bottom-up models in which the theoretical uncertainties are under control, it is remarkable that the key ingredients of such constructions were discovered first in top-down model building. We outline how a successful unification of bottom-up and top-down ideas and techniques may guide us towards a new era of precision flavor model building in which future experimental results can give us crucial insights into the UV completion of the SM.

Neutrino flavor mixing with approximate μ-τ symmetry within the low-scale minimal linear seesaw model

Neutrino flavor mixing is explained within the recently proposed low-scale minimal linear seesaw model of neutrino mass generation, a variant of the standard linear seesaw led by a Dirac pair of extra sterile neutrinos which is odd under a discrete [Formula: see text] symmetry and has a mass at or below the GeV scale. The tri-bimaximal mixing and its deviations are derived straightforwardly on the basis of the symmetry between [Formula: see text] and [Formula: see text] flavors, without introducing non-abelian discrete flavor symmetries in the first place.

Nonstandard neutrino interactions and mu-tau reflection symmetry

Nonstandard interactions (NSIs), possible subleading effects originating from new physics beyond the Standard Model, may affect the propagation of neutrinos and eventually contribute to measurements of neutrino oscillations. Besides this, $ \mu-\tau $ reflection symmetry, naturally predicted by non-Abelian discrete flavor symmetries, has been very successful in explaining the observed leptonic mixing patterns. In this work, we study the combined effect of both. We present an $S_4$ flavor model with $\mu-\tau$ reflection symmetry realized in both neutrino masses and NSIs. Under this formalism, we perform a detailed study for the upcoming neutrino experiments DUNE and T2HK. Our simulation results show that under the $\mu-\tau $ reflection symmetry, NSI parameters are further constrained and the mass ordering sensitivity is less affected by the presence of NSIs.

Modular symmetry and non-Abelian discrete flavor symmetries in string compactification

We study the modular symmetry in magnetized D-brane models on $T^2$. Non-Abelian flavor symmetry $D_4$ in the model with magnetic flux $M=2$ (in a certain unit) is a subgroup of the modular symmetry. We also study the modular symmetry in heterotic orbifold models. The $T^2/Z_4$ orbifold model has the same modular symmetry as the magnetized brane model with $M=2$, and its flavor symmetry $D_4$ is a subgroup of the modular symmetry.

Systematic analysis of Dirac neutrino masses from a dimension five operator

We perform a systematic study of the Dirac neutrino masses which arise from a dimension five effective operator with a singlet scalar. We identify all possible realizations of this operator at tree level and one-loop level. The corresponding predictions for the particle content and neutrino mass matrix are presented. We add a ${Z}_{2}$ symmetry to forbid the renormalizable Yukawa coupling, and non-Abelian discrete flavor symmetry can be used to forbid tree level diagrams in non-genuine one-loop models. The electrically neutral particle mediating the loop diagram could be dark matter candidate. We give the possible dark matter particles and the restrictions on the parameter $\ensuremath{\alpha}$ for each model.

Update on two-zero textures of the Majorana neutrino mass matrix in light of recent T2K, Super-Kamiokande and NOνA results**Supported in part by the Innovation Program of the Institute of High Energy Physics (Y4515570UI), National Youth Thousand Talents Program, and the CAS Center for Excellence in Particle Physics (CCEPP)

The latest results from atmospheric and accelerator neutrino experiments indicate that the normal neutrino mass ordering m1 < m2 < m3, a maximal leptonic CP-violating phase δ = 270° and the second octant of neutrino mixing angle θ23 > 45° are favored. In light of new experimental results, we update previous phenomenological studies on two-zero textures of the Majorana neutrino mass matrix Mν, in the flavor basis where the charged-lepton mass matrix Ml is diagonal. When the 1σ ranges of neutrino mixing parameters are taken into account, only four (i.e., A1, 2 and B2,4) among seven two-zero patterns of Mν show the aforementioned features of neutrino mass spectrum, mixing angle θ23 and CP-violating phase δ, and thus are compatible with the latest neutrino oscillation data. The correlative relations among neutrino masses and mixing parameters have been derived analytically for these four patterns, and the allowed regions of neutrino mixing angles and the CP-violating phase are also given. Possible realizations of four viable two-zero textures via non-Abelian discrete flavor symmetries are discussed.

Gauge extension of non-Abelian discrete flavor symmetry

We investigate a gauge theory realization of non-Abelian discrete flavor sym-metries and apply the gauge enhancement mechanism in heterotic orbifold models to field-theoretical model building. Several phenomenologically interesting non-Abelian discrete symmetries are realized effectively from a U(1) gauge theory with a permutation symmetry. We also construct a concrete model for the lepton sector based on a U(1)2 ⋊ S 3 symmetry.

Non-Abelian discrete flavor symmetries of 10D SYM theory with magnetized extra dimensions

We study discrete flavor symmetries of the models based on a ten-dimensional supersymmetric Yang-Mills (10D SYM) theory compactified on magnetized tori. We assume non-vanishing non-factorizable fluxes as well as the orbifold projections. These setups allow model-building with more various flavor structures. Indeed, we show that there exist various classes of non-Abelian discrete flavor symmetries. In particular, we find that S 3 flavor symmetries can be realized in the framework of the magnetized 10D SYM theory for the first time.

New interpretation of the recent result of AMS-02 and multi-component decaying dark matters with non-Abelian discrete flavor symmetry

Recently the AMS-02 experiment has released the data of positron fraction with much small statistical error. Because of the small error, it is no longer easy to fit the data with a single dark matter for a fixed diffusion model and dark matter profile. In this paper, we propose a new interpretation of the data that it originates from decay of two dark matter. This interpretation gives a rough threshold of the lighter DM component. When DM decays into leptons, the positron fraction in the cosmic ray depends on the flavor of the final states, and this is fixed by imposing non-Abelian discrete symmetry in our model. By assuming two gauge-singlet fermionic decaying DM particles, we show that a model with non-Abelian discrete flavor symmetry, e.g. $T_{13}$, can give a much better fitting to the AMS-02 data compared with single dark matter scenario. Few dimension six operators of universal leptonic decay of DM particles are allowed in our model since its decay operators are constrained by the $T_{13}$ symmetry. We also show that the lepton masses and mixings are consistent with current experimental data, due to the flavor symmetry.

Non-Abelian discrete R symmetries

We discuss non-Abelian discrete R symmetries which might have some conceivable relevance for model building. The focus is on settings with N=1 supersymmetry, where the superspace coordinate transforms in a one-dimensional representation of the non-Abelian discrete symmetry group. We derive anomaly constraints for such symmetries and find that novel patterns of Green-Schwarz anomaly cancellation emerge. In addition we show that perfect groups, also in the non-R case, are always anomaly-free. An important property of models with non-Abelian discrete R symmetries is that superpartners come in different representations of the group. We present an example model, based on a semidirect product of a Z_3 and a Z_8^R symmetry, to discuss generic features of models which unify discrete R symmetries, entailing solutions to the mu and proton decay problems of the MSSM, with non-Abelian discrete flavor symmetries.

Predictivity of models with spontaneously broken non-Abelian discrete flavor symmetries

In a class of supersymmetric flavor models predictions are based on residual symmetries of some subsectors of the theory such as those of the charged leptons and neutrinos. However, the vacuum expectation values of the so-called flavon fields generally modify the Kähler potential of the setting, thus changing the predictions. We derive simple analytic formulae that allow us to understand the impact of these corrections on the predictions for the masses and mixing parameters. Furthermore, we discuss the effects on the vacuum alignment and on flavor changing neutral currents. Our results can also be applied to non-supersymmetric flavor models.

Dark matter stability from non-Abelian discrete flavor symmetries

We present a mechanism for the dark matter (DM) stability in the framework of a non-Abelian flavour symmetry renormalizable model. The same non-Abelian discrete flavor symmetry which accounts for the observed pattern of neutrino oscillations, spontaneously breaks to a Z2 subgroup which renders DM stable. The simplest scheme leads to a scalar doublet DM potentially detectable in nuclear recoil experiments, inverse neutrino mass hierarchy, hence a neutrinoless double beta decay rate accessible to upcoming searches.

Non-vanishing U e3 under S 3 symmetry

This work proposes two models of neutrino masses that predict non-zero $\theta_{13}$ under the non-Abelian discrete flavor symmetry $\mathbb{S}_3\otimes\mathbb{Z}_2$. We advocate that the size of $\theta_{13}$ is understood as a group theoretical consequence rather than a perturbed effect from the tri-bi-maximal mixing. So, the difference of two models is designed only in terms of the flavor symmetry, by changing the charge assignment of righthanded neutrinos. The PMNS matrix in the first model is obtained from both mass matrices, charged leptons giving rise to non-zero $\theta^l_{13}$ and neutrino masses giving rise to tri-bi-maximal mixing. The physical mixing angles are expressed by a simple relation between $\theta^l_{13}$ and tri-bi-maximal angles to fit the recent experimental results. The other model generates PMNS matrix with non-zero $\theta_{13}$, only from the neutrino mass transformation. The 5 dimensional effective theory of Majorana neutrinos obtained in this framework is tested with phenomenological bounds in the parametric spaces $\sin\theta_{23}, \sin\theta_{12}$ and $m_2/m_3$ vs. $\sin\theta_{13}$.

Phenomenology of dark matter from A 4 flavor symmetry

We investigate a model in which Dark Matter is stabilized by means of a Z2 parity that results from the same non-abelian discrete flavor symmetry which accounts for the observed pattern of neutrino mixing. In our A4 example the standard model is extended by three extra Higgs doublets and the Z2 parity emerges as a remnant of the spontaneous breaking of A4 after electroweak symmetry breaking. We perform an analysis of the parameter space of the model consistent with electroweak precision tests, collider searches and perturbativity. We determine the regions compatible with the observed relic dark matter density and we present prospects for detection in direct as well as indirect Dark Matter search experiments.

Discrete flavor symmetry and minimal seesaw mechanism

This work proposes a neutrino mass model that is derived using the minimal seesaw mechanism, which contains only two right-handed neutrinos, under the non-Abelian discrete flavor symmetry ${\mathbb{S}}_{4}\ensuremath{\bigotimes}{\mathbb{Z}}_{2}$. Two standard model doublets, ${L}_{\ensuremath{\mu}}$ and ${L}_{\ensuremath{\tau}}$, are assigned simultaneously to a $\mathbf{2}$ representation of ${\mathbb{S}}_{4}$. When the scalar fields introduced in this model, in addition to the standard model Higgs, and the leptons are coupled within the symmetry, the seesaw mechanism results in the tribimaximal neutrino mixing. This study examined the possible deviations from tribimaximal mixing related to the experimental data.

Discrete dark matter

We propose a new motivation for the stability of dark matter (DM). We suggest that the same non-abelian discrete flavor symmetry which accounts for the observed pattern of neutrino oscillations, spontaneously breaks to a Z2 subgroup which renders DM stable. The simplest scheme leads to a scalar doublet DM potentially detectable in nuclear recoil experiments, inverse neutrino mass hierarchy, hence a neutrinoless double beta decay rate accessible to upcoming searches, while reactor angle equal to zero gives no CP violation in neutrino oscillations.

Relating neutrino mass and dark matter with discrete flavor symmetry

We propose a new motivation for the stability of dark matter (DM). We suggest that the same non-abelian discrete flavor symmetry which accounts for the observed pattern of neutrino oscillations, spontaneously breaks to a Z2 subgroup which renders DM stable. The simplest scheme leads to a scalar doublet DM potentially detectable in nuclear recoil experiments, inverse neutrino mass hierarchy, hence a neutrinoless double beta decay rate accessible to upcoming searches, while θ13 = 0 gives no CP violation in neutrino oscillations.

S4×Z2flavor symmetry in supersymmetric extraU(1)model

We propose a E_6 inspired supersymmetric model with a non-Abelian discrete flavor symmetry (S_4 group); that is, SU(3)_c x SU(2)_W x U(1)_Y x U(1)_X x S_4 x Z_2. In our scenario, the additional abelian gauge symmetry; U(1)_X, not only solves the mu-problem in the minimal Supersymmetric Standard Model(MSSM), but also requires new exotic fields which play an important role in solving flavor puzzles. If our exotic quarks can be embedded into a S_4 triplet, which corresponds to the number of the generation, one finds that dangerous proton decay can be well-suppressed. Hence, it might be expected that the generation structure for lepton and quark in the SM(Standard Model) can be understood as a new system in order to stabilize the proton in a supersymemtric standard model (SUSY). Moreover, due to the nature of the discrete non-Abelian symmetry itself, Yukawa coupling constants of our model are drastically reduced. In our paper, we show two predictive examples of the models for quark sector and lepton sector, respectively.

Flavor structure from magnetic fluxes and non-Abelian Wilson lines

We study the flavor structure of four-dimensional (4D) effective theories, which are derived from extra dimensional theories with magnetic fluxes and non-Abelian Wilson lines. We study zero-mode wave functions in generic case and compute Yukawa couplings as well as four-point couplings. In our models, we also discuss non-Abelian discrete flavor symmetries such as ${D}_{4}$, $\ensuremath{\Delta}(27)$, and $\ensuremath{\Delta}(54)$. The orbifold background is also studied.