non-Abelian Discrete Symmetry Research Articles

\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${M}_{{W}_{R}}$$\\end{document} dependence of leptogenesis in minimal Left-Right Symmetric Model with different strengths of Type-II seesaw mass

Left Right Symmetric Model (LRSM) being an extension of the Standard model of particle physics incorporates within itself Type-I and Type-II seesaw mass terms naturally. Both the mass terms can have significant amount of contribution to the resulting light neutrino mass within the model and hence on the different phenomenology associated within. In this paper, we have thoroughly analyzed and discussed the implications of specifying different weightages to both the mass terms and also the study has been carried out for different values of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${M}_{{W}_{R}}$$\\end{document} which is mass of the right-handed gauge boson. This paper also gives a deeper insight into the new physics contributions of Neutrinoless Double Beta Decay (0νββ) and their variations with the net baryon asymmetry arising out of the model. Therefore, the main objective of the present paper rests on investigating the implications of imposing different weightage to the type-I and type-II seesaw terms and different values of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${M}_{{W}_{R}}$$\\end{document} on the new physics contributions of 0νββ and net baryon asymmetry arising out as a result of resonant leptogenesis. LRSM in this work has been realized using modular group of level 3, Γ(3) which is isomorphic to non-abelian discrete symmetry group A4, the advantage being the non-requirement of flavons within the model and hence maintaining the minimality of the model.

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.

Minimal left–right symmetric model with A4 modular symmetry

In this paper, we have realized the left–right symmetric model (LRSM) with modular symmetry. Most of the previous works on LRSM have been done considering discrete flavor symmetry, but this work has been carried out using [Formula: see text](3) modular group which is isomorphic to nonabelian discrete symmetry group [Formula: see text]. The advantage of using modular symmetry is the nonrequirement for the use of extra particles called “flavons”. In this model, the Yukawa couplings are expressed in terms of modular forms [Formula: see text]. In this work, we have studied minimal LRSM for both type-I and type-II dominances. Here, we have calculated the values for the Yukawa couplings and then plotted it against the sum of the neutrino masses. The results obtained are well within the experimental limits for the desired values of sum of neutrino masses. We have also briefly analyzed the effects of the implications of modular symmetry on neutrinoless double beta decay with the new physics contributions and the correlation of lepton flavor violation and lightest neutrino mass within the framework of modular symmetric LRSM.

Exploring models with modular symmetry in neutrino oscillation experiments

Our study aims to investigate the viability of neutrino mass models that arise from discrete non-Abelian modular symmetry groups, i.e., ΓN with (N = 1, 2, 3, . ) in the future neutrino experiments T2HK, DUNE, and JUNO. Modular symmetry reduces the usage of flavon fields compared to the conventional discrete flavor symmetry models. Theories based on modular symmetries predict the values of leptonic mixing parameters, and therefore, these models can be tested in future neutrino experiments. In this study, we consider three models based on the A4 modular symmetry, i.e., Model-A, B, and C such a way that they predict different values of the oscillation parameters but still allowed with respect to the current data. In the future, it is expected that T2HK, DUNE, and JUNO will measure the neutrino oscillation parameters very precisely, and therefore, some of these models can be excluded in the future by these experiments. We have estimated the prediction of these models numerically and then used them as input to scrutinize these models in the neutrino experiments. Assuming the future best-fit values of θ23 and δCP remain the same as the current one, our results show that at 5σ C.L, Model-A can be excluded by T2HK whereas Model-B can be excluded by both T2HK and DUNE. Model-C cannot be excluded by T2HK and DUNE at 5σ C.L. Further; our results show that JUNO alone can exclude Model-B at an extremely high confidence level if the future best-fit of θ12 remains at the current-one. We have also identified the region in the θ23 - δCP parameter space, for which Model-A cannot be separated from Model-B in T2HK and DUNE.

Neutrino masses and mixing in minimal inverse seesaw using A4 modular symmetry

In this paper, we construct a model with the help of modular symmetry in the framework of minimal inverse seesaw [ISS(2,3)]. We have used [Formula: see text] modular group which is isomorphic to non-Abelian discrete symmetry group [Formula: see text]. In this group, there are three Yukawa modular forms of weight 2. In this model, we study neutrino masses and mixings for both normal and inverted hierarchies. Use of modular symmetry reduces the need for more number of extra flavons and their specific VEV alignments, as such, minimality of the model is maintained to a great extent. Along with [Formula: see text] symmetry group, we have used [Formula: see text] to restrict certain interaction terms in the Lagrangian. Further, we calculate the effective mass to address the phenomena of neutrinoless double-beta decay ([Formula: see text]). The values of effective mass are found to lie within the bound ([Formula: see text][Formula: see text]eV) as predicted by different [Formula: see text] experiments.

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.

Constructing viable quark mass matrices in the flavor basis using S3 × Z3 symmetry

Non-Abelian discrete symmetry group [Formula: see text] has been used to construct quark mass matrices in the flavor basis. Interestingly, the case when [Formula: see text] is nondiagonal and [Formula: see text] is diagonal, is very much compatible with the presently refined data regarding the quark masses and mixing. However, the other case, when [Formula: see text] is nondiagonal and [Formula: see text] is diagonal, looks to be incompatible with the data.

Scotogenic A5 → A4 Dirac neutrinos with freeze-in dark matter

Radiative Dirac neutrino masses and their mixing are linked to dark matter through the non-Abelian discrete symmetry A5 of the 4-dimensional pentatope, softly broken to A4 of the 3-dimensional tetrahedron. This unifying understanding of neutrino family structure from dark matter is made possible through the interplay of gauge symmetry, renormalizable Lagrangian field theory, and softly broken discrete symmetries. Dark neutral fermions are produced through Higgs decay.

Flavored gauge-mediated supersymmetry breaking models with discrete non-Abelian symmetries

We investigate flavored gauge mediation models in which the Higgs and messenger doublets are embedded in multiplets of the discrete non-Abelian symmetry ${\mathcal{S}}_{3}$. In these theories, the ${\mathcal{S}}_{3}$ symmetry correlates the flavor structure of the quark and lepton Yukawa couplings with the structure of the messenger Yukawa couplings that contribute to the soft supersymmetry breaking mass parameters. We provide a systematic exploration of possible scenarios within this framework that can accommodate hierarchical quark and charged lepton masses, and examine the resulting phenomenological implications in each case. We find a heavier spectrum for the superpartner masses compared to flavored gauge mediation models controlled by Abelian symmetries, which can be directly traced back to the need in our scenarios for two vectorlike pairs of messenger fields for viable electroweak symmetry breaking.

Anomaly of non-Abelian discrete symmetries

We study anomalies of non-Abelian discrete symmetries; which part of non-Abelian group is anomaly free and which part can be anomalous. It is found that the anomaly-free elements of the group $G$ generate a normal subgroup $G_0$ of $G$ and the residue class group $G/G_0$, which becomes the anomalous part of $G$, is isomorphic to a single cyclic group. The derived subgroup $D(G)$ of $G$ is useful to study the anomaly structure. This structure also constrains the structure of the anomaly-free subgroup; the derived subgroup $D(G)$ should be included in the anomaly-free subgroup. We study the detail structure of the anomaly-free subgroup from the structure of the derived subgroup in various discrete groups. For example, when $G=S_n \simeq A_n \rtimes Z_2$ and $G=\Delta(6n^2) \simeq \Delta(3n^2) \rtimes Z_2$, in particular, $A_n$ and $\Delta(3n^2)$ are at least included in the anomaly-free subgroup, respectively. This result holds in any arbitrary representations.

Scalar dark matter in the A4-based texture one-zero neutrino mass model within the inverse seesaw mechanism

Abstract In this paper, we present a model based on A4 discrete flavor symmetry implementing inverse and type-II seesaw mechanisms to have LHC-accessible TeV-scale right-handed neutrino mass and texture one-zero in the resulting Majorana neutrino mass matrix, respectively. We investigate the neutrino and dark matter sectors of the model. Non-Abelian discrete A4 symmetry spontaneously breaks into the Z2 subgroup and hence provides a stable dark matter candidate. To constrain the Yukawa Lagrangian of our model, we impose $Z^{\prime }_2$, Z3, and Z4 cyclic symmetries in addition to the A4 flavor symmetry. In this work we use the recently updated data on cosmological parameters from the Planck Collaboration [N. Aghanim et al. [Planck Collaboration], Astron. Astrophys. A6, 641 (2020)]. For the dark matter candidate mass around 45–55 GeV, we obtain a mediator particle mass (right-handed neutrinos) ranging from 138–155 GeV. The Yukawa couplings are found to be in the range 0.995–1 to have observed the relic abundance of dark matter. We further obtain inverse ($X\equiv \frac{F^2n}{z^2}$) and type-II ($X^{\prime}\equiv f_1 v_{\Delta _{1}}$) seesaw contributions to the 0νββ decay amplitude |Mee|, with the model being consistent with low-energy experimental constraints. In particular, we emphasize that the type-II seesaw contribution to |Mee| is large compared to the inverse seesaw contribution for normally ordered (NO) neutrino masses.

Gravitational wave signatures from discrete flavor symmetries

Non-Abelian discrete symmetries have been widely used to explain the patterns of lepton masses and flavor mixing. In these models, a given symmetry is assumed at a high scale and then is spontaneously broken by scalars (the flavons), which acquire vacuum expectation values. Typically, the resulting leading order predictions for the oscillation parameters require corrections in order to comply with neutrino oscillation data. We introduce such corrections through an explicit small breaking of the symmetry. This has the advantage of solving the cosmological problems of these models without resorting to inflation. The explicit breaking induces an energy difference or “bias” between different vacua and drives the evolution of the domain walls, unavoidably produced after the symmetry breaking, towards their annihilation. Importantly, the wall annihilation leads to gravitational waves which may be observed in current and/or future experiments. We show that a distinctive pattern of gravitational waves with multiple overlapped peaks is generated when walls annihilate, which is within the reach of future detectors. We also show that cosmic walls from discrete flavor symmetries can be cosmologically safe for any spontaneous breaking scale between 1 and 1018 GeV, if the bias is chosen adequately, without the need to inflate the walls away. We use as an example a particular A4 model in which an explicit breaking is included in right-handed neutrino mass terms.

Probing lepton flavor models at future neutrino experiments

Non-Abelian discrete symmetries provide an interesting opportunity to address the flavor puzzle in the lepton sector. However, the number of currently viable models based on such symmetries is rather large. High-precision measurements of the leptonic mixing parameters by future neutrino experiments, including ESSnuSB, T2HK, DUNE, and JUNO, will be crucial to test such models. We show that the complementarity among these experiments offers a powerful tool for narrowing down this broad class of lepton flavor models.

Generating the Cabibbo angle in flavored gauge mediation models with discrete non-Abelian symmetries

We explore the generation of fermion masses and quark mixing angles within flavored gauge mediation models of supersymmetry breaking in which the Higgs and messenger doublets are connected by a discrete non-Abelian symmetry. In this framework, the Higgs-messenger symmetry, which we take for concreteness to be the discrete group $\mathcal{S}_3$, also plays the role of a (partial) family symmetry. We investigate mechanisms for generating mass hierarchies for the lighter quark generations and generating the Cabibbo angle within this class of models. While perturbations of the couplings at the renormalizable level do not lead to phenomenologically viable quark mixing parameters, we show that the Cabibbo angle can be generated via couplings at the nonrenormalizable level and explore the phenomenological implications of this scenario.

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.

Finite family groups for fermionic and leptoquark mixing patterns

We employ a bottom-up and model-independent technique to search for non-Abelian discrete flavour symmetries capable of predicting viable CKM and PMNS matrices alongside of special patterns of leptoquark couplings. In particular, we analyze patterns de- rived when an ultra-violet flavour theory is assumed to break to global Abelian symmetries in Standard Model fermion masses and new Yukawa-like terms sourced by the leptoquark representation. The phenomenology of different classes of these ‘simplified models’ can be explored without reference to explicit model-building assumptions, e.g. the nature of flavour symmetry breaking or any additional field content associated to it, and are also capable of explaining hints of lepton non-universality in {mathcal{R}}_{K^{left(ast right)}} . Assuming experimentally interesting CKM and PMNS matrix elements, our algorithm finds an abundance of predictive non-Abelian flavour groups and therefore provides promising directions for future model building in the flavoured leptoquark space, regardless of whether the anomalous {mathcal{R}}_{K^{left(ast right)}} measurements withstand further experimental scrutiny.

Stitching an asymmetric texture with T13×Z5 family symmetry

We propose $\mathcal{T}_{13} = \mathcal{Z}_{13} \rtimes \mathcal{Z}_3$ as the underlying non-Abelian discrete family symmetry of the asymmetric texture presented in arXiv:1805.10684 [hep-ph]. Its mod 13 arithmetic distinguishes each Yukawa matrix element of the texture. We construct a model of effective interactions that singles out the asymmetry and equates, without fine-tuning, the products of down-quark and charged-lepton masses at a GUT-like scale.

Braiding and Fusion of Non-Abelian Vortex Anyons.

We have studied topology and dynamics of quantum vortices in spin-2 Bose-Einstein condensates. By computationally modeling controllable braiding and fusion of these vortices, we have demonstrated that certain vortices in such spinor condensates behave as non-Abelian anyons. We identify these anyons as fluxon, chargeon, and dyon quasiparticles. The pertinent anyon models are defined by the quantum double of the underlying discrete non-Abelian symmetry group of the condensate ground state order parameter.

Sizable stop mixing in flavored gauge mediation models with discrete non-Abelian symmetries

We analyze a minimal flavored gauge mediation model in which the electroweak Higgs and messenger doublets are embedded in multiplets of a discrete non-Abelian symmetry. In this scenario, the minimal Higgs-messenger sector that is consistent with the 125 GeV Higgs mass has two vectorlike pairs of messenger fields. This scenario is obtained in a specific limit of the superpotential interactions of the Higgs-messenger fields and the matter fields. Due to the structure of the messenger-matter Yukawa couplings in this limit, sizable stop mixing and flavor-diagonal soft supersymmetry breaking parameters are achieved. In most of the parameter space, the masses of the colored superpartners are at most in the 5-6 TeV range.