Yoshio Koide
A no-go theorem in flavor symmetries is reviewed. The theorem asserts that we cannot bring any flavor symmetry into mass matrix model in which number of Higgs scalars is, at most, one for each sector (e.g. H_u and H_d for up- and down-quark sectors, respectively). Such the strong constraint comes from the SU(2)_L symmetry. Possible three options to evade the theorem are discussed.
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We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
We investigate the options for imposing flavor symmetries on a minimal renormalizable non-supersymmetric $\mathrm{SU}(5)$ grand unified theory, without introducing additional flavor-related fields. Such symmetries reduce the number of free parameters in the model and therefore lead to more predictive models. We consider the Yukawa sector of the Lagrangian, and search for all possible flavor symmetries. As a result, we find 25 distinct realistic flavor symmetry cases, with $\mathbb{Z}_2$, $\mathbb{Z}_3$, $\mathbb{Z}_4$, and $\mathrm{U}(1)$ symmetries, and no non-Abelian cases.
The Flavor Puzzle: Textures and Symmetries
该研究探讨粒子物理中味对称性的自上而下起源，提出统一传统味对称性、模对称性与CP变换的“折衷”味方案，发现其模空间不动点/线附近可成功拟合夸克与轻子的质量和混合角。
In this paper we study flavor violation in supersymmetric models with gauged flavor symmetries. There are several sources of flavor violation in these theories. The dominant flavor violation is the tree-level $D$-term contribution to scalar masses generated by flavor symmetry breaking. We present a new approach for suppressing this phenomenologically dangerous effects by separating the flavor-breaking sector from supersymmetry-breaking one. The separation can be achieved in geometrical setups or in a dynamical way. We also point out that radiative corrections from the gauginos of gauged flavor…
We classify explicitly all the possible generalized CP (GCP) symmetries that are definable in $Δ(27)$ flavor models. In total, only 12 transformations are possible. We also show interesting consequences of considering some of them as residual symmetries of the neutrino sector.
For a large set of flavor symmetries, the lowest-dimensional baryon- or lepton-number violating operators in the Standard Model effective field theory (SMEFT) with flavor symmetry are of mass dimension 9. As a consequence, baryon- and lepton-number violating processes are further suppressed with the introduction of flavor symmetries, e.g., the allowed scale associated with proton decay is typically lowered to $10^5$ GeV, which is significantly lower than the GUT scale. To illustrate these features, we discuss Minimal Flavor Violation for the Standard Model augmented by sterile neutrinos.
Modular flavor symmetries provide us with a new, promising approach to the flavor problem. However, in their original formulation the kinetic terms of the standard model fields do not have a preferred form, thus introducing additional parameters, which limit the predictive power of this scheme. In this work, we introduce the scheme of quasi-eclectic flavor symmetries as a simple fix. These symmetries are the direct product of a modular and a traditional flavor symmetry, which are spontaneously broken to a diagonal modular flavor subgroup. This allows us to construct a version of Feruglio's mod…
Recent atmospheric neutrino data at Super-Kamiokande suggest the large flavor mixing of neutrinos. Models for the lepton mass matrix, which give the near-maximal flavor mixing, are discussed in the three family model. Especially, details of the models with the $S_3$ or O(3) flavor symmetry are studied.
In [1] it was shown how the flavor symmetry A4 (or S4) can arise if the three fermion generations are taken to live on the fixed points of a specific 2-dimensional orbifold. The flavor symmetry is a remnant of the 6-dimensional Poincare symmetry, after it is broken down to the 4-dimensional Poincare symmetry through compactification via orbifolding. This raises the question if there are further non-abelian discrete symmetries that can arise in a similar setup. To this end, we generalize the discussion by considering all possible 2-dimensional orbifolds and the flavor symmetries that arise from…
We study the evolution of fermion mass matrices considering the hypothesis of approximate flavor symmetries (AFS) in the Standard Model and a two-Higgs-doublet model. We find that the hierarchical structure is not significantly altered by the running, hence the assumption of AFS is entirely compatible with a grand unification scenario.
The presence of flavor symmetries in the lepton sector may have several consequences for the generation of the baryon asymmetry of the Universe via leptogenesis. We review the mechanism in general type-I, type-II and type-III seesaw models. We then turn to the discussion of the cases when the asymmetry is generated in the context of seesaw models extended with flavor symmetries, before or after flavor symmetry breaking. Finally we explain how the interplay between type-I and type-II seesaws can (or not) lead to viable models for leptogenesis even when there is an exact mixing pattern enforced …
This is an incomplete survey of some non-Abelian discrete symmetries which have been used recently in attempts to understand the flavor structure of leptons and quarks. To support such symmetries, new scalar particles are required. In some models, they are very massive, in which case there may not be much of a trace of their existence at the TeV scale. In other models, they are themselves at the TeV scale, in which case there is a reasonable chance for them to be revealed at the LHC (Large Hadron Collider) at CERN.
We investigate origins of predictive one-zero neutrino mass textures in a systematic way. Here we search Abelian continuous(discrete) global symmetries, and non-Abelian discrete symmetries, and show how to realize these neutrino masses. Then we propose a concrete model involving a dark matter candidate and an extra gauge boson, and show their phenomenologies.
We review the application of non abelian discrete groups to the theory of neutrino masses and mixing, which is strongly suggested by the agreement of the Tri-Bimaximal mixing pattern with experiment. After summarizing the motivation and the formalism, we discuss specific models, based on A4, S4 and other finite groups, and their phenomenological implications, including lepton flavor violating processes, leptogenesis and the extension to quarks. In alternative to Tri-Bimaximal mixing the application of discrete flavor symmetries to quark-lepton complementarity and Bimaximal Mixing is also consi…
Generically, the asymmetric interactions in asymmetric dark matter (ADM) models lead to decaying DM. We show that, for ADM that carries nonzero baryon number, the continuous flavor symmetries that generate the flavor structure in the quark sector also imply a looser lower bound on the mass scale of the asymmetric mediators between the dark and visible sectors. The mediators for $B=2$ ADM that can produce a signal in the future indirect dark matter searches can thus also be searched for at the LHC. For two examples of the mediator models, with either the MFV or Froggatt-Nielsen flavor breaking …
After a brief introduction to what are the basic flavor questions to be addressed, I introduce the underlying ideas of horizontal symmetries, with group $G_H$. For the purposes of specific model building, it is useful to classify models according to the scale at which $G_H$ is broken. I consider the three cases: below $m_t$; somewhat above $m_t$; and at $M_{GUT}$. After a discussion of the shadow sector in the $E_6 \times E_8'$ superstring, there is a summary.
We discuss neutrino mass and mixing models based on discrete flavor symmetries. These models can include a variety of new interactions and non-standard particles such as sterile neutrinos, scalar Higgs singlets and multiplets. We point at connections of the models with leptogenesis and dark matter and the ways to detect the corresponding non-standard particles at intensity and energy frontier experiments.
Evidences of a discrete symmetry behind the pattern of lepton mixing are analyzed. The program of "symmetry building" is outlined. Generic features and problems of realization of this program in consistent gauge models are formulated. The key issues include the flavor symmetry breaking, connection of mixing and masses, {\it ad hoc} prescription of flavor charges, "missing" representations, existence of new particles, possible accidental character of the TBM mixing. Various ways are considered to extend the leptonic symmetries to the quark sector and to reconcile them with Grand Unification. In…
It is shown that the hierarchical structure of the quark mass terms in the standard model suggests a new description of the flavor mixing. The latter is primarily a heavy quark mixing involving the t and b quarks, followed by a mixing exclusively in the u-channel or the d-channel. The complex phase describing CP violation arises only in the light quark sector. The Cabibbo angle is not a basic parameter, but results as a superposition of both the u-channel and d-channel mixing terms. The new description has a number of significant advantages in comparison with all descriptions previously used. …
We discuss the possibility of obtaining a non-abelian discrete flavor symmetry from an underlying continuous, possibly gauged, flavor symmetry SU(2) or SU(3) through spontaneous symmetry breaking. We consider all possible cases, where the continuous symmetry is broken by small representations. "Small" representations are these which couple at leading order to the Standard Model fermions transforming as two- or three-dimensional representations of the flavor group. We find that, given this limited representation content, the only non-abelian discrete group which can arise as a residual symmetry…
We perform a model-independent analysis of the possible residual Klein and generalized CP symmetries associated with arbitrary lepton mixing angles in the case that there are three light Majorana neutrino species. This approach emphasizes the unique role of the Majorana phases and provides a useful framework in which to discuss the origin of the Dirac CP phase in scenarios with spontaneously broken flavor and generalized CP symmetries. The method is shown to reproduce known examples in the literature based on tribimaximal and bitrimaximal mixing patterns, and is used to investigate these issue…
If the hierarchy of quark masses comes out of simultaneous dynamical chiral and flavor symmetry breakings, it is inevitably accompanied by the flavor mixing. Therefore, these phenomena, independent in the standard model and in many of its generalizations, become related since they appear out of the same dynamics. The features of that high energy dynamics may be investigated via accordance with observed mass hierarchy and mixing.
In models with flavor symmetries in the leptonic sector leptogenesis can take place in a very different way compared to the standard leptogenesis scenario. We study the generation of a $B-L$ asymmetry in these kind of models in the flavor symmetric phase pointing out that successful leptogenesis requires (i) the right-handed neutrinos to lie in different representations of the flavor group; (ii) the flavons to be lighter at least that one of the right-handed neutrino representations. When these conditions are satisfied leptogenesis proceeds due to new contributions to the CP violating asymmetr…
When the standard model is extended with right-handed neutrinos the symmetries of the resulting Lagrangian are enlarged with a new global U(1)R Abelian factor. In the context of minimal seesaw models we analyze the implications of a slightly broken U(1)R symmetry on charged lepton flavor violating decays. We find, depending on the R-charge assignments, models where charged lepton flavor violating rates can be within measurable ranges. In particular, we show that in the resulting models due to the structure of the light neutrino mass matrix muon flavor violating decays are entirely determined b…
Flavor and CP Symmetries in the Standard Model Effective Field Theory
本文利用味对称性与重定相对称性对SMEFT中维度6和维度8算符的CP性质进行分类，并通过Hilbert级数与Young张量方法系统枚举CP破坏相位，进而在最小味破坏假设下给出算符的味结构。
We investigate the phenomenology of flavored dark matter (DM). DM stability is guaranteed by an accidental ${\mathcal Z}_3$ symmetry, a subgroup of the standard model (SM) flavor group that is not broken by the SM Yukawa interactions. We consider an explicit realization where the quark part of the SM flavor group is fully gauged. If the dominant interactions between DM and visible sector are through flavor gauge bosons, as we show for Dirac fermion flavored DM, then the DM mass is bounded between roughly $0.5$ TeV and $5$ TeV if the DM multiplet mass is split only radiatively. In general, howe…
Connect discreteness to continuousness in leptonic flavor symmetries
本文提出用群代数（GA）描述轻子质量矩阵对称性，通过对群$S_{4}$生成的198个非平凡元素进行分类，揭示了其唯象后果，将离散性与连续性联系起来。
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 als…
We present a class of models of flavor that rely on the use of flavor symmetries and the Froggart-Nielsen mechanism in extra dimensions. The particle content is that of the standard model plus an additional flavon field; all the fields propagate in universal extra dimensions and the flavor scale is associated with the cutoff of the theory, which in 5D is $\sim 10$ TeV. The Yukawa matrices are generated by higher dimension operators involving flavon fields, whose vacuum expectation values break the flavor symmetry. We apply this framework and present a specific 5D model based on a discrete loca…
We investigate flavored gauge mediation models in which the Higgs and messenger doublets are embedded in multiplets of the discrete non-Abelian symmetry S3. In these theories, the S3 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 cas…
We discuss the neutrino mixing, using the texture 0 mass matrices, which work very well for the quarks. The solar mixing angle is directly linked to the mass ratio of the first two neutrinos. The neutrino masses are hierarchical, but the mass ratios turn out to be much smaller than for quarks. The atmospheric mixing angle is 38$^{\circ}$. The CP violation for leptons should be much smaller than for quarks.
Flavor symmetry plays a crucial role in the standard model of particle physics but its origin is still unknown. We develop a new method (based on outer automorphisms of the Narain space group) to determine flavor symmetries within compactified string theory. A picture emerges where traditional (discrete) flavor symmetries, CP-like symmetries and modular symmetries (like T-duality) of string theory combine to unified flavor symmetries. The groups depend on the geometry of compact space and the geographical location of fields in the extra dimensions. We observe a phenomenon of "local flavor grou…
We propose a model with flavor dependent gauged symmetries of $\displaystyle \prod_{i=1}^3 U(1)_{B_i-L_i}$ with $i$ the family indices. After formulating the renormalizable Yukawa Lagrangian, Higgs potential and kinetic term, we study the lepton sector based on a successful two-zero texture without introducing extra scalar bosons to avoid the dangerous Goldstone bosons. In particular, we discuss the muon related phenomenologies via additional neutral gauge bosons. In our numerical analysis, we explore the allowed parameter space, in which the anomaly of $B \to K^* \bar μμ$ can be explained.
If supersymmetry exists at low energies, it is necessary to understand why the squark spectrum exhibits sufficient degeneracy to suppress flavor changing neutral currents. In this note, we point out that gauged horizontal symmetries can yield realistic quark mass matrices, while at the same time giving just barely enough squark degeneracy to account for neutral $K$-meson phenomenology. This approach suggests likely patterns for squark masses, and indicates that there could be significant supersymmetric contributions to $B-\bar{B}$ and $D-\bar{D}$ mixing and CP violation in the $K$ and $B$ syst…
Modular Flavor Symmetries and Fermion Mass Hierarchies
本文研究模风味对称模型中的费米子质量层级，证明模量真空期望值需位于临界点附近，并分类了临界点处的质量层级，比较了传统与模变体机制。
An introduction to the heavy quark effective theory and its symmetries is given. Some implications of the heavy quark spin and flavor symmetries are discussed. Recent results on fragmentation to quarkonium states are reviewed.
Approximate flavor symmetries in the quark sector have been used as a handle on physics beyond the Standard Model. Due to the great interest in neutrino masses and mixings and the wealth of existing and proposed neutrino experiments it is important to extend this analysis to the leptonic sector. We show that in the see-saw mechanism, the neutrino masses and mixing angles do not depend on the details of the right-handed neutrino flavor symmetry breaking, and are related by a simple formula. We propose several ansätze which relate different flavor symmetry breaking parameters and find that the M…
In this letter we propose a multi-Higgs extension of the standard model with Abelian and non-Abelian discrete symmetries in which the mass matrices of the charged fermions obtained from renormalizable interactions are diagonal. Corrections induced by non-renormalizable interactions deviate these matrices from the diagonal form. Active neutrinos acquire mass only from non-renormalizable interactions. The main entries of the neutrino mass matrix arise only through dimension five operators, while the diagonal entries arise only from dimension six operators.
Grand unified theories with fermions transforming as irreducible representations of a discrete nonabelian flavor symmetry can lead to realistic fermion masses, without requiring very small fundamental parameters. We construct a specific example of a supersymmetric GUT based on the flavor symmetry $Δ(75)$ --- a subgroup of $SU(3)$ --- which can explain the observed quark and lepton masses and mixing angles. The model predicts $\tanβ\simeq 2-5$ and gives a $τ$ neutrino mass $m_ν\simeq M_p/G_F M_{GUT}^2 = 10$ eV, with other neutrino masses much lighter. Combined constraints of light quark masses …
We show how introducing discrete Abelian flavor symmetries can produce texture zeros in the fermion mass matrices, while preserving the correct relationships with the low-energy data on quark and lepton masses. We outline a procedure for defining texture zeros as suppressed entries in Yukawa matrices. These texture zeros can account for the coexistence of the observed large mixing in atmospheric neutrino oscillations with a hierarchy in the neutrino masses, and offer the possibility of alignment of the quark and squark mass matrices, and thus giving a solution to the supersymmetric flavor prob…
In this talk, I will present the general structure of RPV couplings when a Froggatt-Nielsen horizontal symmetry is responsible for the flavor structure of both the SM and the MSSM. For sub-TeV ({\it natural}) SUSY, lepton number must be an accidental symmetry, while low-energy SUSY is still allowed by baryonic RPV, which lowers the MET signature of superparticles decays. The largest RPV coupling involves the stop, and it is constrained between $10^{-3}$ (from FCNCs) and $10^{-9}$ (from LHC searches).
Discrete Abelian symmetries ($\mathbb{Z}_N$) are a common "artifact" of beyond the standard model physics models. They provide different avenues for constructing consistent scenarios for lepton and quark mixing patterns, radiative neutrino mass generation as well as dark matter stabilization. We argue that these symmetries can arise from the spontaneous breaking of the Abelian $U(1)$ factors contained in the global flavor symmetry transformations of the gauge invariant kinetic Lagrangian. This will be the case provided the ultra-violet completion responsible for the Yukawa structure involves s…
The lepton flavor violation $μ\to eγ$, $τ\to eγ$, $τ\toμγ$, $μ\to3e$, $τ\to3e$, $τ\to3μ$ and $μ-e$ conversion in Al and Ti are studied in both the Altarelli-Feruglio $A_4$ model and the $S_4$ model of Ding. The rates of these lepton flavor violation process for the inverted hierarchy neutrino mass spectrum are enhanced considerably by the next to leading order contributions. For both models, we find that the $μ-e$ conversion in Ti is within the precision of next generation experiments in all the parameter space considered, the $μ-e$ conversion in Al should be observable at least in a very sign…
We discuss the predictive power of supersymmetric models with flavor symmetries, focusing on the lepton sector of the standard model. In particular, we comment on schemes in which, after certain `flavons' acquire their vacuum expectation values (VEVs), the charged lepton Yukawa couplings and the neutrino mass matrix appear to have certain residual symmetries. In most analyses, only corrections to the holomorphic superpotential from higher-dimensional operators are considered (for instance, in order to generate a realistic $θ_{13}$ mixing angle). In general, however, the flavon VEVs also modify…
We consider the neutrino masses and mixing in the framework of SO(10) GUTs with hidden sector consisting of fermionic and bosonic SO(10) singlets and flavor symmetries. The framework allows to disentangle the CKM physics responsible for the CKM mixing and different mass hierarchies of quarks and leptons and the neutrino new physics which produces smallness of neutrino masses and large lepton mixing. The framework leads naturally to the relation $U_{PMNS} \sim V_{CKM}^{\dagger} U_0$, where structure of $U_0$ is determined by the flavor symmetry. The key feature of the framework is that apart fr…
We study the effects of considering nontrivial unphysical lepton sector phases on the group theoretical properties of the flavor and generalized CP symmetry elements in the case where there are three light, distinct Majorana neutrino species. We highlight the similarities and differences between the charged lepton and neutrino sectors and further elucidate the group properties of the flavor and generalized CP symmetry elements. We show how the inclusion of these leptonic phases affects the bottom-up constructions of these symmetry elements and discuss the implications for top-down model buildi…
The experimental data on atmospheric and solar neutrinos suggest that there is near-maximal mixing between ν_μand ν_τbut that their masses are hierarchically separated. In models of Abelian horizontal symmetries, mixing of O(1) generically implies that the corresponding masses are of the same order of magnitude. We describe two new mechanisms by which a large hierarchy between strongly mixed neutrinos can be achieved in this framework. First, a discrete Abelian symmetry can give the desired result in three ways: mass enhancement, mixing enhancement and mass suppression. Second, holomorphic zer…
We discuss a linear seesaw model with local $U(1)_{B-L}$ and modular $A_4$ symmetries. The neutrino mass matrix for linear seesaw mechanism is realized by $U(1)_{B-L}$ charge assignment and the nature of modular $A_4$ symmetry. We formulate neutrino mass and carry our numerical analysis showing some predictions for observables in neutrino sector. Remarkably, the case of inverted neutrino mass ordering (IO) is realized by a specific region around $τ=ω=e^{2πi/3}$, which is favored by a string theory. Thus, our prediction would be very strong in case of IO.
Attention is called to potentially dangerous lepton-flavor violation (LFV) induced by the D-terms of additional U(1) flavor-dependent gauge symmetries in supersymmetric models. In such models, LFV persists despite an arbitrarily high scale for the U(1) breaking and despite arbitrarily small gauge couplings. In light of recent experimental observations of neutrino oscillations, these models are highly motivated experimentally and theoretically. Taking into account also the recent measurement of the muon anomalous magnetic moment, strong bounds are calculated for the magnitude of the D-term-indu…
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.
Following the way proposed recently by Hernandez and Smirnov, we seek possible residual symmetries in the quark sector with a focus on the von Dyck groups. We begin with two extreme cases in which both $θ_{13}$ and $θ_{23}$ or only $θ_{13}$ are set to zero. Then, cases where all the Cabibbo-Kobayashi-Maskawa parameters are allowed to take nonzero values are explored. The $Z_7$ symmetry is favorable to realize only the Cabibbo angle. On the other hand, larger groups are necessary in order to be consistent with all the mixing parameters. Possibilities of embedding the obtained residual symmetrie…
We study non-abelian discrete flavor symmetries, which can appear in magnetized brane models. For example, $D_4$, $Δ(27)$ and $Δ(54)$ can appear and matter fields with several representations can appear. We also study the orbifold background, where non-abelian flavor symmetries are broken in a certain way.
Heterotic orbifolds can explain the origin of flavor symmetries and the flavor representations of matter fields in particle physics as a result of the geometric properties of the associated string states in the compact space. After a review of the method to obtain flavor symmetries in these models, we determine the most frequent non-Abelian flavor symmetries appearing in promising Abelian heterotic orbifolds. Interestingly, these symmetries correspond only to D_4, Delta(54) and products of these symmetries and Abelian factors. A large set of promising models exhibits purely Abelian flavor symm…
Multiple realizations of modular flavor symmetries and their phenomenology
本研究以有限模群$T'$为例，指出有限模群的指定不能唯一确定模味对称性，并揭示不同实现会改变模形式性质、唯象特征及模型容纳质量等级的能力。
In an attempt to understand the observed patterns of lepton and quark masses, models invoking a flavor symmetry $G_f$, under which the Standard Model generations are charged, have been proposed. One particularly successful symmetry, U(2), has been extensively discussed in the literature. The Yukawa matrices in models based on this symmetry reproduce the observed mass ratios in the lepton and quark sectors. The features of the symmetry that determine the texture of the Yukawa matrices can be found in other symmetries as well. We present a model based on a minimal, non-Abelian discrete symmetry …
We analyze neutrino masses and Lepton Flavor Violation (LFV) in charged leptons with a minimal ansatz about the breaking of the U(3)^5 flavor symmetry, consistent with the U(2)^3 breaking pattern of quark Yukawa couplings, in the context of supersymmetry. Neutrino masses are expected to be almost degenerate, close to present bounds from cosmology and $0νββ$ experiments. We also predict $s_{13} \approx s_{23} |V_{td}|/|V_{ts}| \approx 0.16$, in perfect agreement with the recent DayaBay result. For slepton masses below 1 TeV, barring accidental cancellations, we expect $\cB(μ\to e γ) > 10^{-13}$…
Flavored Peccei-Quinn symmetries in the minimal $ν$DFSZ model
本文研究了在最简νDFSZ模型中，利用风味化的PQ对称性实现轴子暗物质及味违反耦合的约束。
We study the role of a very general type of flavor symmetry in controlling the strength of R-parity violation in supersymmetric models. We assume that only leptons are charged under a global symmetry whose breaking induces lepton number (and, hence, R-parity) violation. The charge assignments of leptons under this symmetry are such that the total number of independent lepton number violating couplings is reduced from 39 to 6. The most severe constraints on these flavor-correlated couplings arise from neutrino masses and mixing as well as from the non-observation of K_L -> eμ. We find that such…
We examine a common origin of four-dimensional flavor, CP, and $U(1)_R$ symmetries in the context of heterotic string theory with standard embedding. We find that flavor and $U(1)_R$ symmetries are unified into the $Sp(2h+2, \mathbb{C})$ modular symmetries of Calabi-Yau threefolds with $h$ being the number of moduli fields. Together with the $\mathbb{Z}_2^{\rm CP}$ CP symmetry, they are enhanced to $GSp(2h+2, \mathbb{C})\simeq Sp(2h+2, \mathbb{C})\rtimes \mathbb{Z}_2^{\rm CP}$ generalized symplectic modular symmetry. We exemplify the $S_3, S_4, T^\prime, S_9$ non-Abelian flavor symmetries on e…
In this talk we discuss the implications of the Minimal Supersymmetric Standard Model augmented by a single U(1) anomalous family symmetry for neutrino masses and mixing angles. The left-handed neutrino states are provided with Majorana masses through a dimension-five operator in the absence of right handed neutrino components. Assuming symmetric lepton mass matrices, the model predicts inverse hierarchical neutrino mass spectrum, theta_13=0 and large mixing while at the same time it provides acceptable mass matrices for the charged fermions.
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