We obtain a relationship between the hierarchies of mixing angles and of masses pertinent to the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix and the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) lepton mixing matrix. Using this relationship, we argue that the more severe hierarchy of the charge-$\frac{2}{3}$ quark masses requires that the CKM matrix be close to a unit matrix whereas the milder hierarchy of the neutrino masses allows the PMNS matrix to depart markedly from the CKM matrix and contain large mixing angles of the type that are observed.
We give a general analysis of neutrino mixing in the seesaw mechanism with three flavors. Assuming that the Dirac and u-quark mass matrices are similar, we establish simple relations between the neutrino parameters and individual Majorana masses. They are shown to depend rather strongly on the physical neutrino mixing angles. We calculate explicitly the implied Majorana mass hierarchies for parameter sets corresponding to different solutions to the solar neutrino problem.
Flavor mixing and the quark mass spectrum are intimately related. In view of the observed strong hierarchy of the quark and lepton masses and of the flavor mixing angles it is argued that the description of flavor mixing must take this into account. One particular interesting way to describe the flavor mixing emerges, which is particularly suited for models of quark mass matrices based on flavor symmetries. We conclude that the unitarity triangle important for $B$ physics should be close to or identical to a rectangular triangle. $CP$ violation is maximal in this sense.
In SO(10) models with a vectorial fourth generation of down quarks and leptons, the structure of the neutrino Majorana and Dirac mass matrices generically coincide with those of up- and down-quarks, respectively. Then the small neutrino mass hierarchy follows from the mismatch of the up and down quark mass hierarchies and we can accommodate naturally a normal hierarchy. The effective CP violating phases in the quark sector, neutrino oscillations and leptogenesis are unrelated.
We present a fully perturbative mechanism that naturally generates mass hierarchies for the Standard Model (SM) fermions in a flavor-blind sector. The dynamics generating the mass hierarchies can therefore be independent from the source of flavor violation, and hence this dynamics may operate at a much lower scale. This mechanism works by dynamically enforcing simultaneous diagonalization - alignment - among a set of flavor-breaking spurions, as well as generating highly singular spectra for them. It also has general applications in model building beyond the SM, wherever alignment between exot…
We present a model which contains three Abelian symmetries beyond the standard model. One is anomalous {\it \` a la} Green-Schwarz, and family-independent; the other two are family symmetries. All are broken at a large scale by stringy effects. The model is predictive in the neutrino sector: large mixing between $ν_μ-ν_τ$, and {\cal O}$(λ^3)$ $ν_e-ν_μ$ mixings. Its natural cut-off is the gauge unification scale, orders of magnitude below the perturbative string cut-off.
In this paper we study renormalization-group evolutions of Yukawa matrices enhanced by Kaluza-Klein excited modes and analyze their infrared fixed-point structure. We derive necessary conditions to obtain hierarchies between generations on the fixed point. These conditions restrict how the fields in the models can extend to higher dimension. Several specific mechanisms to realize the conditions are presented. We also take account of generation mixing effects and find a scenario where the mixing angles become small at low energy even with large initial values at high-energy scale. A toy model i…
We construct a supersymmetric model based on $T'\otimes Z_3\otimes Z_9$ flavor symmetry. At the leading order, the charged lepton mass matrix is not diagonal, $T'$ is broken completely, and the hierarchy in the charged lepton masses is generated naturally. Nearly tri-bimaximal mixing is predicted, subleading effects induce corrections of order $λ^2$, where $λ$ is the Cabibbo angle. Both the up quark and down quark mass matrices textures of the well-known U(2) flavor theory are produced at the leading order, realistic hierarchies in quark masses and CKM matrix elements are obtained. The vacuum …
We investigate the neutrino masses and mixing patten in a version of the $SU(3)_c\otimes SU(3)_L\otimes U(1)_X$ model with one extra exotic charged lepton per family as introduced by Ozer. It is shown that an extended scalar sector, together with a discrete $Z_2$ symmetry, is able to reproduce a consistent lepton mass spectrum without a hierarchy in the Yukawa coupling constants, the former as a carefull balance between one universal see-saw and two radiative mechanisms.
In the presence of independent generations of leptons, I show that the same type of ambiguity in the mass spectrum arises as was discussed in ref.[1] for neutral kaons. It results from the freedom to add to their Majorana mass matrix, usually taken to be symmetric, an antisymmetric term which vanishes as soon as fermions belonging to different generations anticommute. In the simple examples proposed, dealing with two generations, this procedure introduces an extra (mass) parameter $ρ$, which is shown to connect the (CP violating) mixing angle to the hierarchy of neutrino masses. We use this op…
In view of the observed strong hierarchy of the quark and lepton masses and of the flavor mixing angles it is argued that the description of flavor mixing must take this into account. One particular interesting way to describe the flavor mixing, which, however, is not the one used today, emerges, which is particularly suited for models of quark mass matrices based on flavor symmetries. We conclude that the unitarity triangle important for B physics should be close to or identical to a rectangular triangle. CP violation is maximal in this sense.
It is argued taking into account the observed mass spectra of the leptons and quarks that the phenomenon of flavor mixing is intimately related to the mass spectra. We discuss a particularly interesting way to describe the flavor mixing which is particularly suited for models of quark mass matrices based on flavor symmetries. CP violated is maximal or class to being maximal in our approach.
We study the connection between quark and lepton mass matrices in a supersymmetric SO(10) GUT model in six dimensions, compactified on an orbifold. The physical quarks and leptons are mixtures of brane and bulk states. This leads to a characteristic pattern of mass matrices and high-energy CP violating phases. The hierarchy of up and down quark masses determines the CKM matrix and most charged lepton and neutrino masses and mixings. The small hierarchy of neutrino masses is a consequence of the mismatch of the up and down quark mass hierarchies. The effective CP violating phases in the quark s…
We analyze in the four-generation model the first measurement of the branching ratio of rare kaon decay $K^+\toπ^+ν\bar{nu}$, along with the other processes of $K_L-K_S$ mass difference $Δm_K$, CP-violating parameter $ε_K, B_d-\bar{B_d}$ mixing, $B_s-\bar{B_s}$ mixing, $B(K_L\toμ\barμ)$, and the upper bound values of $D^0-\bar{D^0}$ mixing and $B(K_L\toπ^0ν\barν)$, and try to search for mixing of the fourth generation in the hierarchical mixing scheme of the Wolfenstein parametrization. Using the results for the mixing of the fourth generation, we discuss predictions of the $D^0-\bar{D^0}$ mix…
We construct a simple model of fermion masses based on a spontaneously broken S3 X Z3 flavour group. At the leading order, in the neutrino sector S3 is broken down to a ν_μ-ν_τparity subgroup that enforces a maximal atmospheric mixing angle and a vanishing θ_{13}. In the charged lepton sector the ν_μ-ν_τparity is maximally broken and the resulting mass matrix is nearly diagonal. The charged lepton mass hierarchy is automatically reproduced by the S3 symmetry breaking parameter alone. A careful analysis shows that, after the inclusion of all relevant subleading effects, the model predicts θ_{23…
We study the general dependence of mixing angles on heavy fermion masses when mass hierarchies exist among the fermions. For two generations and small Cabibbo angle, this angle is directly shown to scale like $μ_1/m_s \pm μ_2/m_c$, where $|μ_1| \ll m_s, |μ_2| \ll m_c$ are independent mass scales. For $n=3$ generations, we extend to the Yukawa matrices of $u$- and $d$-type quarks the property that the $2\times 2$ upper-left sub-matrix of the Cabibbo-Kobayashi-Maskawa matrix $K$ is a good approximation to the Cabibbo matrix $C$. Then, without any additional Ansatz concerning the existence of mas…
We present a $D_4$ flavored extension of the SM which provides an intuitive reasoning for the masses and mixing patterns in the quark sector. In our model, the Cabibbo mixing angle stems purely from the scalar sector dynamics. In fact, the orders of magnitude of the CKM matrix elements are readily obtained from the hierarchical nature of the vacuum expectation values. Moreover, we also show that the smallness of the off-Cabibbo elements in the CKM matrix is strongly connected to the heaviness of the third generation of quarks.
We propose a scheme, based on Δ(27) flavor symmetry and supplemented by other discrete symmetries and inverse seesaw mechanism, where both the light neutrino masses and the deviation from tri-bimaximal mixing matrix can be linked to the source of lepton number violation. The hierarchies of the charged leptons are explained. We find that the quark masses including their hierarchies and the mixing can also be constructed in a similar way.
We show how quark and lepton mass hierarchies can be reproduced in the framework of modular symmetry. The mechanism is analogous to the Froggatt-Nielsen (FN) mechanism, but without requiring any Abelian symmetry to be introduced, nor any Standard Model (SM) singlet flavon to break it. The modular weights of fermion fields play the role of FN charges, and SM singlet fields with non-zero modular weight called weightons play the role of flavons. We illustrate the mechanism by analysing $A_4$ (modular level 3) models of quark and lepton (including neutrino) masses and mixing, with a single modulus…
We incorporate clockwork mechanism into the Standard Model flavour sector and show that the observed pattern of fermion masses and mixing can be obtained without any unnaturally small or large parameter in the fundamental theory. By introducing $N_f$ pairs of vectorlike fermions, as clockwork gears, for each generation of the Standard Model fermions and setting up a characteristic clockwork potential, it is shown that the inter-generational mass hierarchies are determined by $N_f$. For a given type of fermions, strong or mild hierarchy in the masses and mixing parameters can be obtained by tak…
We explore a mechanism for generating the Yukawa hierarchies by displacing the left- and right-handed components of the Standard Model fermions in a higher-dimensional space. We find a unique configuration of displacements which fits all quark and lepton masses and mixing angles, with a prediction for the strange quark mass m_s = 120 MeV.
Parity nonconservation led Lee and Yang (1956) to the hypothesis of additional fermions with properties that mirror those of usual particles. It is shown here that the well-known observed qualitative structure of the quark mixing matrix (CKM matrix) is precisely reproduced when usual quark mass hierarchies result from mass hierarchies of heavy mirror generations. The last ones are of the Lee--Yang type only. The usual quark spectrum is formed likewise the see--saw spectrum of the neutrino physics. The lightest mirror quark is closely related with the t quark and might be available even in a re…
We calculate the quark flavor mixing matrix $V$ based on the Hermitian quark mass matrices $M^{}_{\rm u}$ and $M^{}_{\rm d}$ with vanishing $(1,1)$, $(1,3)$ and $(3,1)$ entries. The popular leading-order prediction $|V^{}_{ub}/V^{}_{cb}| \simeq \sqrt{m^{}_u/m^{}_c}$ is significantly modified, and the result agrees with the current experimental value. We find that behind the strong {\it mass} hierarchy of up- or down-type quarks is the weak {\it texture} hierarchy of $M^{}_{\rm u}$ or $M^{}_{\rm d}$ characterized by an approximate seesaw-like relation among its $(2,2)$, $(2,3)$ and $(3,3)$ elem…
This proceeding is based on arXiv:0905.3044. We analyze the problem of the hierarchy of masses and mixings in orientifold realizations of the Standard Model. We present a bottom-up brane configuration that can generate such hierarchies.
Observed reactor and atmospheric neutrino oscillation mixing values appear to be related to the neutrino scale ratio $\sqrt{Δm^2_{sol}/Δ^2_{ATM}}$ in a way that suggest that the neutrino mass matrix can be expanded as a power series by using this ratio as the smallness parameter. This approach provides a simple and natural way to expose the inner hierarchies among neutrino mass terms, which amounts to also explain the solar oscillation mixing as well as solar oscillation scale. We explore a class of mass matrix textures that realize this scenario, for both normal and inverted neutrino mass hie…
A model based on the local gauge group SU(3)_c x SU(3)_L x U(1)_X without particles with exotic electric charges is shown to be able to provide the quark mass spectrum and their mixing, by means of universal see-saw mechanisms, avoiding a hierarchy in the Yukawa coupling constants.
Flavour symmetries of Froggatt-Nielsen type can naturally reconcile the large quark and charged lepton mass hierarchies and the small quark mixing angles with the observed small neutrino mass hierarchies and their large mixing angles. We point out that such a flavour structure, together with the measured neutrino mass squared differences and mixing angles, strongly constrains yet undetermined parameters of the neutrino sector. Treating unknown O(1) parameters as random variables, we obtain surprisingly accurate predictions for the smallest mixing angle, sin^2(2 theta_13) = 0.07 (+0.11)(-0.05),…
We explore the possibility of distinguishing neutrino mass hierarchies through the neutrino signal from dark matter annihilation at neutrino telescopes. We consider a simple extension of the standard model where the neutrino masses and mixing angles are obtained via the type-II seesaw mechanism as an explicit example. We show that future extensions of IceCube neutrino telescope may detect the neutrino signal from DM annihilation at the Galactic Center and inside the Sun, and differentiate between the normal and inverted mass hierarchies, in this model.
Motivated by effective low energy models of string origin, we discuss the neutrino masses and mixing within the context of the Minimal Supersymmetric Standard Model supplemented by a U(1) anomalous family symmetry and additional Higgs singlet fields charged under this extra U(1). In particular, we interpret the solar and atmospheric neutrino data assuming that there are only three left-handed neutrinos which acquire Majorana masses via a lepton number violating dimension-five operator. We derive the general form of the charged lepton and neutrino mass matrices when two different pairs of singl…
A neutrino mass matrix model M_νwith M_ν^T =M_νand a model with its inverse matrix form \widetilde{M}_ν= m_0^2 (M_ν^*)^{-1} can be diagonalized by the same mixing matrix U_ν. It is investigated whether a scenario which provides a matrix model M_νwith normal mass hierarchy can also give a model with an inverted mass hierarchy by considering a model with an inverse form of M_ν.
Flavor physics is about particle mass-degeneracy-deviations (DMD) and mixing and especially about hierarchies of those deviations. On the one hand there is no established theory of particle flavor at present; on the other hand there are growing data indications on interesting empirical flavor regularities that are described here by two semi-empirical rules: quadratic DMD-hierarchy and Dirac-Majorana DMD-duality rules. First rule unites neutrino solar-atmospheric hierarchy parameter with charged lepton (CL) and quark mass-ratio hierarchies and simultaneously unites the hierarchies in the mixing…
The explanation of various observed phenomena such as large angle neutrino oscillations, hierarchies of charged fermion masses and CKM mixings, and apparent baryon number conservation may have a common origin. We show how this could occur in 5D SUSY SU(5) supplemented by a ${\cal U}(1)$ flavor symmetry and additional matter supermultiplets called 'copies'. In addition, the proton decays into $p\to Kν$, with an estimated lifetime of order $10^{33}-10^{36}$ yrs. Other decay channels include $Ke$ and $Kμ$ with comparable rates. We also expect that BR$(μ\to eγ)\sim $BR$(τ\to μγ)$.
We propose models to explain the hierarchies of the quark masses and mixing by utilizing the $S_4^\prime$ modular flavor symmetry. The hierarchy is realized by the modulus $τ$ stabilized at $\mathrm{Im}\,τ\gg 1$, where the residual $Z_4^T$ symmetry is approximately unbroken and the Froggatt-Nielsen mechanism works. It is found that the quark hierarchies are realized only in a few cases of quark representations. We study two models with assigning the modular weights, so that the observed quark hierarchies are explained in the cases of both small and large ratios of the top to bottom Yukawa coup…
We investigate the possibility of constructing models of R-violating LQD Yukawa couplings using a single U(1) flavour-symmetry group and supermultiplet charge assignments that are compatible with the known hierarchies of quark and lepton masses. The mismatch of mass and current eigenstates inferred from the known charged-current mixing induces the propagation of strong phenomenological constraints on some R-violating couplings to many others. Applying these constraints, we look for flavour-symmetry models that are consistent with different squark-production hypotheses devised to explain the po…
We investigate the feasibility of probing the neutrino mass hierarchy and the mixing angle $ϕ_{13}$ with the neutrino burst from a future supernova. An inverse power-law density $ρ\sim r^{n} $ with varying $n$ is adopted in the analysis as the density profile of a typical core-collapse supernova. The survival probabilities of $ν_{e}$ and $\barν_{e}$ are shown to reduce to two-dimensional functions of $n$ and $ϕ_{13}$. It is found that in the $n-\sin^{2} ϕ_{13}$ parameter space, the 3D plots of the probability functions exhibit highly non-trivial structures that are sensitive to the mass hierar…
We analyze the problem of the hierarchy of masses and mixings in orientifold realizations of the Standard Model. We find bottom-up brane configurations that can generate such hierarchies.
We present a supersymmetric standard model with three gauged Abelian symmetries, of a type commonly found in superstrings. One is anomalous, the other two are $E_6$ family symmetries. It has a vacuum in which only these symmetries are broken by stringy effects. It reproduces all observed quark and charged lepton Yukawa hierarchies, and the value of the Weinberg angle. It predicts three massive neutrinos, with mixing that can explain both the small angle MSW effect, and the atmospheric neutrino anomaly. The Cabibbo angle is expressed in terms of the gauge couplings at unification. It conserves …
Neutrino-oscillation solutions for the atmospheric neutrino anomaly and the solar neutrino deficit can determine the texture of the neutrino mass matrix according to three types of neutrino mass hierarchies as Type A: $m_1^{} \ll m_2^{} \ll m_3^{}$, Type B: $m_1^{} \sim m_2^{} \gg m_3^{}$, and Type C: $m_1^{} \sim m_2^{} \sim m_3^{}$, where $m_i$ is the $i$-th generation neutrino absolute mass. The relative sign assignments of neutrino masses in each type of mass hierarchies play the crucial roles for the stability against quantum corrections. Actually, two physical Majorana phases in the lept…
The mass hierarchies of quarks and charged leptons as well as a large $\n_\m$-$\n_\t$ mixing angle are naturally explained by the Frogatt-Nielsen mechanism with a nonparallel family structure of chiral charges. We extend this mechanism to right-handed neutrinos. Their out-of-equilibrium decay generates a cosmological baryon asymmetry whose size is quantized in powers of the hierarchy parameter $\e^2$. For the simplest hierarchy pattern the neutrino mass $\bar{m}_\n= (m_{\n_\m}m_{\n_\t})^{1/2} \sim 10^{-2}$ eV, which is inferred from present indications for neutrino oscillations, implies a bary…
We present a supersymmetric model of quark and lepton based on $S_4\times Z_3\times Z_4$ flavor symmetry. The $S_4$ symmetry is broken down to Klein four and $Z_3$ subgroups in the neutrino and the charged lepton sectors respectively. Tri-Bimaximal mixing and the charged lepton mass hierarchies are reproduced simultaneously at leading order. Moreover, a realistic pattern of quark masses and mixing angles is generated with the exception of the mixing angle between the first two generations, which requires a small accidental enhancement. It is remarkable that the mass hierarchies are controlled …
Large mixing parameters of neutrino mass eigenstates in the neutrino flavor eigenstates are determined, and interpreted as closely related to the neutrino and charged lepton mass-ratio patterns. The three known seemingly different charged lepton and quasi-degenerate neutrino deviation-from-extreme hierarchies are shown to be three particular manifestations of one unifying quadratic hierarchy-rule in lepton flavor physics.
The spontaneous breaking of the $SU(3)^5$ quark/lepton flavor symmetry by means of three multiplets of scalar `Yukawa fields' admits vacua with one O(1) and two vanishing vacuum expectation values (vevs) for each multiplet. If the number of generations is equal to three, and only in this case, the vanishing vevs are lifted to exponentially suppressed entries by the inclusion of symmetry invariant logarithmic terms. A strong hierarchy for the Yukawa couplings and a quark mixing matrix that approaches a diagonal form are obtained in a natural way from O(1) parameters. This scenario provides a co…
We present a predictive scheme for fermion masses and mixings based on supersymmetric SO(10) which provides an understanding of the observed hierarchies in the charged fermion sector including CKM mixings. In the neutrino sector bi-large mixing can be realized, while the third leptonic mixing angle $θ_{13}\simeq 0.01 - 0.2$.
After the Higgs boson discovery, it is established that the Higgs mechanism explains electroweak symmetry breaking and generates the masses of all particles in the Standard Model, with the possible exception of neutrino masses. The hierarchies among fermion masses and mixing angles remain however unexplained. We propose a new class of two Higgs doublet models in which a flavor symmetry broken at the electroweak scale addresses this problem. The models are strongly constrained by electroweak precision tests and the fact that they produce modifications to Higgs couplings and flavor changing neut…
We study the neutrino mass matrix in supersymmetric models in which the quark and charged lepton mass hierarchies and also the suppression of baryon or lepton number violating couplings are all explained by horizontal $U(1)_X$ symmetry. It is found that the neutrino masses and mixing angles suggested by recent atmospheric and solar neutrino experiments arise naturally in this framework which fits in best with gauge-mediated supersymmetry breaking with large $\tanβ$. This framework highly favors the small angle MSW oscillation of solar neutrinos, and determine the order of magnitudes of all the…
Flavour symmetries are fundamental tools in the search for an explanation to the flavour puzzle: fermion mass hierarchies, the neutrino mass ordering, the differences between the mixing matrices in the quark and lepton sector, can all find an explanation in models where the fermion generations undergo specific geometric relations. An overview on the implementation of continuous symmetries in the flavour sector is presented here, focussing on the lepton sector.
Using the family symmetry, in the neutrino mass matrix we remove the Yukawa coupling (arising in the Dirac type mass between the heavy neutrinos and light lepton doublets) dependence in the double seesaw mechanism so that it is directly proportional to the mass matrix $m^{(nn)}$ of heavy Majorana neutrinos. The family symmetry is supposed to be broken spontaneously at high energy scale so that the neutrino mass matrix is given by the family symmetry at high energy scale. With the permutation symmetry $S_3$, we note a variety of possible mass hierarchies arising distinctly in neutrinos, charged…
We suggest simple models which produce the suitable fermion mass hierarchies and flavor mixing angles based on the 6 dimensional N=1 supersymmetric SO(10) grand unified theory compactified on a $T^2/(Z_2 \times Z_2')$ orbifold. We introduce 6D and 5D matter fields, which contains the 1st and 2nd generation matter fields as the zero modes, respectively. The 3rd generation matter fields are located on a 4D brane. The Yukawa couplings for bulk fields are suppressed by volume factors from extra dimensions. The suitable fermion mass hierarchies and flavor mixings are generated by the volume suppres…
It is shown that an idea proposed in 1996 that relates in a qualitatively correct way the inter-family mass hierarchies of the up quarks, down quarks, charged leptons, and neutrinos, can be combined with a predictive scheme recently proposed for relating quark mixing and neutrino mixing. In the resulting model, the entire flavor structure of the quarks and leptons is expressible in terms of two "master matrices": a diagonal matrix that gives the inter-family mass ratios, and an off-diagonal matrix that controls all flavor mixing.
We introduce a new parameterisation of the effect of unknown corrections from new physics on quark and lepton mass matrices. This parameterisation is used in order to study how the hierarchies of quark masses and mixing angles are modified by random perturbations of the Yukawa matrices. We discuss several examples of flavour relations predicted by different textures, analysing how these relations are influenced by the random perturbations. We also comment on the unlikely possibility that unknown corrections contribute significantly to the hierarchy of masses and mixings.
