Quark sector ofS3models: Classification and comparison with experimental data

The charged fermion masses of the three generations exhibit the two strong hierarchies m3≫m2≫m1. We assume that also neutrino masses satisfy mν3>mν2>mν1 and derive the consequences of the hierarchical spectra on the fermionic mixing patterns. The quark and lepton mixing matrices are built in a general framework with their matrix elements expressed in terms of the four fermion mass ratios, mu/mc, mc/mt, md/ms and ms/mb, and me/mμ, mμ/mτ, mν1/mν2 and mν2/mν3, for the quark and lepton sector, respectively. In this framework, we show that the resulting mixing matrices are consistent with data for both quarks and leptons, despite the large leptonic mixing angles. The minimal assumption we take is the one of hierarchical masses and minimal flavor symmetry breaking that strongly follows from phenomenology. No special structure of the mass matrices has to be assumed that cannot be motivated by this minimal assumption. This analysis allows us to predict the neutrino mass spectrum and set the mass of the lightest neutrino well below 0.01 eV. The method also gives the 1σ allowed ranges for the leptonic mixing matrix elements. Contrary to the common expectation, leptonic mixing angles are found to be determined solely by the four leptonic mass ratios without any relation to symmetry considerations as commonly used in flavor model building. Still, our formulae can be used to build up a flavor model that predicts the observed hierarchies in the masses — the mixing follows then from the procedure which is developed in this work.

We construct a supersymmetric model with the flavor symmetry D 14 in which the CKM matrix element | V u d | can take the value | V u d | = cos ( π 14 ) ≈ 0.97493 implying that the Cabibbo angle θ C is sin ( θ C ) ≈ | V u s | ≈ sin ( π 14 ) ≈ 0.2225 . These values are very close to those observed in experiments. The value of | V u d | ( θ C ) is based on the fact that different Z 2 subgroups of D 14 are conserved in the up and down quark sector. In order to achieve this, D 14 is accompanied by a Z 3 symmetry. The spontaneous breaking of D 14 is induced by flavons, which are scalar gauge singlets. The quark mass hierarchy is partly due to the flavor group D 14 and partly due to a Froggatt–Nielsen symmetry U ( 1 ) FN under which only the right-handed quarks transform. The model is natural in the sense that the hierarchies among the quark masses and mixing angles are generated with the help of symmetries. The issue of the vacuum alignment of the flavons is solved up to a small number of degeneracies, leaving four different possible values for | V u d | . Out of these, only one of them leads to a phenomenological viable model. A study of the Z 2 subgroup breaking terms shows that the results achieved in the symmetry limit are only slightly perturbed. At the same time they allow | V u d | ( θ C ) to be well inside the small experimental error bars.

In this article we review the phenomenological consequences of radiative flavor-violation (RFV) in the MSSM. In the model under consideration the U(3)^3 flavor symmetry of the gauge sector is broken in a first step to U(2)^3 by the top and bottom Yukawa couplings of the superpotential (and possibly also by the bilinear SUSY-breaking terms). In a second step the remaining U(2)^3 flavor symmetry is softly broken by the trilinear A-terms in order to obtain the measured quark masses and the CKM matrix of the Standard Model (SM) at low energies. The phenomenological implications of this model depend on the actual choice of the SUSY breaking A-terms. If the CKM matrix is generated in the down sector (by A^d), Bs->mu^+mu^- receives non-decoupling contributions from Higgs penguins which become important already for moderate values of tan(beta). Also the Bs mixing amplitude can be significantly modified compared to the SM prediction including a potential induction of a new CP-violating phase (which is not possible in the MSSM with MFV).

In this work, discuss neutrino masses and mixings in the framework of a minimal S3 symmetric extension of the Standard Model. In this model, the mass matrices of all fermions take the same generic form with two texture zeroes. The mass matrices of the neutrinos and charged leptons are re-parameterized in terms of their eigenvalues, then the neutrino mixing matrix, VPMNS, is computed and exact, explicit analytical expressions for the neutrino mixing angles as functions of the masses of neutrinos and charged leptons are obtained in excellent agreement with the latest experimental data. We also compute the branching ratios of some selected flavour-changing neutral current (FCNC) processes, as well as the contribution of the exchange of neutral flavour-changing scalars to the anomaly of the magnetic moment of the muon, as functions of the masses of charged leptons and the neutral Higgs bosons. We find that the S3 × Z2 flavour symmetry and the strong mass hierarchy of the charged leptons strongly suppress the FCNC processes in the leptonic sector, well below the present experimental bounds by many orders of magnitude. The contribution of FCNC's to the anomaly of the muon's magnetic moment is small, but not negligible.

Minimal mixing of quarks and leptons in the SU(3) theory of flavour

Flavour symmetries have been used to constrain both quark and lepton mixing parameters. In particular, they can be used to completely fix the mixing angles. For the lepton sector, assuming that neutrinos are Majorana particles, we have derived the complete list of mixing patterns achievable in this way, as well as the symmetry groups associated to each case. Partial computer scans done in the past have hinted that such list is limited, and this does indeed turn out to be the case. In addition, most mixing patterns are already 3-sigma excluded by neutrino oscillation data.

The quark-lepton complementarity (QLC) relations indicate a deep structure that interrelates quarks and leptons. We propose new scenarios, in a seesaw framework with discrete $A_4$ flavor symmetry, which can accommodate the QLC relations and the nonzero neutrino mixing angle $\theta_{13}$ together with all the available neutrino experimental data, in a consistent way to generate the Cabibbo-Kobayashi-Maskawa (CKM) matrix for the quark mixing. Certain effective dimension-5 operators are introduced, which induce a deviation of the lepton mixing matrix from the tribimaximal mixing (TBM) pattern and lead the quark mixing matrix to the CKM one in form. We explicitly demonstrate three different possibilities of constructing the charged lepton mixing matrix and point out that the {\it phases} of whose elements play a crucial role to satisfy the QLC relations. We find that for the reactor mixing angle $\theta_{13}$ its possible values can vary around the center value $\sin \theta_{13} \simeq \lambda /\sqrt{2}$ ($\lambda \simeq 0.22$ being the Cabbibo angle) and have the lower bound $\theta_{13} \gtrsim 3.5^{\circ}$. We also show that sizable leptonic CP violation characterized by the Jarlskog invariant $|J_{\rm CP}|\sim{\cal O}(10^{-2})$ is allowed, which is expected to be tested in the future experiments such as the upcoming long baseline neutrino oscillation ones.

We show how the neutrino mixing angles and oscillation phase can be predicted from tri-bimaximal neutrino mixing, corrected by charged lepton mixing angles which are related to quark mixing angles via quark-lepton unification. The tri-bimaximal neutrino mixing can naturally originate from the see-saw mechanism via constrained sequential dominance (CSD), where CSD can result from the vacuum alignment of a non-Abelian family symmetry such as SO(3). We construct a realistic model of quark and lepton masses and mixings based on SO(3) family symmetry with quark-lepton unification based on the Pati-Salam gauge group. The atmospheric angle is predicted to be approximately maximal $\theta_{23}= 45^\circ$, corrected by the quark mixing angle $\theta_{23}^{\mathrm{CKM}}\approx 2.4^\circ$, with the correction controlled by an undetermined phase in the quark sector. The solar angle is predicted by the tri-bimaximal complementarity relation: $\theta_{12}+ \frac{1}{\sqrt{2}}\frac{\theta_{\mathrm{C}}}{3} \cos (\delta - \pi) \approx 35.26^\circ $, where $\theta_{\mathrm{C}}$ is the Cabibbo angle and $\delta$ is the neutrino oscillation phase. The reactor angle is predicted to be $\theta_{13} \approx \frac{1}{\sqrt{2}}\frac{\theta_{\mathrm{C}}}{3}\approx 3.06^\circ$. The MNS neutrino oscillation phase $\delta$ is predicted in terms of the solar angle to be $\cos (\delta - \pi) \approx (35.26^\circ - \theta_{12}^\circ)/3.06^\circ $. These predictions can all be tested by future high precision neutrino oscillation experiments, thereby probing the nature of high energy quark-lepton unification.

Motivated by the recent resurrection of the evidence for an eV scale sterile neutrino from the MiniBooNE experiment, we revisit one of the most minimal seesaw model known as the minimal extended seesaw that gives rise to a 3+1 light neutrino mass matrix. We consider the presence of A_{4} flavour symmetry which plays a non-trivial role in generating the structure of the neutrino mass matrix. Considering a diagonal charged lepton mass matrix and generic vacuum alignments of A_{4} triplet flavons, we classify the resulting mass matrices based on their textures. Keeping aside the disallowed texture zeros based on earlier studies of 3+1 neutrino textures, we categorise the remaining ones based on texture zeros, mu –tau symmetry in the 3times 3 block and hybrid textures. After pointing out the origin of such 3+1 neutrino textures to A_{4} vacuum alignments, we use the latest 3+1 neutrino oscillation data and numerically analyse the texture zeros and mu –tau symmetric cases. We find that a few of them are allowed from each category predicting interesting correlations between neutrino parameters. We also find that all of these allowed cases prefer normal hierarchical pattern of light neutrino masses over inverted hierarchy.

We study the phenomenology of simplified $Z′$ models with a global $U(2)^{3}$ flavour symmetry in the quark sector, broken solely by the Standard Model Yukawa couplings. This flavour symmetry, known as less-minimal flavour violation, protects $ΔF=2$ processes from dangerously large new physics (NP) effects, and at the same time provides a free complex phase in $b→s$ transitions, allowing for an explanation of the hints for additional direct CP violation in kaon decays ($ϵ′/ϵ$) and in hadronic $B$-decays ($B→Kπ$ puzzle). Furthermore, once the couplings of the $Z′$ boson to the leptons are included, it is possible to address the intriguing hints for NP (above the 5σ level) in $b→sℓ^{+}ℓ^{−}$ transitions. Taking into account all flavour observables in a global fit, we find that $ϵ′/ϵ$, the $B→Kπ$ puzzle and $b→sℓ^{+}ℓ^{−}$ data can be explained simultaneously. Sizeable CP violation in $b→sℓ^{+}ℓ^{−}$ observables, in particular $A_{8}$, is predicted, which can be tested in the near future, and an explanation of the $B→Kπ$ and $ϵ′/ϵ$ puzzles leads to effects in di-jet tails at the LHC, that are not far below the current limits. Once $b→sℓ^{+}ℓ^{−}$ is included, cancellations in di-muon tails, possibly by a second $Z′$, are required by LHC data.

Neutrino oscillation experiments have confirmed that neutrinos are massive particles and that lepton flavors are mixed. To explain the observed lepton mass spectra and flavor mixing patterns, flavor symmetry plays a crucial and unique role. In this paper, we propose a useful symmetry-breaking scheme by applying within both charged-lepton and neutrino sectors at the mass-matrix level. For the three distinct residual subgroups , , and that are under consideration, we systematically analyze the various parameterizations of the lepton mass matrices. It is shown that all three scenarios are in good agreement with current neutrino oscillation data. Notably, within the latest best-fit values of neutrino oscillation parameters, the predicted values of the Dirac CP-violating phase δ are , , and , respectively. To further assess the viability of the model, a comprehensive numerical analysis is performed by utilizing neutrino oscillation parameters at the level. It is found that the allowed ranges of δ are , , and , which all fall within its range. These results indicate that the proposed symmetry-breaking scheme can naturally explain the realistic lepton mass hierarchy and mixing pattern, thereby providing valuable theoretical perspectives for future research.

The generation of the fermion mass hierarchy in the standard model of particle physics is a long-standing puzzle. The recent discoveries from neutrino physics suggest that the mixing in the lepton sector is large compared to the quark mixings. To understand this asymmetry between the quark and lepton mixings is an important aim for particle physics. In this regard, two promising approaches from the theoretical side are grand unified theories and family symmetries. In this paper we try to understand certain general features of grand unified theories with Abelian family symmetries by taking the simplest $SU(5)$ grand unified theory as a prototype. We construct an $SU(5)$ toy model with $U(1{)}_{F}\ensuremath{\bigotimes}{\mathbb{Z}}_{2}^{\ensuremath{'}}\ensuremath{\bigotimes}{\mathbb{Z}}_{2}^{\ensuremath{'}\ensuremath{'}}\ensuremath{\bigotimes}{\mathbb{Z}}_{2}^{\ensuremath{'}\ensuremath{'}\ensuremath{'}}$ family symmetry that, in a natural way, duplicates the observed mass hierarchy and mixing matrices to lowest approximation. The system for generating the mass hierarchy is through a Froggatt-Nielsen type mechanism. One idea that we use in the model is that the quark and charged lepton sectors are hierarchical with small mixing angles while the light neutrino sector is democratic with larger mixing angles. We also discuss some of the difficulties in incorporating finer details into the model without making further assumptions or adding a large scalar sector.

We explore in detail the effective matter fermion mass sum-rules in a class of renormalizable SUSY $SO(10)$ grand unified models where the quark and lepton mass and mixing patterns originate from nondecoupling effects of an extra vector matter multiplet living around the unification scale. If the renormalizable type-II contribution governed by the $SU(2{)}_{L}$-triplet in ${54}_{H}$ dominates the seesaw formula, we obtain an interesting correlation between the maximality of the atmospheric neutrino mixing and the proximity of ${y}_{s}/{y}_{b}$ to $|{V}_{cb}|$ in the quark sector.

On-mass-shell renormalization of fermion mixing matrices

In this work we propose an extension to the Standard Model in which we consider a type-III two-Higgs-doublet model (2HDM) plus massive neutrinos and the horizontal flavor symmetry ${S}_{3}$ ($\ensuremath{\nu}2\mathrm{HDM}\ensuremath{\bigotimes}{S}_{3}$). In the above framework and with the explicit breaking of flavor symmetry ${S}_{3}$, the Yukawa matrices in the flavor-adapted basis are represented by means of a matrix with two texture zeros. Also, the active neutrinos are considered as Majorana particles and their masses are generated through the type-I seesaw mechanism. The unitary matrices that diagonalize the mass matrices, as well as the flavor-mixing matrices, are expressed in terms of fermion mass ratios. Consequently, in the mass basis the entries of the Yukawa matrices naturally acquire the form of the so-called Cheng-Sher ansatz. For the leptonic sector of $\ensuremath{\nu}2\mathrm{HDM}\ensuremath{\bigotimes}{S}_{3}$, we compare, through a ${\ensuremath{\chi}}^{2}$ likelihood test, the theoretical expressions of the flavor-mixing angles with the masses and flavor-mixing leptons current experimental data. The results obtained in this ${\ensuremath{\chi}}^{2}$ analysis are in very good agreement with the current experimental data. We also obtain allowed value ranges for the ``Dirac-like'' phase factor, as well as for the two Majorana phase factors. Furthermore, we study the phenomenological implications of these numerical values of the $CP$-violation phases on the neutrinoless double-beta decay, and for long baseline neutrino oscillation experiments such as T2K, $\mathrm{NO}\ensuremath{\nu}\mathrm{A}$, and DUNE.