CKM Mixing Matrix Research Articles

Towards understanding fermion masses and mixings

The Standard Model does not constrain the form of the Yukawa matrices and thus the origin of fermion mass hierarchies and mixing pattern remains puzzling. On the other hand, there are intriguing relations between the quark masses and their weak mixing angles, such as the well-known relationship [Formula: see text] for the Cabibbo angle, which may point towards specific textures of Yukawa matrices hypothesized by Harald Fritzsch at the end of the 70s. Though the original ansatz of Fritzsch is excluded by the experimental data, one can consider its minimal modification which consists in introducing an asymmetry between the 23 and 32 entries in the down-quark Yukawa matrix. We show that this structure is perfectly compatible with the present precision data on quark masses and CKM mixing matrix, and theoretically it can be obtained in the context of [Formula: see text] model with inter-family [Formula: see text] symmetry. We also discuss some alternative approaches which could give a natural description of the fermion mass spectrum and weak mixing pattern.

Minimally modified Fritzsch texture for quark masses and CKM mixing

The Standard Model does not constrain the form of the Yukawa matrices and thus the origin of fermion mass hierarchies and mixing pattern remains puzzling. On the other hand, there are intriguing relations between fermion masses and mixing angles which may point towards specific textures of Yukawa matrices. One of the classic hypothesis is the zero texture proposed by Fritzsch which is, however, excluded by present precision tests since it predicts a too large value of |Vcb| as well as a too small value of the ratio |Vub/Vcb|. In this paper we discuss a minimal modification which still maintains the six zero entries as in the original Fritzsch ansatz. This modification consists in introducing an asymmetry between the 23 and 32 entries in the down-quark Yukawa matrix. We show that this flavour structure can naturally emerge in the context of models with inter-family SU(3)H symmetry. We present a detailed analysis of this Fritzsch-like texture by testing its predictions and showing that it is perfectly compatible with the present precision data on quark masses and CKM mixing matrix.

Modular invariant A4 models for quarks and leptons with generalized CP symmetry

We perform a systematical analysis of the A4 modular models with generalized CP for the masses and flavor mixing of quarks and leptons, and the most general form of the quark and lepton mass matrices is given. The CP invariance requires all couplings real in the chosen basis and thus the vacuum expectation value of the modulus τ uniquely breaks both the modular symmetry and CP symmetry. The phenomenologically viable models with minimal number of free parameters and the results of fit are presented. We find 20 models with 7 real free parameters that can accommodate the experimental data of lepton sector. We then apply A4 modular symmetry to the quark sector to explain quark masses and CKM mixing matrix, the minimal viable quark model is found to contain 10 free real parameters. Finally, we give two predictive quark-lepton unification models which use only 16 real free parameters to explain the flavor patterns of both quarks and leptons.

A comparative study between the modified Fritzsch and nearest neighbor interaction textures

From the mass textures’ point of view, we present a comparative study of the [Formula: see text] flavor symmetry in the left–right symmetry model (LRSM) and the baryon minus lepton model (BLM) taking into account their predictions on the CKM mixing matrix. To do this, we recover the already studied quark mass matrix, that comes from some published papers, and under certain strong assumptions, one can show that there are predictive scenarios in the LRSM and BLM where the modified Fritzsch and nearest neighbor interaction (NNI) textures drive, respectively, the quark mixings. As the main result, the CKM mixing matrix is in good agreement with the last experimental data in the flavored BLM model.

B\u2013L Model with mathbf{S}_{3} symmetry

We make a scalar extension of the B–L gauge model where the mathbf{S}_{3} non-abelian discrete group drives mainly the Yukawa sector. Motived by the large and small hierarchies among the quark and active neutrino masses, respectively, the quark and lepton families are not treated on the same footing under the assignment of the discrete group. As a consequence, the nearest neighbor interaction (NNI) textures appear in the quark sector, leading to the CKM mixing matrix, whereas in the lepton sector, a soft breaking of the mu leftrightarrow tau symmetry in the effective neutrino mass, which comes from type I see-saw mechanism, provides a non-maximal atmospheric angle and a non-zero reactor angle.

CP violation of quarks in A4 modular invariance

We discuss the quark mass matrices in the A4 modular symmetry, where the A4 triplet of Higgs is introduced for each up-quark and down-quark sectors, respectively. The model has six real parameters and two complex parameters in addition to the modulus τ. By inputting six quark masses and three CKM mixing angles, we can predict the CP violation phase δ and the Jarlskog invariant JCP. The predicted ranges of δ and JCP are consistent with the observed values. The absolute value of Vub is smaller than 0.0043, while Vcb is larger than 0.0436. In conclusion, our quark mass matrices with the A4 modular symmetry can reproduce the CKM mixing matrix completely with observed quark masses.

Flavored non-minimal left\u2013right symmetric model fermion masses and mixings

A complete study on the fermion masses and flavor mixing is presented in a non-minimal left–right symmetric model (NMLRMS) where the mathbf{S}_{3}otimes mathbf{Z}_{2}otimes mathbf{Z}^{e}_{2} flavor symmetry drives the Yukawa couplings. In the quark sector, the mass matrices possess a kind of generalized Fritzsch textures that allow us to fit the CKM mixing matrix in good agreement to the latest experimental data. In the lepton sector, on the other hand, a soft breaking of the mu leftrightarrow tau symmetry provides nonzero and nonmaximal reactor and atmospheric angles, respectively. The inverted and degenerate hierarchies are favored in the model where a set of free parameters is found to be consistent with the current neutrino data.

Third family quark–lepton unification at the TeV scale

We construct a model of quark–lepton unification at the TeV scale based on an SU(4) gauge symmetry, while still having acceptable neutrino masses and enough suppression in flavor changing neutral currents. An approximate U(2) flavor symmetry is an artifact of family-dependent gauge charges leading to a natural realization of the CKM mixing matrix. The model predicts sizeable violation of PMNS unitarity as well as a gauge vector leptoquark U1μ=(3,1,2/3) which can be produced at the LHC – both effects within the reach of future measurements. In addition, recently reported experimental anomalies in semi-leptonic B-meson decays, both in charged b→cτν and neutral b→sμμ currents, can be accommodated.

Fermion masses and mixing in SU(5)×D4 × U(1) model

We propose a supersymmetric SU(5)×Gf GUT model with flavor symmetry Gf=D4×U(1) providing a good description of fermion masses and mixing. The model has twenty eight free parameters, eighteen are fixed to produce approximative experimental values of the physical parameters in the quark and charged lepton sectors. In the neutrino sector, the TBM matrix is generated at leading order through type I seesaw mechanism, and the deviation from TBM studied to reconcile with the phenomenological values of the mixing angles. Other features in the charged sector such as Georgi–Jarlskog relations and CKM mixing matrix are also studied.

CKM angle γ measurements at LHCb

The CKM angle γ remains the least known parameter of the CKM mixing matrix. The precise measurement of this angle, as a Standard Model benchmark, is a key goal of the LHCb experiment. We present four recent CP violation studies related to the measurement of γ, including amplitude analysis of B± → DK± decays, the ADS/GLW analysis of B± → DK*0 decays and the time-dependent analysis of B± → DK±sK± decays.

Constraining multi-Higgs flavour models

To study a flavour model with a non-minimal Higgs sector one must first define the symmetries of the fields; then identify what types of vacua exist and how they may break the symmetries; and finally determine whether the remnant symmetries are compatible with the experimental data. Here we address all these issues in the context of flavour models with any number of Higgs doublets. We stress the importance of analysing the Higgs vacuum expectation values that are pseudo-invariant under the generators of all subgroups. It is shown that the only way of obtaining a physical CKM mixing matrix and, simultaneously, non-degenerate and non-zero quark masses is requiring the vacuum expectation values of the Higgs fields to break completely the full flavour group, except possibly for some symmetry belonging to baryon number. The application of this technique to some illustrative examples, such as the flavour groups Delta(27), A4 and S3, is also presented.

Flavor-changing neutral currents in the minimal 3-3-1 model revisited

We show that in the minimal 3-3-1 model the flavor changing neutral currents (FCNCs) do not impose necessarily strong constraints on the mass of the $Z^\prime$ of the model if we also consider the neutral scalar contributions to such processes, like the neutral mesons mass difference and rare semileptonic decays. We first obtain numerical values for all the mixing matrices of the model i.e., the unitary matrices that rotate the left- and right-handed quarks in each charge sector which give the correct mass of all the quarks and the CKM mixing matrix. Then, we find that there is a range of parameters in which the neutral scalar contributions to these processes may interfere with those of the $Z^\prime$, implying this vector boson may be lighter than it has been thought.

CHARGED LEPTON CORRECTION TO TRI-BIMAXIMAL LEPTON MIXING AND ITS IMPLICATIONS TO NEUTRINO PHENOMENOLOGY

The recent results from Daya Bay and RENO reactor neutrino experiments have firmly established that the smallest reactor mixing angle θ13 is nonvanishing at the 5 σ level, with a relatively large value, i.e. θ13 ≈ 9°. Using the fact that the neutrino mixing matrix can be represented as [Formula: see text], where Ul and Uν result from the diagonalization of the charged lepton and neutrino mass matrices and Pν is a diagonal matrix containing the Majorana phases and assuming the tri-bimaximal (TBM) form for Uν, we investigate the possibility of accounting for the large reactor mixing angle due to the corrections of the charged lepton mixing matrix. The form of Ul is assumed to be that of CKM mixing matrix of the quark sector. We find that with this modification it is possible to accommodate the large observed reactor mixing angle θ13. We also study the implications of such corrections on the other phenomenological observables.

UNIVERSALITY OF QUARK–LEPTON MASS MATRIX

The recently observed lepton mixing angle θ13 of the MNS mixing matrix is well incorporated in a universal mixing hypothesis between quark and lepton sectors. This hypothesis asserts that, in the charged lepton diagonal base, all other mass matrices for up- and down-type quarks and light neutrinos are diagonalized by the same unitary matrix except for the phase elements. It is expressed as V CKM = U MNS (δ′)†PU MNS (δ) for quark mixing matrix V CKM and lepton mixing matrix U MNS (δ) in the phenomenological level. Here P is a diagonal phase mass matrix. δ′ is a slightly different phase parameter from the Dirac CP-violating phase δ = 1.1π (best fit) in the MNS lepton mixing matrix.

Neutrino mass determination from a four-zero texture mass matrix

We analyze the different parametrizations of a general four-zero texture mass matrices for quarks and leptons, that are able to reproduce the CKM and PMNS mixing matrices. This study is done through a Chi-Square analysis. In quark sector, only four solutions are found to be compatible with CKM mixing matrix. In leptonic sector, using the last experimental results about the mixing angles in the neutrino sector, our Chi-Square analysis shows a preferred value for m_nu_3 to be around 0.05 eV independently of the parametrization of the four-zero texture mass matrices chosen for the charged leptons and neutrinos.

Heavy vector-like top partners at the LHC and flavour constraints

Abstract We consider the phenomenology at the Large Hadron Collider of new heavy vector-like quarks which couple mainly to the third generation quarks via Yukawa interactions, with special emphasis on non-standard doublet representations which are less constrained from present data. We also discuss in detail the flavour limits at tree level and loop level and implications of a generalised CKM mixing matrix to these cases.

Quark mixing in the discrete dark matter model

We consider a model in which dark matter is stable as it is charged under a Z 2 symmetry that is residual after an A 4 flavour symmetry is broken. We consider the possibility to generate the quark masses by charging the quarks appropriately under A 4 . We find that it is possible to generate the CKM mixing matrix by an interplay of renormalisable and dimension-six operators. In this set-up, we predict the third neutrino mixing angle to be large and the dark matter relic density to be in the correct range. Low energy observables – in particular meson–antimeson oscillations – are hard to facilitate. We find that only in a situation where there is a strong cancellation between the Standard Model contribution and the contribution of the new Higgs fields, B meson oscillations are under control.

FlavorΔ(54)inSU(5)supersymmetric model

We design a supersymmetric SU (5) GUT model using \Delta (54), a finite non-abelian subgroup of SU (3)f . Heavy right handed neutrinos are introduced which transform as three-dimensional repre-sentation of our chosen family group. The model successfully reproduces the mass hierarchical mass structures of the Standard Model, and the CKM mixing matrix. It then provides predictions for the light neutrino with a normal hierarchy and masses such that m{\nu},1 \approx 5\times10-3 eV, m{\nu}, 2 \approx 1\times 10-2 eV, and m{\nu},3 \approx 5 \times 10-2 eV. We also provide predictions for masses of the heavy neutrinos, and correc- tions to the tri-bimaximal matrix that fit within experimental limits, e.g. a reactor angle of -7.31o. A simple modification to our model is introduced at the end and is shown to also produce predictions that fall well within those limits.

Bimaximal mixing and large θ 13 in a SUSY SU(5) model based on S 4

The recent analyses of the world neutrino data, including the T2K and MINOS results, point toward a statistically significant deviation of theta13 from zero. In this paper we present a SUSY SU(5) model based on the discrete S4 group which predicts a large theta13 of order lambdaC, lambdaC being the Cabibbo angle. The other mixing angles in the neutrino sector are all compatible with current experimental data. In the quark sector, the entries of the CKM mixing matrix as well as the mass hierarchies in both up and down quark sectors are well reproduced and only a small enhancement is needed to reproduce lambdaC.

Stability of dark matter from the [formula omitted] flavor group

We study a model based on the dihedral group D4 in which the dark matter is stabilized by the interplay between a remnant Z2 symmetry, of the same spontaneously broken non-abelian group, and an auxiliary Z2f introduced to eliminate unwanted couplings in the scalar potential. In the lepton sector the model is compatible with normal hierarchy only and predicts a vanishing reactor mixing angle, θ13=0. Since mν1=0, we also have a simple prediction for the effective mass in terms of the solar angle: |mββ|=|mν2|sin2θ⊙∼10−3 eV. There also exists a large portion of the model parameter space where the upper bounds on lepton flavor violating processes are not violated. We incorporate quarks in the same scheme finding that a description of the CKM mixing matrix is possible and that semileptonic K and D decays mediated by flavor changing neutral currents are under control.