Quark Mass Matrices Research Articles

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.

Three generations of Higgses and the cyclic groups

Multi-Higgs doublet models are interesting extensions of the Standard Model that can be related to flavor. The reason is that most flavor models usually involve the presence of several additional scalar fields. In this work we present an analysis that shows that for renormalizable flavor models based on the cyclic group of order N, if there is one flavored SU(2) double Higgs per generation, the smallest N that can be used to reproduce the Nearest-Neighbor-Interaction texture for the quark mass matrices is N=5. Results for the Higgs spectrum and consistency under K–K¯ mixing in a specific model with Z5 are also presented.

Non-Abelian discrete gauge symmetries in 4d string models

We study the realization of non-Abelian discrete gauge symmetries in 4d field theory and string theory compactifications. The underlying structure generalizes the Abelian case, and follows from the interplay between gaugings of non-Abelian isometries of the scalar manifold and field identifications making axion-like fields periodic. We present several classes of string constructions realizing non-Abelian discrete gauge symmetries. In particular, compactifications with torsion homology classes, where non-Abelianity arises microscopically from the Hanany-Witten effect, or compactifications with non-Abelian discrete isometry groups, like twisted tori. We finally focus on the more interesting case of magnetized branes in toroidal compactifications and quotients thereof (and their heterotic and intersecting duals), in which the non-Abelian discrete gauge symmetries imply powerful selection rules for Yukawa couplings of charged matter fields. In particular, in MSSM-like models they correspond to discrete flavour symmetries constraining the quark and lepton mass matrices, as we show in specific examples.

Spontaneous CP Violation Jarlskog Invariant in SM⊗S3

In our days, CP (Charge Parity) violation in the Standar Model of fundamental interactions still remains as an open problem. It is well known that explicit CP violation may be included by impossing complex Yukawa couplings in the Yukawa sector or complex Higgs couplings in exttended Higgs sectors with more than one Higgs field. It is desirable to have a fundamental CP violation theory, in that sence, we analyse the diferent secenarios for Spontaneous CP violation in an exteded Higgs model with three Higgs fields and a discrete flavour permutational symmetry S3. Spontaneous CP violation effects contribute to the Higgs mass matrix, as well as, up and down quark mass matrices. This complex quark mass matrices allow us to study the conditions for a non-vanishing Jarlskog invariant J which provides a necessary and sufficient contribution for a spontaneous CPV coming from SM ⊗ S3

Invariants, alignment and the pattern of fermion masses and mixing

We show that the main features of the pattern of fermion masses and mixing can be expressed in terms of simple relations among weak-basis invariants. In the quark sector, we identify the weak-basis invariants which signal the observed alignment of the up and down quark mass matrices in flavour space. In the lepton sector, we indicate how a set of conditions on weak-basis invariants can lead to the observed pattern of leptonic mixing, including the recent measurement of Ue3 by the Daya Bay Collaboration. We also show the usefulness of these invariants in the study of specific ansätze for the flavour structure of fermion mass matrices.

Validity of quasi-degenerate neutrino mass models and their predictions on baryogenesis

Quasi-degenerate neutrino mass models (QDN) which can explain the current data on neutrino masses and mixings, are studied. In the first part, we study the effect of CP-phases on QDN mass matrix (mLL) obeying μ–τ symmetry in normal hierarchical (QD-NH) and inverted hierarchical (QD-IH) patterns. The numerical predictions are consistent with observed data on (i) solar mixing angle (θ12) which lies below tri-bimaximal (TBM) value, (ii) absolute neutrino masses consistent with 0νββ decay mass parameter (mee) and (iii) cosmological upper bound ∑i3mi. mLL is parameterized using only two unknown parameters (ϵ,η) within μ–τ symmetry. The second part deals with the estimation of observed baryon asymmetry of the universe (BAU) where we consider the Majorana CP violating phases (α,β) and the Dirac neutrino mass matrix (mLR). mLR is taken as either the charged lepton or the up quark mass matrix. α, β is derived from the heavy right-handed Majorana mass matrix MRR. MRR is generated from mLL and mLR through inversion of Type-I seesaw formula. The predictions for BAU are nearly consistent with observations for flavoured thermal leptogenesis scenario for Type-IA in both QD-NH and QD-IH models. We also observe some enhancement effects in flavour leptogenesis compared to non-flavour leptogenesis by a magnitude of order one. In non-thermal leptogenesis QD-NH Type-IA is the only model consistent with observed data on baryon asymmetry. QD-NH model appears to be more favourable than those of QD-IH. The predicted inflaton mass needed to produce the BAU is found to be Mϕ∼1010 GeV corresponding to the reheating temperature TR=106 GeV. The present analysis shows that the three absolute neutrino masses may exhibit quasi-degenerate pattern in nature.

Novel sources of Flavor Changed Neutral Currents in the 331 RHN model

Sources of Flavor Changed Neutral Currents (FCNC) emerge naturally from a well motivated framework called 3-3-1 with right-handed neutrinos model, 331 RHN for short, mediated by an extra neutral gauge boson Z′. Following previous work we calculate these sources and in addition we derive new ones coming from CP-even and -odd neutral scalars which appear due to their non-diagonal interactions with the physical standard quarks. Furthermore, by using 4 texture zeros for the quark mass matrices, we derive the mass difference terms for the neutral mesons systems K 0– $\bar{K}^{0}$ , D 0– $\bar{D}^{0}$ and B 0– $\bar{B^{0}}$ and show that, though one can discern that the Z′ contribution is the most relevant one for mesons oscillations purposes, scalar contributions play a role also in this processes and hence it is worthwhile to investigate them and derive new bounds on space of parameters. In particular, studying the B 0– $\bar {B^{0}}$ system we set the bounds M Z′≳4.2 TeV and $M_{S_{2}},M_{I_{3}} \gtrsim7.5~\mbox{TeV}$ in order to be consistent with the current measurements.

STATISTICAL COMPARISON OF QUARK MASS MATRICES IN THE PHYSICAL BASIS

Using the four best measured moduli of the flavor mixing matrix (|V ud |, |V us |, |V cd |, |V cs |), the Jarlskog invariant J(V), and the quark masses at MZ energy scale as experimental constraints, a statistical comparison of three different types of quark mass matrices in the physical basis is performed. The mass matrices in question are the Chaturvedi–Gupta–Sánchez-Colón (CGS), the Fritzsch and the Gupta–Rajpoot types. With nine parameters the best fits are obtained using a Gupta–Rajpoot-type matrix while with seven parameters the best fits are obtained using the CGS-type matrix. The stability of our analysis with respect to evolution of the quark masses is also presented.

Symmetryless dark matter

It is appealing to stabilize dark matter by the same discrete symmetry that is used to explain the structure of quark and lepton mass matrices. However, to generate the observed fermion mixing patterns, any flavor symmetry must necessarily be broken, rendering dark matter unstable. We study singlet, doublet and triplet SU(2) multiplets of both scalar and fermion dark matter candidates and enumerate the conditions under which no d < 6 dark matter decay operators are generated even in the case if the flavor symmetry is broken to nothing. We show that the VEVs of flavon scalars transforming as higher multiplets (e.g. triplets) of the flavor group must be at the electroweak scale. The most economical way for that is to use SM Higgs boson(s) as flavons. Such models can be tested by the LHC experiments. This scenario requires the existence of additional Froggatt-Nielsen scalars that generate hierarchies in Yukawa couplings. We study the conditions under which large and small flavor breaking parameters can coexist without destabilizing the dark matter.

Nearest-neighbor-interactions from a minimal discrete flavor symmetry withinSU(5)grand unification

A flavour symmetry based on Z_4 is analysed in the context of SU(5) Grand Unification with the standard fermionic content plus three right-handed neutrinos. The role of Z_4 is to forbid some Yukawa couplings of up- and down-quarks to Higgs scalars such that the quark mass matrices M_u, M_d have Nearest-Neighbour-Interaction (NNI) structure, once they are generated through the electroweak symmetry breaking. It turns out in this framework that Z_4 is indeed the minimal discrete symmetry and its implementation requires the introduction of at least two Higgs quintets, which leads to a two Higgs doublet model at low energy scale. Due to the SU(5) unification, it is shown that the charged lepton mass matrix develops also NNI form. However, the effective neutrino mass matrix exhibits a non parallel pattern, in the framework of the type-I seesaw mechanism. Analysing all possible zero textures allowed by gauge-horizontal symmetry SU(5) x Z_4, it is seen that only two patterns are in agreement with the leptonic experimental data and they could be further distinguished by the light neutrino mass spectrum hierarchy. It is also demonstrated that Z_4 freezes out the possibility of proton decay through exchange of colour Higgs triplets at tree-level.

The CKM matrix with maximal CP violation from [formula omitted] symmetry

The recent accurate determination of the CKM parameters including the maximal CP phase π2 enables us to write down the up-type and down-type quark mass matrices to a high degree of accuracy. The lightest element (u¯u element) of the quark mass texture (not the mass eigenvalue) has a power λ6 where λ=sinθC. The CP phase of 2π divided by an integer hints a discrete symmetry. Since λ6 is the highest power of λ among the quark mass matrix elements, we present as an example a possibility that the maximal CP phase π2 is obtainable from a supersymmetric Z12 discrete symmetry model.

POSSIBLE TEXTURES OF THE FERMION MASS MATRICES

Texture specific fermion mass matrices have played an important role in understanding several features of fermion masses and mixings. In the present work, we have given an overview of all possible cases of Fritzsch-like as well as non-Fritzsch-like texture 6 and 5 zero fermion mass matrices. Further, for the case of texture 4 zero Fritzsch-like quark mass matrices, the issue of the hierarchy of the elements of the mass matrices and the role of their phases have been discussed. Furthermore, the case of texture 4 zero Fritzsch-like lepton mass matrices has also been discussed with an emphasis on the hierarchy of neutrino masses for both Majorana and Dirac neutrinos.

Yukawaon model with U(3)×O(3) family symmetries

A quark and lepton mass matrix model with family symmetries U(3)×O(3) is investigated on the basis of the so-called Yukawaon model. In the present model, quarks and leptons are assigned to (ℓ, ec, uc) ∼ (3, 3, 3*) of U(3) and (q, dc, νc) ∼ (3, 3, 3) of O(3). Then, the neutrino mass matrix is given by Mν = mDM−1RmTD with mD∝⟨Φe⟩, where the charged lepton mass matrix Me is given by Me = k⟨Φe⟩⟨ΦTe⟩. A merit in considering U(3)×O(3) lies in that we can lower the cutoff scale Λ in the Yukawaon model.

Baryogenesis via leptogenesis from quark-lepton symmetry and a compact heavyNRspectrum

By demanding a compact spectrum for the right-handed neutrinos and an approximate quark-lepton symmetry inspired from $SO(10)$ gauge unification (assuming a Dirac neutrino mass matrix close to the up quark mass matrix), we construct a fine-tuning scenario for baryogenesis via leptogenesis. We find two solutions with a normal hierarchy, with the lightest neutrino mass ${m}_{1}$ different from zero, providing an absolute scale for the spectrum. In the approximations of the model, there are three independent $CP$ phases: ${\ensuremath{\delta}}_{L}$ (that we take of the order of the quark Kobayashi-Maskawa phase) and the two light neutrino Majorana phases $\ensuremath{\alpha}$ and $\ensuremath{\beta}$. A main conclusion is that, although this general scheme is rather flexible, in some regions of parameter space we find that the necessary baryogenesis with its sign is given in terms of the ${\ensuremath{\delta}}_{L}$ phase alone. The light Majorana phases can also be computed, and they turn out to be close to $\ensuremath{\pi}/2$ or very small. Moreover, $SO(10)$ breaks down to the Pati-Salam group $SU(4)\ifmmode\times\else\texttimes\fi{}SU(2)\ifmmode\times\else\texttimes\fi{}SU(2)$ at the expected natural intermediate scale of about ${10}^{10}--{10}^{11}\text{ }\text{ }\mathrm{GeV}$. A prediction is made for the effective mass in $(\ensuremath{\beta}\ensuremath{\beta}{)}_{0\ensuremath{\nu}}$ decay, the ${\ensuremath{\nu}}_{e}$ mass, and the sum of all light neutrino masses.

Right unitarity triangles and tri-bimaximal mixing from discrete symmetries and unification

We propose new classes of models which predict both tri-bimaximal lepton mixing and a right-angled Cabibbo–Kobayashi–Maskawa (CKM) unitarity triangle, α ≈ 90 ° . The ingredients of the models include a supersymmetric (SUSY) unified gauge group such as SU ( 5 ) , a discrete family symmetry such as A 4 or S 4 , a shaping symmetry including products of Z 2 and Z 4 groups as well as spontaneous CP violation. We show how the vacuum alignment in such models allows a simple explanation of α ≈ 90 ° by a combination of purely real or purely imaginary vacuum expectation values (vevs) of the flavons responsible for family symmetry breaking. This leads to quark mass matrices with 1–3 texture zeros that satisfy the “phase sum rule” and lepton mass matrices that satisfy the “lepton mixing sum rule” together with a new prediction that the leptonic CP violating oscillation phase is close to either 0°, 90°, 180°, or 270° depending on the model, with neutrino masses being purely real (no complex Majorana phases). This leads to the possibility of having right-angled unitarity triangles in both the quark and lepton sectors.

Texture zeros for the Standard Model quark mass matrices

A way of counting free parameters in the quark mass matrices of the standard model, including the constraints coming from weak basis transformations, is presented; this allow to understand the exact physical meaning of the parallel and non-parallel texture zeros which appear in some "ans\"{a}tz" of the $3\times 3$ quark mass matrices, including the CP violation phenomena in the analysis, it is shown why the six texture zeros are ruled out. Finally, a five texture zeros "ans\"{a}tze" which properly copes with all experimental constrains, including the angles of the unitary triangle, is presented.

Non-Hermitian perturbations to the Fritzsch textures of lepton and quark mass matrices

We show that non-Hermitian and nearest-neighbor-interacting perturbations to the Fritzsch textures of lepton and quark mass matrices can make both of them fit current experimental data very well. In particular, we obtain θ23≃45° for the atmospheric neutrino mixing angle and predict θ13≃3° to 6° for the smallest neutrino mixing angle when the perturbations in the lepton sector are at the 20% level. The same level of perturbations is required in the quark sector, where the Jarlskog invariant of CP violation is about 3.7×10−5. In comparison, the strength of leptonic CP violation is possible to reach about 1.5×10−2 in neutrino oscillations.

Yukawa couplings and fermion mass structure in F-theory GUTs

The calculation of Yukawa couplings in F-theory GUTs is developed. The method is applied to the top and bottom Yukawa couplings in an SU(5) model of fermion masses based on family symmetries coming from the SU(5)_\perp factor in the underlying E(8) theory. The remaining Yukawa couplings involving the light quark generations are determined by the Froggatt Nielsen non-renormalisable terms generated by heavy messenger states. We extend the calculation of Yukawa couplings to include massive states and estimate the full up and down quark mass matrices in the SU(5) model. We discuss the new features of the resulting structure compared to what is usually assumed for Abelian family symmetry models and show how the model can give a realistic quark mass matrix structure. We extend the analysis to the neutrino sector masses and mixing where we find that tri-bi-maximal mixing is readily accommodated. Finally we discuss mechanisms for splitting the degeneracy between the charged leptons and the down quarks and the doublet triplet splitting in the Higgs sector.

P/CPconservingCP/Pviolation solves strongCPproblem

We find a solution to the strong $CP$ problem that may be testable at the LHC and future colliders. In this solution $CP$ is broken by parity conserving terms, while parity breaking vacuum expectation values conserve $CP$. The quark mass matrix is Hermitian at the tree level, and the strong $CP$ phase is generated only in loops where $CP$ and $P$ violating sectors interact. A full vectorlike quark family with parity symmetric mass terms that violate $CP$ softly is predicted. Since no Higgs vacuum expectation values [other than the $SU(2{)}_{L}$ breaking weak-scale vacuum expectation value] contribute to the masses of the new quarks, they can be naturally light, independent of parity breaking and other high energy scales.

Left-right symmetry at LHC

We revisit the issue of the limit on the scale of Left-Right symmetry breaking. We focus on the minimal SU(2)_L x SU(2)_R x U(1)_B-L gauge theory with the seesaw mechanism and discuss the two possibilities of defining Left-Right symmetry as parity or charge conjugation. In the commonly adopted case of parity, we perform a complete numerical study of the quark mass matrices and the associated left and right mixing matrices without any assumptions usually made in the literature about the ratio of vacuum expectation values. We find that the usual lower limit on the mass of the right-handed gauge boson from the K mass difference, M_WR>2.5TeV, is subject to a possible small reduction due to the difference between right and left Cabibbo angles. In the case of charge conjugation the limit on M_WR is somewhat more robust. However, the more severe bounds from CP-violating observables are absent in this case. In fact, the free phases can also resolve the present mild discrepancy between the Standard Model and CP-violation in the $B$-sector. Thus, even in the minimal case, both charged and neutral gauge bosons may be accessible at the Large Hadron Collider with spectacular signatures of lepton number violation.