Dirac Mass Matrix Research Articles

Texture Dirac Mass Matrices and Lepton Asymmetry in the Minimal Seesaw Model with Tri-Bimaximal Mixing

We examined the minimal seesaw mechanism of 3 × 2 Dirac matrix by starting our analysis with the masses of light neutrinos with tri/bi-maximal mixing in the basis where the charged-lepton Yukawa matrix and heavy Majorana neutrino mass matrix are diagonal. We found all possible Dirac mass textures which contain one zero entry or two in the matrix.

SpontaneousCPviolation inA4×SU(5)with constrained sequential dominance 2

We revisit a two right-handed neutrino model with two texture zeros, namely an indirect model based on ${A}_{4}$ with the recently proposed new type of constrained sequential dominance (CSD2), involving vacuum alignments along the $(0,1,\ensuremath{-}1{)}^{T}$ and $(1,0,2{)}^{T}$ directions in flavor space, which are proportional to the neutrino Dirac mass matrix columns. In this paper we construct a renormalizable and unified indirect ${A}_{4}\ifmmode\times\else\texttimes\fi{}SU(5)$ model along these lines and show that, with spontaneous $CP$ violation and a suitable vacuum alignment of the phases, the charged lepton corrections lead to a reactor angle in good agreement with results from Daya Bay and RENO. The model predicts a right-angled unitarity triangle in the quark sector and a Dirac $CP$ violating oscillation phase in the lepton sector of $\ensuremath{\delta}\ensuremath{\approx}130\ifmmode^\circ\else\textdegree\fi{}$, while providing a good fit to all quark and lepton masses and mixing angles.

BIPAIR NEUTRINO MIXING AND LEPTOGENESIS

We estimate the baryon–photon ratio in the Universe via the leptogenesis scenario in the framework of the minimal seesaw model with a minimally modified bipair neutrino mixing. We assume that one of the elements of the 3 × 2 Dirac mass matrix mD is exactly zero. It turns out that the lepton asymmetry as well as baryon number of the Universe definitely depends on the reactor neutrino mixing angle in the cases of (mD)11 = 0 and (mD)12 = 0. The allowed region of the Majorana CP phase is separated into three regions related to the assumption of either (mD)11 = 0, (mD)21, 31 = 0 or (mD)12 = 0.

Large $\theta_{13}^{\nu}$ and unified description of quark and lepton mixing matrices

We present a revised version of the so-called “yukawaon model”, which was proposed for the purpose of a unified description of the lepton mixing matrix U PMNS and the quark mixing matrix V CKM. It is assumed from a phenomenological point of view that the neutrino Dirac mass matrix M D is given with a somewhat different structure from the charged lepton mass matrix M e , although M D =M e was assumed in the previous model. As a result, the revised model predicts a reasonable value sin22θ 13∼0.07 with keeping successful results for other parameters in U PMNS as well as V CKM and quark and lepton mass ratios.

S3model for lepton mass matrices with nearly minimal texture

We propose a simple extension of the electroweak standard model based on the discrete ${S}_{3}$ symmetry that is capable of realizing a nearly minimal Fritzsch-type texture for the Dirac mass matrices of both charged leptons and neutrinos. This is achieved with the aid of additional ${Z}_{5}$ and ${Z}_{3}$ symmetries, one of which can be embedded in $U(1{)}_{B\ensuremath{-}L}$. Five complex scalar singlet fields are introduced in addition to the standard model with right-handed neutrinos. Although more general, the modified texture of the model retains the successful features of the minimal texture without fine-tuning; namely, it accommodates the masses and mixing of the leptonic sector and relates the emergence of large leptonic mixing angles with the seesaw mechanism. For large deviations of the minimal texture, both quasidegenerate spectrum or inverted hierarchy are allowed for neutrino masses.

Quasidegenerate neutrinos in type II seesaw models

We present an analysis of normal and inverted hierarchical neutrino mass models within the framework of tri-bi-maximal (TBM) mixing. Considering the neutrinos to be quasi-degenerate (QDN), we study two different neutrino mass models with mass eigenvalues $(m_1, -m_2, m_3)$ and $(m_1, m_2, m_3)$ for both normal hierarchical (NH) and inverted hierarchical (IH) cases. Parameterizing the neutrino mass matrix using best fit oscillation and cosmology data for a QDN scenario, we find the right-handed Majorana mass matrix using type I seesaw formula for two types of Dirac neutrino mass matrices: charged lepton (CL) type and up quark (UQ) type. Incorporating the presence of type II seesaw term which arises naturally in generic left-right symmetric models (LRSM) along with type I term, we compare the predictions for neutrino mass parameters with the experimental values. Within such a framework and incorporating both oscillation as well as cosmology data, we show that QDN scenario of neutrino masses can still survive in nature with some minor exceptions. A viable extension of the standard model with an abelian gauged flavor symmetry is briefly discussed which can give rise to the desired structure of the Dirac and Majorana mass matrices.

Algebraic description of external and internal attributes of fundamental fermions

To describe external and internal attributes of fundamental fermions, a theory of multi-spinor fields is developed on an algebra, a triplet algebra, which consists of all the triple-direct-products of Dirac γ-matrices. The triplet algebra is decomposed into the product of two subalgebras, an external algebra and an internal algebra, which are exclusively related with external and internal characteristic of the multi-spinor field named triplet fields. All elements of the external algebra which is isomorphic to the original Dirac algebra Aγ are invariant under the action of permutation group S3 which works to exchange the order of the Aγ elements in the triple-direct-product. The internal algebra is decomposed into the product of two 42 dimensional algebras, called the family and color algebras, which describe the family and color degrees of freedom. The family and color algebras have fine substructures with "trio plus solo" (3 + 1) conformations which are irreducible under the action of S3. The triplet field has trio plus solo family modes with ordinary tricolor quark and colorless solo lepton components. To incorporate the Weinberg-Salam mechanism, it is required to introduce two types of triplet fields, a left-handed doublet and right-handed singlets of electroweak iso-spin. It is possible to qualify the Yukawa interaction and to make a new interpretation of its coupling constants naturally in an intrinsic mechanism of the triplet field formalism. The ordinary Higgs mechanism leads to the Dirac mass matrices which can explain all data of quark sector within experimental accuracy.

Common origin ofμ−τandCPbreaking in the neutrino seesaw, baryon asymmetry, and hidden flavor symmetry

We conjecture that all $CP$ violations (both Dirac and Majorana types) arise from a common origin in the neutrino seesaw. With this conceptually attractive and simple conjecture, we deduce that $\ensuremath{\mu}\mathrm{\text{\ensuremath{-}}}\ensuremath{\tau}$ breaking shares the common origin with all $CP$ violations. We study the common origin of $\ensuremath{\mu}\mathrm{\text{\ensuremath{-}}}\ensuremath{\tau}$ and $CP$ breaking in the Dirac mass matrix of seesaw Lagrangian (with right-handed neutrinos being $\ensuremath{\mu}\mathrm{\text{\ensuremath{-}}}\ensuremath{\tau}$ blind), which uniquely leads to inverted mass ordering of light neutrinos. We then predict a very different correlation between the two small $\ensuremath{\mu}\mathrm{\text{\ensuremath{-}}}\ensuremath{\tau}$ breaking observables ${\ensuremath{\theta}}_{13}\ensuremath{-}0\ifmmode^\circ\else\textdegree\fi{}$ and ${\ensuremath{\theta}}_{23}\ensuremath{-}45\ifmmode^\circ\else\textdegree\fi{}$, which can saturate the present experimental upper limit on ${\ensuremath{\theta}}_{13}$. This will be tested against our previous normal mass-ordering scheme by the ongoing oscillation experiments. We also analyze the correlations of ${\ensuremath{\theta}}_{13}$ with Jarlskog invariant and neutrinoless $\ensuremath{\beta}\ensuremath{\beta}$-decay observable. From the common origin of $CP$ and $\ensuremath{\mu}\mathrm{\text{\ensuremath{-}}}\ensuremath{\tau}$ breaking in the neutrino seesaw, we establish a direct link between the low energy $CP$ violations and the cosmological $CP$ violation for baryon asymmetry. With these we further predict a lower bound on ${\ensuremath{\theta}}_{13}$, supporting the ongoing probes of ${\ensuremath{\theta}}_{13}$ at Daya Bay, Double Chooz, and RENO experiments. Finally, we analyze the general model-independent ${\mathbb{Z}}_{2}\ensuremath{\bigotimes}{\mathbb{Z}}_{2}$ symmetry structure of the light neutrino sector, and map it into the seesaw sector, where one of the ${\mathbb{Z}}_{2}$'s corresponds to the $\ensuremath{\mu}\mathrm{\text{\ensuremath{-}}}\ensuremath{\tau}$ symmetry ${\mathbb{Z}}_{2}^{\ensuremath{\mu}\ensuremath{\tau}}$ and another the hidden symmetry ${\mathbb{Z}}_{2}^{s}$ (revealed in our previous work) which dictates the solar mixing angle ${\ensuremath{\theta}}_{12}$. We derive the physical consequences of this ${\mathbb{Z}}_{2}^{s}$ and its possible partial violation in the presence of $\ensuremath{\mu}\mathrm{\text{\ensuremath{-}}}\ensuremath{\tau}$ breaking (with or without the neutrino seesaw), regarding the ${\ensuremath{\theta}}_{12}$ determination and the correlation between $\ensuremath{\mu}\mathrm{\text{\ensuremath{-}}}\ensuremath{\tau}$ breaking observables.

Neutrino mass hierarchy and the origin of leptonic flavor mixing from the right-handed sector

We consider a neutrino mass model where all leptonic mixing is induced by a heavy Majorana sector through the seesaw type I mechanism, while the Dirac mass matrices are diagonal. Such a pattern occurs naturally in grand unified theories. Constraints on the parameters of the models are considered and it is shown that a normal neutrino mass hierarchy is preferred. The lightest neutrino mass is typically small, leading to nonobservable rates for neutrinoless double beta decay in the normal hierarchy case.

SEESAW AND LEPTOGENESIS: A TRIANGULAR ANSATZ

A triangular ansatz for the seesaw mechanism and baryogenesis via leptogenesis is explored. In a basis where both the charged lepton and the Majorana mass matrix are diagonal, the Dirac mass matrix can generally be written as the product of a unitary times a triangular matrix. We assume the unitary matrix to be the identity and then an upper triangular Dirac matrix. Constraints from bilarge lepton mixing and leptogenesis are studied.

Extension of an empirical charged lepton mass relation to the neutrino sector

It is known that the charged lepton masses obey to high precision an interesting empirical relation (Koide relation). In turn, the light neutrino masses cannot obey such a relation. We note that if neutrinos acquire their mass via the seesaw mechanism, the empirical mass relation could hold for the masses in the Dirac and/or heavy Majorana mass matrix. Examples for the phenomenological consequences are provided. We furthermore modify the mass relation for light neutrino masses including their Majorana phases, and show that it can be fulfilled in this case as well, with interesting predictions for neutrinoless double beta decay.

Unified theory for external and internal attributes and symmetries of fundamental fermions

An unorthodox unified theory is developed to describe external and internal attributes and symmetries of fundamental fermions, quarks and leptons. Basic ingredients of the theory are an algebra which consists of all the triple-direct-products of Dirac γ-matrices and a triple-spinor-field, called a triplet field, defined on the algebra. The algebra possesses three commutative subalgebras which describe, respectively, the external spacetime symmetry, the family structure and the internal color symmetry of quarks and leptons. The triplet field includes threefold (fourfold) repetitional modes of spin ½ component fields with SU(3) (SU(4)) color symmetry. It is possible to qualify the Yukawa interaction and to make a new interpretation of its coupling constants naturally in an intrinsic mechanism of the triplet field formalism. The Dirac mass matrices with quasi-democratic structure are derived as an illustration.

Hybrid textures in minimal seesaw mass matrices

In the context of the minimal seesaw framework, we discuss the implications of Dirac and Majorana mass matrices in which two properties coexist, namely, equalities among matrix elements and texture zeros. Among the large number of general possibilities, only 12 patterns are found to be consistent with the global neutrino oscillation data at the level of the most minimal number of free parameters. The predictions of the allowed textures for mass hierarchy, θ 13 and effective mass governing neutrino-less double beta decay are discussed. We also explore the possibility of having non-zero CP violation for each allowed solution. We find that only one allowed solution can accommodate both low and high energy CP violation. We discuss the prediction of this solution for leptogenesis and explore the correlation, between leptogenesis and low energy CP violation.

Dirac Mass Matrices in Gauge Field Theory of Horizontal Symmetry

We investigate Dirac mass matrices derived in the gauge field theory of a horizontal symmetry generated by a central extension of the Pauli algebra. Through numerical analyses of the observed data of the charged fermion masses and the flavor mixing matrix of quarks, values of free parameters in the mass matrices are determined and several empirical relations are found among the Yukawa coupling constants. As one specific feature of the theory, we find different orderings in squared mass eigenvalues for the up and down quark sectors.

Neutrino masses in the left-right symmetry model with a family symmetry

Based on the SU (2) L ×SU(2) R × U (1) model with an U (1) family symmetry, we obtain the lepton flavor mixing matrix and research on the neutrino masses. In the model we consider, the Lagragian density which yields the Dirac masses for the leptons is U (1) family invariant, so both the mass matrix for the charge leptons and the Dirac mass matrix for the neutrinos are of the Fritzsch-type. But, generally speaking, neutrinos may have also Majorana masses. In that situation, the effective mass matrix for the light neutrinos is no longer of the Fritzsch type. We make some assumptions on the phases of the neutrino Majorana mass matrix to avoid diagonalizing the non-hermitian matrix. Then, we obtain the lepton flavor mixing matrix. The numerical calculation which is based on the lepton flavor mixing matrix shows that the model we consider may not fit the present result of the neutrino mixing experiment.

Radiative transmission of lepton flavor hierarchies

We discuss a one loop model for neutrino masses which leads to a seesaw-like formula with the difference that the charged lepton masses replace the unknown Dirac mass matrix present in the usual seesaw case. This is a considerable reduction of parameters in the neutrino sector and predicts a strong hierarchical pattern in the right handed neutrino mass matrix that is easily derived from a U(1)H family symmetry. The model is based on the left–right gauge group with an additional Z4 discrete symmetry which gives vanishing neutrino Dirac masses and finite Majorana masses arising at the one loop level. Furthermore, it is one of the few models that naturally allow for large (but not necessarily maximal) mixing angles in the lepton sector. A generalization of the model to the quark sector requires three iso-spin singlet vector-like down type quarks, as in E6. The model predicts an inert doublet type scalar dark matter.

Minimal textures in seesaw mass matrices and their low and high energy phenomenology

In an attempt to find minimal scenarios we study the implications of Dirac and Majorana mass matrices with texture zeros within the type I seesaw mechanism. For the Dirac mass matrices we consider 5 zero textures which we show to be the most minimal form that can successfully account for low energy phenomenology if the Majorana mass matrices are chosen minimal as well. For those, we consider both diagonal and even more minimal non-diagonal forms. The latter can be motivated e.g. by simple U(1) flavour symmetries and have two degenerate eigenvalues. We classify the allowed textures and discuss the ramifications for leptogenesis and lepton flavour violation.

Scaling in the neutrino mass matrix, [formula omitted] symmetry and the see-saw mechanism

The scaling hypothesis postulates proportionality of two columns of the Majorana neutrino mass matrix in the flavor basis. This ansatz was shown to lead to an inverted hierarchy and Ue3=0. We discuss theoretical and phenomenological properties of this hypothesis. We show that (i) the neutrino mass matrix with scaling follows as a consequence of a generalized μ–τ symmetry imposed on the type-I see-saw model; (ii) there exists a unique texture for the Dirac mass matrix mD which leads to scaling for arbitrary Majorana matrix MR in the context of the type-I see-saw mechanism; (iii) unlike in the μ–τ symmetric case, a simple model with two right-handed neutrinos and scaling can lead to successful leptogenesis both with and without the inclusion of flavor effects.

Determining the heavy seesaw neutrino mass matrix from low-energy parameters

We explore how the seesaw sector in neutrino mass models may be constrained through symmetries to be completely determined in terms of low-energy mass, mixing angle and CP-violating phase observables. The key ingredients are intra-family symmetries to determine the neutrino Dirac mass matrix in terms of the charged-lepton or quark mass matrices, together with inter-family or flavor symmetries to determine diagonalization matrices. Implications for leptogenesis and collider detection of heavy neutral leptons are discussed. We show that leptogenesis can succeed in small regions of parameter space for the case where the neutrino Dirac mass matrix equals the up-quark mass matrix. The model where the neutrino Dirac mass matrix equals the charged-lepton mass matrix can yield a heavy neutral lepton as light as about 1 TeV, but detecting such a particle will be difficult.

Relation between Heavy Neutrino Mass and Majorana CP Phase in a Minimal Seesaw Leptogenesis Scenario

The recent neutrino oscillation experiments have provided us with robust evidence that neutrinos have tiny masses.1) An attractive idea is given by the seesaw mechanism2) which explains the smallness of the neutrino masses through the existence of right-handed Majorana neutrinos. Among many realistic seesaw models existing in the literature, the minimal seesaw model contains only two right-handed Majorana neutrinos, thus it is the most economical one.3) Also, the seesaw mechanism provides a very natural explanation of the baryon asymmetry in the universe through the baryogenesis via leptogenesis scenarios.4) Baryon asymmetry has been measured using the Wilkinson Microwave Anisotropy Probe (WMAP) as a baryonphoton ratio ηB = (6.1 −0.2)× 10−10.5) In this paper, we study the relation between the heavy-neutrino mass and the Majorana CP phase in a minimal seesaw leptogenesis scenario with tri/bi-maximal mixing. Generally, when we use the so-called reconstruction formula to estimate the baryon-photon ratio, at least one of the elements in the Dirac mass matrix is fixed to zero; we denote it by b2 = 0.6),7) Recently, we have pointed out that we can take not only b2 = 0 but also nonzero b2, e.g., b2 = X where X is any constant, to use the reconstruction formula.8) In the following analysis, we use the reconstruction formula with nonzero b2 to estimate the relation between the heavy-neutrino mass and the Majorana CP phase.