The quark-lepton complementarity (QLC) is very suggestive in understanding possible relations between quark and lepton mixing matrices. We explore the QLC relations in all the possible angle-phase parametrizations and point out that they can approximately hold in five parametrizations. Furthermore, the vanishing of the smallest mixing angles in the CKM and PMNS matrices can make sure that the QLC relations exactly hold in those five parametrizations. Finally, the sensitivity of the QLC relations to radiative corrections is also discussed.
The PMNS and CKM matrices are phenomenologically close to symmetric, and a symmetric form could be used as zeroth-order approximation for both matrices. We study the possible theoretical origin of this feature in flavor symmetry models. We identify necessary geometric properties of discrete flavor symmetry groups that can lead to symmetric mixing matrices. Those properties are actually very common in discrete groups such as $A_{4}$, $S_{4}$ or $Δ(96)$. As an application of our theorem, we generate a symmetric lepton mixing scheme with $θ_{12}=θ_{23}=36.21^{\circ};θ_{13}=12.20^{\circ}$ and $δ=0…
Generalizing a previous model to accommodate the third quark family and CP violation, we present a $T^{'}$ model which predicts tribimaximal neutrino (PMNS) mixings while the central predictions for quark mixings are $|V_{td}/V_{ts}| = 0.245$ and $|V_{ub}/V_{cb}| = 0.237$ with a predicted CP violating KM phase $δ_{KM} = 65.8^{0}$. All these are acceptably close to experiment, including the KM phase for which the allowed values are $63^{0} < δ_{KM} < 72^{0}$, and depend only on use of symmetry $T^{'} \times Z_2$ to define the model and no additional parameters.
The CKM and PMNS matrices have been constructed based on the latest measurements, largely free from theoretical inputs as well as likely NP effects in the case of the former. To facilitate the construction of the CKM matrix in the PDG representation as well as in view of the comparatively large error in the measured value of the CP violating phase δ, the possibility of its construction from the tree level measured CKM elements has also been explored using the unitarity triangle. In view of the persistent difference between the |V_{ub}| exclusive and inclusive values, we have carried out separa…
The complementarity between the quark and lepton mixing matrices is shown to provide a robust prediction for the neutrino mixing angle $θ_{13}^{PMNS}$. We obtain this prediction by first showing that the matrix $V_M$, product of the CKM and PMNS mixing matrices, may have a zero (1,3) entry which is favored by experimental data. Hence models with bimaximal or tribimaximal forms of the correlation matrix $V_M$ are quite possible. Any theoretical model with a vanishing (1,3) entry of $V_M$ that is in agreement with quark data, solar, and atmospheric mixing angle leads to $θ_{13}^{PMNS}=(9{^{+1}_{…
After the successful investigation and confirmation of non zero $θ_{13}^{PMNS}$ by various experiments, we are standing at a square where we still encounter a number of issues, which are to be settled. In this paper, we have extended our recent work towards a precise prediction of the $θ_{23}^{PMNS}$ mixing angle, taking into account the neutrino mass hierarchy. We parameterize the non-trivial correlation between quark (CKM) and lepton (PMNS) mixing matrices in quark-lepton complementarity (QLC) model as $V_{c}= U_{CKM}. ψ. U_{PMNS}$, where $ψ$ is a diagonal phase matrix. Monte Carlo simulatio…
In the light of recent experimental results on $θ_{13}^{pmns}$, we re-investigate the complementarity between the quark and lepton mixing matrices and obtain predictions for most unsettled neutrino mixing parameters like $θ_{23}^{pmns}$ and CP violating phase invariants $J$, $S_1$ and $S_2$. This paper is motivated by our previous work where in a QLC model we predicted the value for $θ_{13}^{pmns}=(9{^{+1}_{-2}})^\circ$, which was found to be in strong agreement with the experimental results. In the QLC model the non-trivial correlation between CKM and PMNS mixing matrices is given by a correl…
Recent experiments show that the top-right corner element ($U_{e3}$) of the PMNS, like that ($V_{ub}$) of the CKM, matrix is small but nonzero, and suggest further via unitarity that it is smaller than the bottom-left corner element ($U_{τ1}$), again as in the CKM case ($V_{ub} < V_{td}$). An attempt in explaining these facts would seem an excellent test for any model of the mixing phenomenon. Here, it is shown that if to the assumption of a universal rank-one mass matrix, long favoured by phenomenologists, one adds that this matrix rotates with scale, then it follows that (A) by inputting the…
The dodeca symmetry is designed to obtain the Cabibbo angle $θ_C^{\rm CKM}$ approximately $15^{\rm o}$ and the (11) element of $\Vp$ as $\cos 30^{\rm o}$, leading to $θ_1^{\rm PMNS}+θ_C^{\rm CKM}\simeq 45^{\rm o}$. This leading order dodeca symmetric $\Vp$ is corrected by small parameters, especially as an expansion in terms of a small parameter $β$. Neglecting two Majorana phases, the expression of $\Vp$ contains four parameters: a small $β$, and three $\Od(1)$ parameters $A,B,$ and $δ$. From the neutrino oscillation data, we present two parametrizations and estimate their $β$'s.
The non-zero Dirac phases $δ^q$ and $δ^l$ in the CKM and PMNS mixing matrices signify CP violation. In general they are independent. Experimental data including recent T2K results show, however, that in the original KM parameterization for the mixing matrix, the sum $δ^q_{\rm KM} + δ^l_{\rm KM}$ is close to zero with $δ^q_{\rm KM}$ to be approximately $π/2$. The KM parameterization may have provided some hints that these phases are actually related and CP is maximally violated. We show that this sum rule can be accommodated in models with spontaneous CP violation where both phases originate fr…
We analyse a possible connection between CP violations in the quark and lepton sectors, parametrised by the CKM and PMNS phases. If one assumes that CP breaking arises from complex Yukawa couplings, both in the quark and lepton sectors, the above connection is not possible in general, since Yukawa couplings in the two sectors have independent flavour structures. We show that both the CKM and PMNS phases can instead be generated by a vacuum phase in a class of two Higgs doublet models, and in this case a connection may be established. This scenario requires the presence of scalar FCNC at tree l…
We propose a simple model for the spontaneous CP violation based on $SU(2)_{L}\times U(1)_{Y}\times A_{4}\times CP\times Z_{2}$ symmetry for quarks and leptons in a seesaw framework. In our model CP is spontaneously broken at high energies, after breaking of flavor symmetry, by a complex vacuum expectation value of $A_{4}$-triplet and gauge singlet scalar field. And, certain effective dimension-5 operators are introduced in the quark Lagrangian as an equal footing, which lead the quark mixing matrix to the Cabibbo-Kobayashi-Maskawa (CKM) one in the form, while the lepton Lagrangian is renormal…
Investigating the CKM matrix in different parametrization schemes, it is noticed that those schemes can be divided into a few groups where the sine values of the CP phase for each group are approximately equal. Using those relations, several approximate equalities among the elements of CKM matrix are established. Assuming them to be exact, there are infinite numbers of solutions and by choosing special values for the free parameters in those solutions, several textures presented in literature are obtained. The case can also be generalized to the PMNS matrix for the lepton sector. In parallel, …
Several approximate equalities among the matrix elements of CKM and PMNS imply that hidden symmetries may exist and be common for both quark and neutrino sectors. The CP phase of the CKM matrix ($δ_{\rm CKM}$) is involved in these equalities and can be investigated when these equalities turn into several equations. As we substitute those experimentally measured values of the three mixing angles into the equations for quarks, it is noted that one of the equations which holds exactly has a solution $δ_{\rm CKM}=68.95^\circ$. That value accords with $(69.1^{+2.02}_{-3.85})^\circ$ determined from …
Observing the CKM matrix elements written in different parametrization schemes, one can notice obvious relations among the sine-values of the CP phases in those schemes. Using the relations, we establish a few parametrization-independent equations, by which the matrix elements of the CKM matrix can be completely fixed up to a universal parameter. If it is true, we expect that there should exist a hidden symmetry in the nature which determines the relations. Moreover, it requires a universal parameter, naturally it would be the famous Jarlskog invariant which is also parametrization independent…
We discuss the relations between the mixing angles and the mixing matrices of quarks and leptons. With Raidal's numerical relations, we parametrize the lepton mixing (PMNS) matrix with the parameters of the quark mixing (CKM) matrix, and calculate the products of $V_{\mathrm{CKM}}U_{\mathrm{PMNS}}$ and $U_{\mathrm{PMNS}}V_{\mathrm{CKM}}$. Also, under the conjectures $V_{\mathrm{CKM}}U_{\mathrm{PMNS}}=U_{\mathrm{bimax}}$ or $U_{\mathrm{PMNS}}V_{\mathrm{CKM}}=U_{\mathrm{bimax}}$, we get the PMNS matrix naturally, and test Raidal's relations in these two different versions. The similarities and t…
We study the possibility of identifying the CP violating phases in the PMNS mixing matrix in the lepton sector and also that in the CKM mixing matrix in the quark sector with the phase responsible for the spontaneous CP violation in the Higgs potential, and some implications. Since the phase in the CKM mixing matrix is determined by experimental data, the phase in the lepton sector is therefore also fixed. The mass matrix for neutrinos is constrained leading to constraints on the Jarlskog CP violating parameter $J$, and the effective mass $<m_{ββ}>$ for neutrinoless double beta decay. The Yuka…
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.
Inspired by a new relation $θ_{13}^{\rm PMNS}={θ_C}/{\sqrt{2}}$ observed from the relatively large $θ_{13}^{\rm PMNS}$, we find that the combination of this relation with the quark-lepton complementarity and the self-complementarity results in correlations of the lepton mixing angles with the quark mixing angles. We find that the three mixing angles in the PMNS matrix are all related to the Wolfenstein parameter $λ$ in the quark mixing, so they are also correlated. Consequently, the PMNS matrix can be parameterized by $λ$, A, and a Dirac CP-violating phase $δ$. Such parametrizations for the PM…
In the scenario with four generation quarks and leptons and using a 3 + 1 neutrino model having one sterile and the three standard active neutrinos with a $4 \times 4$ unitary transformation matrix, $U_{PMNS_{4}}$, we perform a model-based analysis using the latest global data and determine bounds on the sterile neutrino parameters i.e. the neutrino mixing angles. Motivated by our previous results, where, in a quark-lepton complementarity (QLC) model we predicted the values of $θ_{13}^{PMNS}=(9_{-2}^{+1})^{\circ}$ and $θ_{23}^{PMNS}=(40.60_{-0.3}^{+0.1})^{\circ}$. In the QLC model the non-triv…
It is suggested that there is an underlying symmetry which relates the quark and lepton sectors. Namely, among the mixing matrix elements of CKM for quarks and PMNS for leptons there exist complementarity relations at a high energy scale (such as the see-saw or even the GUT scales). Assuming that the relations would remain during the matrix elements running down to the EW scale. Observable breaking of the rational relation is attributed to existence of sterile neutrinos which mix with the active neutrino to result in the observable PMNS matrix. We show that involvement of a sterile in the (3+1…
I will talk on our new theory on baryogenesis through type-II leptogenesis which is different from the well-known type-I leptogenesis. I will comment on the Jarlskog phases, $δ_{\rm CKM}$ and $δ_{\rm PMNS}$, in the CKM and PMNS matrices. In the type-II leptogenesis, the PMNS phase is used for Sakharov's condition on the global quantum number generation in the Universe. For this to be effective, the SU(2)$\times$U(1) gauge symmetry must be broken during the leptogenesis epoch.
A unified description of fermionic mixing is proposed which assumes that in certain basis ($i$) a single complex unitary matrix $V$ diagonalizes mass matrices of all fermions to the leading order, ($ii$) the SU(5) relation $M_d=M_l^T$ exists between the mass matrices of the down quarks and the charged leptons, and ($iii$) $M_d^\dagger=M_d$. These assumptions automatically lead to different mixing patterns for quarks and leptons: quarks remain unmixed to leading order ($i. e. V_{CKM}=1$) while leptons have non-trivial mixing given by a symmetric unitary matrix $V^0_{PMNS} = V^T V$. $V$ depends …
We revisit mixing sum rule relations in the lepton and quark sectors under the assumption that the 1-3 elements of the flavour mixing matrices ($V^u_L,V^d_L,V^e_L,V^ν_L$) are zero in the flavour basis. We consider the exact relations resulting from the validity of this "zero 1-3 flavour mixing hypothesis" and analyse their implications based on the current experimental data, including effects from RG running. In particular, we analyse how the existing precise measurement of $θ_{13}^\mathrm{PMNS}$ allows to derive predictions for $θ_{23}^\mathrm{PMNS}$ in models with constrained $θ_{12}^\mathrm…
The recent observations of the leptonic mixing angle θ^PMNS_13 are consistent with θ^PMNS_13 = θ_C / \sqrt2 (with θ_C being the Cabibbo angle θ^CKM_12). We discuss how this relation can emerge in Grand Unified Theories (GUTs) via charged lepton corrections. The key ingredient is that in GUTs the down-type quark Yukawa matrix and the charged lepton Yukawa matrix are generated from the same set of GUT operators, which implies that the resulting entries are linked and differ only by group theoretical Clebsch factors. This allows a link θ^e_12 = θ_C to be established, which can induce θ^PMNS_13 = …
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 $\sin^2 2θ_{13} \sim 0.07$ with keeping successful results for other parameters in $U_{PMNS}$ as well a…
Formation of quark and lepton mass matrices through intermediate states of heavy mirror fermions is capable of reproducing main qualitative properties of weak mixing matrices (CKM and PMNS matrices). The reproduction includes the hierarchy of CKM matrix elements, a general form of the PMNS matrix, involving the smallness of the neutrino mixing angle θ_{13}, and leads to very small neutrino masses. For leptons, these properties appear only for the Dirac nature of SM neutrino and its inverse spectrum. In such a lepton system, not only do spontaneous mirror symmetry violation and the observed mas…
The complementarity between the quark and lepton mixing matrices is shown to provide robust predictions. We obtain these predictions by first showing that the matrix V_M, product of the quark (CKM) and lepton (PMNS) mixing matrices, may have a zero (1,3) entry which is favored by experimental data. We obtain that any theoretical model with a vanishing (1,3) entry of V_M that is in agreement with quark data, solar, and atmospheric mixing angle leads to $θ_{13}^{PMNS}=(9{^{+1}_{-2}})^\circ$. This value is consistent with the present 90% CL experimental upper limit. We also investigate the predic…
We investigate the prediction on the lepton phases in theories with a non trivial correlation between quark (CKM) and lepton (PMNS) mixing matrices. We show that the actual evidence, under the only assumption that the correlation matrix $V^M$ product of $CKM$ and $PMNS$ has a zero in the entry $(1,3)$, gives us a prediction for the three CP-violating invariants $J$, $S_1$, and $S_2$. A better determination of the lepton mixing angles will give a strong prediction of the CP-violating invariants in the lepton sector. These will be tested in the next generation experiments. To clarify how our pre…
We rewrite the Yukawa interactions of the standard model in terms of flavour-dependent vacuum structure to address the family mass hierarchy and CP violation in both the quark sector and lepton sector. It is realized for the first time that the Lagrangian only includes the same number of degrees of freedom as phenomenological observables with no requirement of extra particles or any new symmetry. The quark and lepton mass hierarchy arises as a natural result of the close-to-flat vacuum in flavour space. The CP violation in CKM and PMNS is explained as a general quantum phase between weak gauge…
A flavor structure with minimal parameters is proposed to address the fermion mass hierarchy and flavor mixing for quarks and leptons. Yukawa interaction is reconstructed in a new basis to show a homological flat structure for up-type quarks, down-type quarks, charged leptons and Dirac neutrinos. A $SO(2)_{LR}^f$ flavor symmetry is found from the hierarchy masses of quarks and leptons, which dominated CKM mixing for quarks and PMNS for leptons. Since the minimal flavor structure successfully addresses CKM and PMNS even in the mass hierarchy limit, mass hierarchy and flavor mixing are two indep…
We propose an $S_{4}$ flavor model based on supersymmetric (SUSY) SU(5) GUT. The first and third generations of \textbf{10} dimensional representations in SU(5) are all assigned to be $1_{1}$ of $S_{4}$. The second generation of \textbf{10} is to be $1_{2}$ of $S_{4}$. Right-handed neutrinos of singlet \textbf{1} and three generations of $\bar{\textbf{5}}$ are all assigned to be $3_{1}$ of $S_{4}$. The VEVs of two sets of flavon fields are allowed a moderate hierarchy, that is $\langleΦ^ν\rangle \sim λ_{c}\langleΦ^{e}\rangle$. Tri-Bimaximal (TBM) mixing can be produced at both leading order (L…
A preliminary determination of the Dirac phase in the PMNS matrix is $\dell\approx -\fracπ{2}$. A rather accurately determined Jarlskog invariant $J$ in the CKM matrix is close to the maximum. Since the phases in the CKM and PMNS matrices will be accurately determined in the future, it is an interesting problem to relate these two phases. This can be achieved in a families-unified grand unification if the weak CP violation is introduced spontaneously {\it à la} Froggatt and Nielsen at a high energy scale, where only one meaningful Dirac CP phase appears.
A neutrino mass matrix model with a bilinear form $M_ν= k_ν(M_D M_R^{-1} M_D^T)^2$ is proposed within the framework of the so-called yukawaon model, which has been proposed for the purpose of a unified description of the lepton mixing matrix $U_{PMNS}$ and the quark mixing matrix $V_{CKM}$. The model has only two adjustable parameters for the PMNS mixing and neutrino mass atios. (Other parameters are fixed from the observed quark and charged lepton mass ratios and the CKM mixing.) The model gives reasonable values $\sin^2 2θ_{12} \simeq 0.85$ and $\sin^2 2θ_{23} \sim 1$ and $\sin^2 2θ_{13} \si…
We show that the next-to-leading order corrections in the quark-lepton complementarity are important to explain the observed pattern of neutrino mixing. In particular, the next-to-leading order corrections 1) lead to a deviation of θ_{23} from maximal mixing, 2) reduce the predicted value of $\sin^2 2θ_{13}$ by 9.8%, 3) provide the same value of $\sin^2 θ_{12}$ as that of the tri-bimaximal mixing. This is shown by calculating $\sin^2 2θ_{ij} (i,j=1,2,3)$ to ${\cal O}(λ^6)$ in the framework in which the product of the CKM and PMNS matrices is bimaximal.
We employ a bottom-up and model-independent technique to search for non-Abelian discrete flavour symmetries capable of predicting viable CKM and PMNS matrices alongside of special patterns of leptoquark couplings. In particular, we analyze patterns derived when an ultra-violet flavour theory is assumed to break to global Abelian symmetries in Standard Model fermion masses and new Yukawa-like terms sourced by the leptoquark representation. The phenomenology of different classes of these `simplified models' can be explored without reference to explicit model-building assumptions, e.g. the nature…
We compute the effect of non diagonal neutrino mass in l_i -> l_j gamma in SUSY theories with non trivial Quark-Lepton complementarity and a flavor symmetry. The correlation matrix V_M=U_{CKM}U_{PMNS} is such that its (1,3) entry, as preferred by the present experimental data, is zero. We do not assume that $V_M$ is bimaximal. Quark-Lepton complementarity and the flavor symmetry strongly constrain the theory and we obtain a clear prediction for the contribution to mu -> e gamma and the tau decays tau -> e gamma and tau -> mu gamma. If the Dirac neutrino Yukawa couplings are degenerate but the …
We propose the lepton mixing matrix at high energy scale to be connected to quark mixing matrix by the similar transformation. The similarity between CKM and PMNS significantly narrows down the ranges in physical parameters. The condition requires $\sinθ_{13}$ not to be larger than 0.15, masses to be of quasi-degenerate normal ordering, and $\tanβ$ to be large.
The neutrino oscillation data find a good approximation in the so-called tri-bimaximal pattern. Recently a paper appeared showing that also the bimaximal pattern, which is already ruled out by the measurements, could be a very good starting point in order to describe the lepton mixing. In this paper I review both the flavour structures and then I present an explicit flavour model based on the discrete group S4, in which the PMNS mixing matrix is of the bimaximal form in first approximation and after it receives corrections which bring it in agreement with the data. The resulting spectrum of li…
In Type-I seesaw model, the lepton flavor mixing matrix (PMNS matrix) and the quark flavor mixing matrix (CKM matrix) may be connected implicitly through a relation between the neutrino Dirac Yukawa coupling $Y_D$ and the quark Yukawa couplings. In this paper, we study whether $Y_D$ can satisfy, in the flavor basis where the charged lepton Yukawa and right-handed neutrino Majorana mass matrices are diagonal, the relation $Y_D \propto {\rm diag}(y_d,y_s,y_b)V_{CKM}^T$ or $Y_D \propto {\rm diag}(y_u,y_c,y_t)V_{CKM}^*$ without contradicting the current experimental data on quarks and neutrino osc…
In a simplified renormalizable model where the neutrinos have PMNS (Pontecorvo-Maki-Nakagawa-Sakata) mixings tan$^{2} θ_{12} = {1/2}, θ_{13}=0, θ_{23} = π/4$ and with flavor symmetry $T^{'}$ there is a corresponding prediction where the quarks have CKM (Cabibbo-Kobayashi-Maskawa) mixings tan$2 Θ_{12} = \frac{\sqrt{2}}{3}, Θ_{13}=0, Θ_{23} =0$.
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…
Right-handed neutrinos in supersymmetric models can act as the source of lepton flavor violation (LFV). We present experimental implications of lepton flavor-violating processes within a supersymmetric type-I seesaw framework in the three-extra-parameter non-universal Higgs model (NUHM3) for large (PMNS-like) and small (CKM-like) Yukawa mixing scenarios. We highlight LFV predictions for the natural (low $Δ_{\rm EW}$) portion of parameter space. Our numerical analysis includes full 2-loop renormalization group running effects for the three neutrino masses and mass matrices. We show the projecte…
The high scale mixing unification hypothesis recently proposed by three of us (R. N. M., M. K. P. and G. R.) states that if at the seesaw scale, the quark and lepton mixing matrices are equal then for quasi-degenerate neutrinos, radiative corrections can lead to large solar and atmospheric mixings and small reactor angle at the weak scale in agreement with data. Evidence for quasi-degenerate neutrinos could, within this framework, be interpreted as a sign of quark-lepton unification at high scale. In the current work, we extend this model to show that the hypothesis works quite successfully in…
We point out that the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix $V_{\rm CKM}$ and the Maki-Nakagawa-Sakata (MNS) lepton mixing matrix $V_{\rm MNS}$ can naturally be correlated in a class of seesaw models with grand unification, but the texture of their correlation matrix ${\cal F}_ν$ is rather nontrivial. The bimaximal mixing pattern of ${\cal F}_ν$ is disfavored by current data, and other special forms of ${\cal F}_ν$ may suffer from fine-tuning of the free phase parameters in fitting the so-called quark-lepton complementarity relation. A straightforward calculation of ${\cal F}_ν$ …
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 $θ_{13}$ 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 le…
We present a model of neutrino masses within the framework of the EW-$ν_R$ model in which the experimentally desired form of the PMNS matrix is obtained by applying an $A_4$ symmetry to the \emph{Higgs singlet sector} responsible for the neutrino Dirac mass matrix. This mechanism naturally avoids potential conflict with the LHC data which severely constrains the Higgs sector, in particular the Higgs doublets. Moreover, by making a simple $ans\ddot{a}tz$ we extract $\mathcal{M}_l {\mathcal{M}_l}^\dagger$ for the charged lepton sector. A similar $ans\ddot{a}tz$ is proposed for the quark sector. …
To include the quark sector, the $A_{5}\equiv I$ (icosahedron) four generation lepton model is extended to a binary icosahedral symmetry $I'$ flavor model. We find the masses of fermions, including the heavy sectors, can be accommodated. At leading order the CKM matrix is the identity and the PMNS matrix, resulting from same set of vacua, corresponds to tribimaximal mixings.
We propose a universal form for quark and lepton mass matrices, which applies in a ``leading order'' approximation where $CP$-violating phases are ignored. Down-quark mass ratios are successfully predicted in our scheme using the measured CKM mixing angles as input. Assuming an additional discrete symmetry in the neutrino sector, we obtain the ``golden ratio'' pattern in the leading-order PMNS mixing matrix; in addition we predict an inverted neutrino mass hierarchy with $m_1\simeq m_2 \simeq74 meV$, $m_3\simeq 55 meV$, and neutrinoless double beta decay mass parameter $m_{0νββ}\simeq 33~ meV$…
We analyze a class of supersymmetric SO(10) grand unified theories with type II seesaw for neutrino masses, where the contribution to PMNS matrix from the neutrino sector has an exact tri-bi-maximal (TBM) form, dictated by a broken S_4 symmetry. The Higgs fields that determine the fermion masses are two 10 fields and one 126 field, with the latter simultaneously contributing to neutrino as well as charged fermion masses. Fitting charged fermion masses and the CKM mixings lead to corrections to the TBM mixing that determine the final PMNS matrix with the predictions theta_{13} ~ 4-6 degrees and…
I report the analysis performed on fermion masses and mixing, including neutrino mixing, within the context of a model with hierarchical radiative mass generation mechanism for light charged fermions, mediated by exotic scalar particles at one and two loops, respectively, meanwhile the neutrinos get Majorana mass terms at tree level through the Yukawa couplings with two SU(2)_L Higgs triplets. All the resulting mass matrices in the model, for the u, d, and e fermion charged sectors, the neutrinos and the exotic scalar particles, are diagonalized in exact analytical form. Quantitative analysis …
Relation between the lepton and quark mixings: $U_{PMNS} \approx V_{CKM}^{\dagger} U_X$, where $U_X$ is the BM or TBM mixing matrices, implies the quark-lepton (Grand) unification and existence of hidden sector with certain flavor symmetries. The latter couples to the visible sector via the neutrino portal and is responsible for $U_X$, as well as for smallness of neutrino mass. GUT ensures appearance of $\sim V_{CKM}$ in the lepton mixing. General features of this scenario (inverse or double seesaw, screening of the Dirac structures, basis fixing symmetry) are described and two realizations ar…
We re-evaluate neutrino mixing patterns according to the latest T2K result for a larger mixing angle $θ_{13}$, and find that the PMNS mixing matrix has larger deviations from bimaximal (BM) and tribimaximal (TB) mixing patterns than previously expected. We also find that several schemes connecting PMNS and CKM mixing matrices can accommodate the latest T2K result nicely. As necessary updates to former works, we make new triminimal expansions of PMNS mixing matrix based on BM and TB mixing patterns. We also propose a new mixing pattern with a self-complementary relation between the mixing angle…
In the Standard Model, we obtain a non-Fritzsch like configuration with five texture zeros for the quark mass matrices. This matrix generates the quark masses, the inner angles of the CKM unitary triangle, and the CP-violating phase in the quark sector. This work can be applied to the PMNS matrix in the lepton sector, by assuming Dirac masses for the neutrinos, where non-trivial predictions for the neutrino masses and mixing angles are expected.
