arXiv subjects
Publications and source records attributed to Hiroyuki Nishiura.
Stimulated by a successful quark mass matrix model based on U(3)$\times$U(3)$'$ family symmetry, a phenomenological neutrino mass matrix for the Majorana neutrinos $(ν_L, ν_R^c, N_L, N_R^c)$ is proposed. The model has only three adjustable parameters. Nevertheless, the model gives reasonable predictions for the neutrino masses, mixings, and CP violating phases in the neutrino mixing matrix.
Recently, we have proposed a quark mass matrix model based on U(3)$\times$U(3)$'$ family symmetry, in which up- and down-quark mass matrices $M_u$ and $M_d$ are described only by complex parameters $a_u $ and $a_d $, respectively. When we use charged lepton masses as additional input values, we can successfully obtain predictions for quark masses and Cabibbo-Kobayashi-Maskawa mixing. Since we have only one complex parameter $a_q$ for each mass matrix $M_q$, we can obtain a parameter-independent mass relation by using three equations for ${\rm Tr}[H_q]$, ${\rm Tr}[H_q H_q]$ and ${\rm det}H_q$, where $H_q \equiv M_q M_q^\dagger$ ($q=u, d$). In this paper, we investigate its parameter-independent feature of the quark mass relation in the model.
We have already proposed a quark and lepton mass matrix model based on U(3)$\times$U(3)$'$ family symmetry as the so-called Yukawaon model, in which the U(3) symmetry is broken by VEVs of flavons $(Φ_f)_i^{\ α}$ which are $({\bf 3}, {\bf 3}^*)$ of U(3)$\times$U(3)$'$. The model has successfully provided the unified description of quark and lepton masses and mixings by using the observed charged lepton masses as only family-number dependent input parameters. Our next concern is scales of VEVs of the flavons. In the present paper, we estimate the magnitudes of the VEV scales of flavons of the model which is newly reconstructed without changing the previous phenomenological success of parameter fitting for masses and mixings of quarks and leptons. We estimate that VEVs of flavons with $({\bf 8+1}, {\bf 1})$, $({\bf 3}, {\bf 3}^*)$, and $({\bf 1}, {\bf 8+1})$ are of 25the orders of $10$ TeV, $10^4$ TeV, and $10^7$ TeV, respectively.
Recently, we proposed a unified mass matrix model for quarks and leptons, in which, mass ratios and mixings of the quarks and neutrinos are described by using only the observed charged lepton mass values as family-number-dependent parameters and only six family-number-independent free parameters. In spite of quite few parameters, the model gives remarkable agreement with observed data (i.e. CKM mixing, PMNS mixing and mass ratios). Taking this phenomenological success seriously, we give a formulation of the so-called Yukawaon model in details from a theoretical aspect, especially for the construction of superpotentials and $R$ charge assignments of fields. The model is considerably modified from the previous one, while the phenomenological success is kept unchanged.
We propose a unified mass matrix model for quarks and leptons, in which sixteen observables of mass ratios and mixings of the quarks and neutrinos are described by using no family number-dependent parameters except for the charged lepton masses and only six family number-independent free parameters. The model is constructed by extending the so-called "Yukawaon" model to a seesaw type model with the smallest number of possible family number-independent free parameters. As a result, once the six parameters is fixed by the quark mixing and the mass ratios of quarks and neutrinos, no free parameters are left in the lepton mixing matrix. The results are in excellent agreement with the neutrino mixing data. We predict $δ_{CP}^\ell =-68^\circ$ for the leptonic $CP$ violating phase and $\langle m\rangle\simeq 21$ meV for the effective Majorana neutrino mass.
We propose a simple phenomenological model of quarks-leptons mass matrices having fundamentally universal symmetry structure. These mass matrices consist of democratic and semi-democratic mass matrix terms commonly to the neutrino and the quark sectors and have only eight free parameters. We show that this mass matrix model well reproduces all the observed values of the MNS lepton and the CKM quark mixing angles, the neutrino mass squared difference ratio, and quark mass ratios, with an excellent agreement. The model also predicts $δ_{CP}^\ell =-94^\circ$ for the leptonic $CP$ violating phase and $\langle m\rangle\simeq 0.0073$ eV for the effective Majorana neutrino mass.
It is shown that the so-called "Yukawaon" model can give a unified description of masses, mixing and $CP$ violation parameters of quarks and leptons without using any hierarchical (family number-dependent) parameters besides the charged lepton masses. Here, we have introduced a phase matrix $P={\rm daig}(e^{i ϕ_1}, e^{i ϕ_2}, e^{i ϕ_3})$ with the phase parameters $(ϕ_1, ϕ_2, ϕ_3)$ which are described in terms of family number-independent parameters, together with using only the charged lepton mass parameters as the family number-dependent parameters. In this paper, the $CP$ violating phase parameters $δ_{CP}^q$ and $δ_{CP}^\ell$ in the standard expression of $V_{CKM}$ and $U_{PMNS}$ are predicted as $δ_{CP}^q \simeq 72^\circ$ and $δ_{CP}^\ell \simeq -76^\circ$, respectively, i.e. $δ_{CP}^\ell \sim - δ_{CP}^q$.
In the so-called "Yukawaon" model, the (effective) Yukawa coupling constants $Y_f^{eff}$ are given by vacuum expectation values (VEVs) of scalars $Y_f$ (Yukawaons) with $3\times 3$ components. In this brief report, we change VEV forms $ $ in the previous paper into a unified form. Therefore, parameter fitting for quark and lepton masses and mixings is revised. Especially, we obtain predicted values of neutrino mixing $\sin^2 2θ_{13}$ and a leptonic $CP$ violating phase $δ_{CP}^\ell$ which are consistent with the observed curve in the $(\sin^2 2θ_{13}, δ_{CP}^\ell)$ reported by T2K group recently.
In the so-called ``yukawaon" model, the (effective) Yukawa coupling constants $Y_f^{eff}$ are given by vacuum expectation values (VEVs) of scalars $Y_f$ (yukawaons) with $3\times 3$ components. In the present model, all of the VEV matrices $\langle Y_f \rangle$ are given by a bilinear form of VEVs of flavons $Φ_f$, $\langle Y_f \rangle_i^{\ j} = k_f \langle Φ_f\rangle_{ik} \langle \barΦ_f\rangle^{kj}$, where $Φ_f$ is assigned to ${\bf 6}$ of U(3) family symmetry. As input parameters with family-number dependent values, we use only charged lepton mass values. Under this formulation, we can give reasonable values of quark and lepton masses and their mixings. A $CP$ violating phase $δ_{CP}^\ell=26^\circ$ in the lepton sector is predicted. The effective Majorana neutrino mass is also predicted.
A simple form of neutrino mass matrix which has only two free parameters is proposed from a phenomenological point of view. Using this mass matrix, we succeed to reproduce all the observed values for the MNS lepton mixing angles and the neutrino mass squared difference ratio. Our model also predicts $δ_ν= 155^\circ$ for the Dirac CP violating phase in the lepton sector and the effective neutrino mass $\langle m \rangle=6.3\times 10^{-3}$ eV in the neutrinoless double beta decay.
In the so-called "yukawaon" model, the (effective) Yukawa coupling constants $Y_f^{eff}$ are given by vacuum expectation values (VEVs) of scalars $Y_f$ (yukawaons) with $3\times 3$ components. So far, yukawaons $Y_f$ have been assigned to ${\bf 6}$ or ${\bf 6}^*$ of U(3) family symmetry, so that quarks and leptons were not anomaly free in U(3). In this paper, yukawaons are assigned to ${\bf 8}+{\bf 1}$ of U(3), so that quarks and leptons are anomaly free. Since VEV relations among yukawaons are also considerably changed, parameter fitting of the model is renewed. After fixing our free parameters by observed mass ratios, we have only two and one remaining free parameters for quark and lepton mixings, respectively. We obtain successful predictions for the quark and lepton mixing parameters including magnitudes of $CP$ violation. The effective Majorana neutrino mass is also predicted.
Averaged neutrino masses defined by $\la m_ν\ra_{ab} \equiv\left| \sum_{j=1}^{3}U_{aj}U_{bj}m_j\right|$ ($a,b=e,μ,τ$) are reanalyzed using up-to-date observed MNS parameters and neutrino masses by the neutrino oscillation experiments together with the cosmological constraint on neutrino masses. The values of $\la m_ν\ra_{ab}$ are model-independently evaluated in terms of effective neutrino mass defined by $\overline{m_ν}\equiv\left(\sum |U_{ej}|^2m_j^2\right)^{1/2}$ which is observable in the single beta decay. We obtain lower bound for $\langle m_ν\rangle_{ee}$ in the inverted hierarchy(IH) case, $17~\mbox{meV} \leq \langle m_ν\rangle_{ee}$ and one for $\langle m_ν\rangle_{τμ}$ in the normal hierarchy(NH) case, $5~\mbox{meV}\leq \langle m_ν\rangle_{τμ}$. We also obtain that all the averaged masses $\la m_ν\ra_{ab}$ have upper bounds which are at most $80~\mbox{meV}$.
The universality hypothesis for quark and lepton mixing matrices (CKM and MNS) is further developed. This hypothesis explains why the CKM is almost diagonal whereas the MNS is almost maximally mixed. If this hypothesis is true, the Dirac CP violating phase of the MNS mixing matrix is bounded around $π$ or 0. Quark-lepton mass matrices which realizes this hypothesis are constructed, showing simple power law relations among mass matrices for up-type, down-type quarks and neutrinos.
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 $\sin^2 2θ_{13} \sim 0.09$ together with $R_ν\equiv Δm^2_{21}/Δm^2_{32} \sim 0.03$. Our prediction of the effective neutrino mass $ $ in the neutrinoless double beta decay takes a sizable value $< m >\simeq 0.0034$ eV.
The recently observed lepton mixing angle $θ_{13}$ 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 $V_{CKM}= U_{MNS}(δ^\prime)^\dagger P U_{MNS}(δ)$ 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. $δ^\prime$ is a slightly different phase parameter from the Dirac CP violating phase $δ=1.1π$ (best fit) in the MNS lepton mixing matrix.
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 as $V_{CKM}$ and quark and lepton mass ratios.
On the basis of the so-called "yukawaon" model, we found out a special form of the neutrino mass matrix $M_ν$ which gives reasonable predictions. The $M_ν$ is given by a multiplication form made of charged lepton mass matrix $M_e$ and up-quark mass matrix $M_u$. This $M_ν$ has no adjustable parameters except for those in $M_e$ and $M_u$. Here, $M_e$ and $M_u$ are described by one parameter $a_e$ (real) and two parameters $a_u$ (complex), respectively, and those parameters are constrained by their observed mass ratios. With this form of $M_ν$, in spite of having only three parameters, the $M_ν$ can give reasonable predictions $\sin^2 2θ_{atm} \simeq 0.99$, $\sin^2 2θ_{13} \simeq 0.015$, $Δm^2_{21}/Δm^2_{32} \simeq 0.030$, $< m_{ee}> \simeq 0.0039$ eV, and so on, by using observed values of $m_e/m_μ$, $m_μ/m_τ$, $m_c/m_t$, and $\sin^2 θ_{solar}$ as input values.
A new yukawaon model is investigated under a family symmetry U(3)\times S_3. In this model, all vacuum expectation values (VEVs) of the yukawaons, , are described in terms of a fundamental VEV matrix <Φ_0> as in the previous yukawaon model, but the assignments of quantum number for fields are different from the previous ones: the fundamental yukawaon Φ_0 is assigned to (3,3) of U(3) \times U(3), which is broken into (3,1+2) of U(3) \times S_3, although quarks and leptons are still assigned to triplets of U(3) and yukawaons Y_f are assigned to 6^* of U(3). Then, VEV relations among Yukawaons become more concise considerably than the previous yukawaon models. By adjusting parameters, we can fit not only quark mixing parameters but also lepton mixing parameters together with their mass ratios.