arXiv subjects

Masaki J. S. Yang

Publications and source records attributed to Masaki J. S. Yang.

At least 37 records · Page 2Linked to original sources

arXiv2024

Chiral perturbative reconstruction of the complex orthogonal matrix $R$ in Casas--Ibarra parameterization

In this letter, we perform a chiral perturbative analysis by singular values $m_{Di}$ of the Dirac mass matrix $m_{D}$ for the type-I seesaw mechanism. In the basis where $m_{D} = V m_{D}^{\rm diag} U^{\dagger}$ is diagonal, the mass matrix of right-handed neutrinos $M_{R}$ is written by $M_{R} = m_{D}^{\rm diag} m^{-1} m_{D}^{\rm diag}$. If the mass matrix of light neutrinos $m$ has an inverse matrix and the singular values $m_{Di}$ are hierarchical ($m_{D1} \ll m_{D2} \ll m_{D3}$), the singular values $M_{i}$ and diagonalization matrix $U$ of $M_{R}$ are obtained perturbatively. By treating $m_{Di}$ and $V$ as input parameters, $m_{D}$ is represented in the basis where $M_{R}$ is diagonal, and we perturbatively derive the orthogonal matrix $R$ in Casas--Ibarra parameterization. As a result, $R$ is independent of $m_{Di}$ in the leading order, and it is reconstructed as an orthonormal basis $R_{i1} \simeq \pm \sqrt{m_{i} / m_{11} } (U_{\rm MNS}^{T} V^{*})_{i1} \, , R_{i2} \simeq \pm ε_{ijk} R_{j3} R_{k1} \, , R_{i3} \simeq \pm {(U_{\rm MNS}^{\dagger} V)_{i3} / \sqrt {m_{i} (m^{-1})_{33}} } $. Here, $m_{i}$ is the masses of light neutrinos and $\pm$ denotes the independent degree of freedom for each column vector.

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arXiv2024

Chiral perturbative solution for the type-I seesaw mechanism in next-to-leading order

In this letter, we perform chiral perturbative diagonalization of the type-I seesaw mechanism by hierarchical singular values $λ_{i}$ of the Dirac mass matrix $m_{D}$ up to the next-to-leading order (NLO). Since the mass matrix of right-handed neutrinos $M_{R}$ has parity symmetries under $λ_{i} \leftrightarrow - λ_{i}$, the singular values $M_{i}$ and mixing angles of diagonalization of $M_{R}$ are written by only even and odd orders of $λ_{i}$ respectively. We confirm this fact by specific perturbative expansions of the third- and the fourth-order by $λ_{i}$. As a result, as long as the chiral perturbation theory is valid, the NLO contributions are generally suppressed by $O(λ_{i}^{2} / \labmda_{j}^{2}) \lesssim 1\%$ compared to the leading-order expressions that have sufficient accuracies.

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arXiv2023

Contribution of Majoron to Hubble tension in gauged U(1)$_{L_μ-L_τ}$ Model

In this paper, we analyze parameter regions that can alleviate the Hubble tension in the U(1)$_{L_μ- L_τ}$ model with the broken lepton number U(1)$_L$ symmetry. As new particles, this model has a U(1)$_{L_μ- L_τ}$ gauge boson $Z'$ and a Majoron $ϕ$, which can affect the early universe and the effective number of neutrino species $N_{\rm eff}$. If $Z'$ and $ϕ$ simultaneously exist in the early universe, $Z'\,$-$\,ϕ$ interaction processes such as $Z'ν_α\leftrightarrow ϕ\barν_β$ occur. The comparison of $N_{\rm eff}$ between the cases with and without the $Z'\,$-$\,ϕ$ interaction processes shows that these processes make a small contribution of $\mathcal{O}(10^{-4})$ to $N_{\rm eff}$, and it does not need to be considered for the alleviation of the Hubble tension. Based on these facts, we calculated $N_{\rm eff}$ for various Majoron parameters without the $Z'\,$-$\,ϕ$ interaction processes to search parameters that could alleviate the Hubble tension. As a result, we found that the U(1)$_{L_μ- L_τ}$ gauge boson and Majoron can alleviate the Hubble tension in some parameter regions, and there is a non-trivial synergy contribution between $Z'$ and $ϕ$. Moreover, the parameter region with a lighter mass $m_ϕ\lesssim 2$ MeV and a larger coupling $λ\gtrsim 10^{-8}$ is excluded because it predicts too large $N_{\rm eff}$, i.e. $N_{\rm eff} \gtrsim 3.5$. The favored and restricted regions of the Majoron parameters depend on the $Z'$ parameters because of the presence of the $Z'$ contribution and synergy one.

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arXiv2023

Chiral perturbative analysis for an almost massless neutrino in the type-I seesaw mechanism

In this paper, we perform chiral perturbative analysis of an approximate lepton number symmetry associated with a sufficiently light neutrino in the type-I seesaw mechanism. For the Dirac mass matrix $m_{D} = (\bm A \, , \bm B \, , \bm C)$, linearly independent components of $\bm C$ from $\bm A$ and $\bm B$ are treated as symmetry-breaking parameters. A deviation in the eigenvector of the massless mode $δ\bm u$ occurs in the first-order perturbation and the lightest mass $m_{1 \, \rm or \, 3} \propto \det m_{D}^{2} / M_{3}$ emerges in the second-order. By solving the perturbation theory, we obtained specific expressions of $δ\bm u$ and $m_{1 \, \rm or \, 3}$. As a result, two complex parameters in $m_{D}$ are bounded to some extent from the eigenvector. These constraints are associated with the chiral symmetry and are not susceptible to renormalization.

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arXiv2023

Chiral perturbative relation for neutrino masses in the type-I seesaw mechanism

In this letter, we perform a perturbative analysis by the lightest singular value $m_{D1}$ of the Dirac mass matrix $m_{D}$ in the type-I seesaw mechanism. A mass relation $M_{1} = m_{D1}^{2}/ |(m_ν)_{11}|$ is obtained for the lightest mass $M_{1}$ of the right-handed neutrino $ν_{R1}$ and the mass matrix of the left-handed neutrinos $m_ν$ in the diagonal basis of $m_{D}$. This relation is rather stable under renormalization because it is gauge-invariant in the SM and associates with the approximate chiral symmetry of $ν_{R1}$. If diagonalization of the Yukawa matrices of leptons $Y_{ν, e}$ has only small mixings, the element $(m_ν)_{11}$ is close to the effective mass $m_{ee}$ of the neutrinoless double beta decay. By assuming $m_{D1} \simeq m_{u,e} \simeq 0.5$ MeV, the lightest mass is about $M_{1} \gtrsim O(100)$ TeV in the normal hierarchy and $M_{1} \sim O(10)$ TeV in the inverted hierarchy. Such a $ν_{R1}$ with a tiny Yukawa coupling $y_{ν1} \sim O(10^{-5})$ can indirectly influence various observations. On the other hand, the famous bound of the thermal leptogenesis $M_{1} \gtrsim 10^{9}$ GeV that requires $m_{D1} \gtrsim 30$ MeV seems to be difficult to reconcile with a simple unified theory without a special condition.

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arXiv2023

General solutions for TM$_{1,2}$ mixing in the minimal type-I seesaw mechanism and phenomenological constraints to Yukawa matrix of neutrinos

In this paper, we concisely represent the general solution for the TM$_{1,2}$ mixing in the type-I minimal seesaw mechanism and show phenomenological constraints of the Yukawa matrix of neutrinos $Y$. First, conditions of $Z_{2}$ symmetry associated with TM$_{1,2}$ restrict two complex parameters. In addition, three complex parameters are constrained from five phenomenological parameters (two neutrino masses $m_{i}$, the mixing angle $θ_{13}$, the Dirac phase $δ$, and the Majorana phase $α$) and the overall phase. As a result, there is only one free complex parameter for $Y$, except for the right-handed neutrino masses $M_{1,2}$. For the TM$_{1}$ mixing with normal hierarchy, the symmetry condition is imposed only on $Y$, and the physical parameters depend on $M_{R}$. In other situations, the dimensionless parameters $(θ_{13}, δ$ and $α)$ do not depend on $M_{R}$ but only on certain combinations of the components of $Y$.

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arXiv2023

Model Building by Coset Space Dimensional Reduction Scheme Using Twelve-Dimensional Coset Spaces

We investigate the twelve-dimensional gauge-Higgs unification models with an eight-dimensional coset space. For each model, we apply the coset space dimensional reduction procedure and examine the particle contents of the resulting four-dimensional theory. Then, some twelve-dimensional SO(18) gauge theories lead to models of the SO(10)\times U(1) grand unified theory in four dimensions, where fermions of the Standard Model appear in multiple generations along with scalars that may break the electroweak symmetry. The representations of the obtained scalars and fermions are summarized.

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arXiv2022

$1/(M_{R})_{33}$ expansion of the type-I seesaw mechanism and partial $Z_{2}$ symmetry for TM$_{1,2}$ mixing

We consider an expansion of the type-I seesaw mechanism by the inverse of the 3-3 matrix element $1/(M_{R})_{33}$ of the mass matrix of right-handed neutrinos $M_{R}$. Conditions of such a situation are obtained for $M_{R}$ and the Dirac mass matrix $m_{D}$. In this case, a partial $Z_{2}$ symmetry such as $S m_{D} P_{} = \pm m_{D} P_{}$ with a projection matrix $P_{} = {\rm diag} ( 1, 1, 0)$ leads to an approximate $Z_{2}$ symmetry by $S$ for the neutrino mass matrix $m_ν$. Such a partial $Z_{2}$ symmetry is desirable in the context of unified theories because it allows hierarchical $m_{D}$ and the large mixing of $m_ν$ simultaneously.

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arXiv2022

Conditions of general $Z_{2}$ symmetry and TM$_{1,2}$ mixing for the minimal type-I seesaw mechanism in an arbitrary basis

In this paper, using a formula for the minimal type-I seesaw mechanism by $LDL^{T}$ (or generalized Cholesky) decomposition, conditions of general $Z_{2}$-invariance for the neutrino mass matrix $m$ is obtained in an arbitrary basis. The conditions are found to be $(M_{22} a_{i}^{+} - M_{12} b_{i}^{+}) \, ( M_{22} a_{j}^{-} - M_{12} b_{j}^{-}) = - \det M \, b_{i}^{+} \, b_{j}^{-}$ for the $Z_{2}$-symmetric and -antisymmetric part of a Yukawa matrix $Y_{ij}^{\pm} \equiv (Y \pm T Y )_{ij} /2 \equiv (a_{j}^{\pm}, b_{j}^{\pm})$ and the right-handed neutrino mass matrix $M_{ij}$. In other words, the symmetric and antisymmetric part of $b_{i}$ must be proportional to those of the quantity $\tilde a_{i} \equiv a_{i} - {M_{12} \over M_{22}} b_{i}$. They are equivalent to the condition that $m$ is block diagonalized by eigenvectors of the generator $T$. These results are applied to three $Z_{2}$ symmetries, the $μ-τ$ symmetry, the TM$_{1}$ mixing, and the magic symmetry which predicts the TM$_{2}$ mixing. For the case of TM$_{1,2}$, the symmetry conditions become $ M_{22}^{2} \, \tilde {a}_{1}^{\rm TBM} \tilde a_{2}^{\rm TBM} = - \det M \, b_{1}^{\rm TBM} b_{2}^{\rm TBM}$ and $ M_{22}^{2} \, \tilde {a}_{1,2}^{\rm TBM} \tilde a_{3}^{\rm TBM} = - \det M \, b_{1,2}^{\rm TBM} b_{3}^{\rm TBM}$ with components $\tilde a_{i}^{\rm TBM}$ and $b_{i}^{\rm TBM}$ in the TBM basis $\mathbf{v}_{1,2,3}$. In particular, for the TM$_{2}$ mixing, the magic (anti-)symmetric Yukawa matrix with $S_{2} Y = \pm Y$ is phenomenologically excluded because it predicts $m_{2}=0$ or $m_{1}, m_{3} = 0$. In the case where Yukawa is not (anti-)symmetric, the mass singular values are displayed without a root sign.

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arXiv2022

Diagonal reflection symmetries, four-zero texture, and trimaximal mixing with predicted $θ_{13}$ in an $A_{4}$ symmeric model

In this paper, we impose a magic symmetry on the neutrino mass matrix $m_ν$ with universal four-zero texture and diagonal reflection symmetries. Due to the magic symmetry, the MNS matrix has trimaximal mixing inevitably. Since the lepton sector has only six free parameters, physical observables of leptons are all determined from the charged leptons masses $m_{ei}$, the neutrino mass differences $Δm_{i1}^{2}$, and the mixing angle $θ_{23}$. This scheme predicts $\sin θ_{13} = 0.149$, that is almost equal to the latest best fit, as a function of the lepton masses $m_{e, μ}$ and the mass differences $Δm_{i1}^{2}$. Moreover, even if the mass matrix has perturbations that break the magic symmetry, the prediction of $\sin θ_{13}$ is retained with good accuracy for the four-zero texture with diagonal reflection symmetries.

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arXiv2022

A formula by $LDL^{T}$ decomposition for the minimal type-I seesaw mechanism and conditions of $CP$ symmetry in an arbitrary basis

In this paper, defining a formula by $LDL^{T}$ decomposition for the minimal type-I seesaw mechanism, we obtain conditions of $CP$ symmetry for the neutrino mass matrix $m$ in an arbitrary basis. The conditions are found to be ${\rm Re\,} (M_{22} a_{i} - M_{12} b_{i}) \, {\rm Im \,} ( M_{22} a_{j} - M_{12} b_{j}) = - \det M \, {\rm Re\,} b_{i} \, {\rm Im \,} b_{j}$ or $ = - \det M \, {\rm Im \,} b_{i} \, {\rm Re\,} b_{j}$ for the Yukawa matrix $Y_{ij} = (a_{j}, b_{j})$ and the right-handed neutrino mass matrix $M_{ij}$. In other words, the real or imaginary part of $b_{i}$ must be proportional to the real or imaginary part of the quantity $(M_{22} a_{i} - M_{12} b_{i})$.

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arXiv2022

Conditions of naturalness and fine-tunings for type-I seesaw mechanism with four-zero texture

In this paper, we search for conditions that the mass matrix of light neutrinos $m_ν$ is not a result of large cancellations for the type-I seesaw mechanism with four-zero texture. For the Yukawa matrix of neutrinos $Y_ν$ and heavy Majorana mass matrix $M_{R}$, these conditions are written as $(Y_ν)_{i2} \propto (m_ν)_{i2} \, \Rightarrow \, (Y_ν)_{i2} \propto (M_{R})_{i2}$. We call them {\it alignment} conditions because they align the certain rows or columns of the three neutrino mass matrices. If these conditions do not hold, the large mixing in $m_ν$ is a result of fine-tuning due to the cancellation of several terms. Then they are required from a viewpoint of naturalness. They give an explanation of the seesaw-invariance of four-zero texture, and place rough restrictions on flavor structures of neutrinos. Under these conditions, $Y_ν$ must have a cascade hierarchy. For $M_{R}$, the 12 submatrix has a similar hierarchy as $Y_ν$ and $m_ν$. However, the 23 submatrix has a waterfall hierarchy without some fine-tuning. Therefore, it is likely that $Y_ν$ and $M_{R}$ have qualitatively different flavor structures. Furthermore, since the conditions restrict CP phases of the matrix elements, they imply existence of a universal generalized CP symmetry in the neutrino sector.

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arXiv2022

A general formula by $LDL^{T}$ decomposition for the type-I seesaw mechanism

By performing an approximate spectral decomposition to the inverse mass matrix of the right-handed neutrinos $M^{-1}$, we obtain a basis-independent formula for the type-I seesaw mechanism. Mathematically, it is based on the generalized Cholesky (or $LDL^{T}$) decomposition of the symmetric matrix $M^{-1} = L D L^{T}$, with a diagonal matrix $D$ and a lower unitriangular matrix $L$. Since the diagonalization of $L$ can be inverted without solving cubic equations, the formula will be useful to investigate general properties of the mechanism, such as flavor symmetries, generalized $CP$ symmetries, and fine-tunings.

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arXiv2021

Resolving the Hubble tension in a U(1)$_{L_μ-L_τ}$ model with Majoron

In this paper, we explore possibilities of resolving the Hubble tension and $(g-2)_μ$ anomaly simultaneously in a U(1)$_{L_μ- L_τ}$ model with Majoron. We only focus on a case where the Majoron $ϕ$ does not exist at the beginning of the universe and is created by neutrino inverse decay $νν\to ϕ$ after electron-positron annihilation. In this case, contributions of the new gauge boson $Z'$ and Majoron $ϕ$ to the effective number of neutrino species $N_{\rm eff}$ can be calculated in separate periods. These contribution are labelled $N'_{\rm eff}$ for the U(1)$_{L_μ- L_τ}$ gauge boson and $ΔN_{\rm eff}^\prime$ for the Majoron. The effective number $N_{\rm eff} = N'_{\rm eff} + ΔN_{\rm eff}^\prime$ is evaluated by the evolution equations of the temperatures and the chemical potentials of light particles in each period. As a result, we found that the heavier $Z'$ mass $m_{Z^\prime}$ results in the smaller $N_{\mathrm{eff}}^\prime$ and requires the larger $ΔN_{\mathrm{eff}}^\prime$ to resolve the Hubble tension. Therefore, compared to previous studies, the parameter region where the Hubble tension can be resolved is slightly shifted toward the larger value of $m_{Z^\prime}$.

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arXiv2021

Almost exact diagonal reflection symmetries and three-zero texture

In this paper, we consider a three-zero texture with diagonal reflection symmetries in the SM. The three-zero texture has two less assumptions ($(M_{u})_{11} , (M_ν)_{11} \neq 0$) than the universal four-zero texture of mass matrices $(M_{f})_{11} = (M_{f})_{13,31} = 0$ for $f = u,d,ν, e$. The texture allows diagonal reflection symmetries to be almost exact and $d$\,-\,$e$ unification. They reproduce the CKM and MNS matrices with accuracies of $O(10^{-4})$ and $O(10^{-3})$. Some perturbative diagonalizations yield two relations with good accuracy for quark mass and mixing. Although this calculation is done in a special basis, it is a general result in a sense, because other textures and generalized $CP$ symmetries exist by some weak basis transformation. By assuming a $d$\,-\,$e$ unified relation ($M_{d} \sim M_{e}$), we obtain the lightest neutrino mass $m_{1} \simeq 2.12\, - \, 5.64\,$[meV] and the effective mass of the double beta decay $|m_{ee}| \simeq 1.23 - 2.15 \,$[meV].

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arXiv2021

Diagonal reflection symmetries and universal four-zero texture

In this paper, we consider a set of new symmetries in the SM, {\it diagonal reflection} symmetries $R \, m_{u,ν}^{*} \, R = m_{u,ν}, ~ m_{d,e}^{*} = m_{d,e}$ with $R =$ diag $(-1,1,1)$. These generalized $CP$ symmetries predict the Majorana phases to be $α_{2,3} /2 \sim 0$ or $π/2$. A realization of reflection symmetries suggests a broken chiral $U(1)_{\rm PQ}$ symmetry and a flavored axion. The axion scale is suggested to be $\langle θ_{u,d} \rangle \sim Λ_{\rm GUT} \, \sqrt{m_{u,d} \, m_{c,s}} / v \sim 10^{12} \, $[GeV]. By combining the symmetries with the four-zero texture, the mass eigenvalues and mixing matrices of quarks and leptons are reproduced well. This scheme predicts the normal hierarchy, the Dirac phase $δ_{CP} \simeq 203^{\circ},$ and $|m_{1}| \simeq 2.5$ or $6.2 \, $[meV]. In this scheme, the type-I seesaw mechanism and a given neutrino Yukawa matrix $Y_ν$ completely determine the structure of right-handed neutrino mass $M_{R}$. An $u-ν$ unification predicts mass eigenvalues to be $ (M_{R1} \, , M_{R2} \, , M_{R3}) = (O (10^{5}) \, , O (10^{9}) \, , O (10^{14})) \, $[GeV].

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arXiv2020

Interplay between $μ$-$τ$ reflection symmetry, four-zero texture and universal texture

In this letter, we consider exact $μ-τ$ reflection symmetries for quarks and leptons. Fermion mass matrices are assumed to be four-zero textures for charged fermions $f = u,d,e$ and a symmetric matrix for neutrinos $ν_{L}$. By a bi-maximal transformation, all the mass matrices lead to $μ-τ$ reflection symmetric forms, which seperately satisfy $T_{u} \, m_{u,ν}^{*} \, T_{u} = m_{u,ν}$ and $T_{d} \, m_{d,e}^{*} \, T_{d} = m_{d,e}$. Reconciliation between the $μ-τ$ reflection symmetries and observed $\sin θ_{13}$ predicts $δ_{CP} \simeq 203^{\circ}$. Moreover, imposition of universal texture $(m_{f})_{11} = 0$ for $f=u,d,ν,e$ predicts the normal hierarchy with the lightest neutrino mass $|m_{1}| = 6.26$ or $2.54$ meV.

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arXiv2019

Lopsided texture compatible with thermal leptogenesis in partially composite Pati--Salam unification

In this paper, we consider a lopsided flavor texture compatible with thermal leptogenesis in partially composite Pati--Salam unification. The Davidson--Ibarra bound $M_{νR1} \gtrsim 10^9$ GeV for the successful thermal leptogenesis can be recast to the Froggatt--Nielsen (FN) charge of the lopsided texture. We found the FN charge $n_{\nu1}$ of the lightest right-handed neutrino $ν_{R1}$ can not be larger than a upper bound, $n_{\nu1} \lesssim 4.5$. From the viewpoint of unification, the FN charges of the neutrinos $n_{νi}$ should be the same to that of other SM fermions. Then, two cases $n_{νi} = n_{qi} = (3,2,0)$ and $ n_{νi} = n_{l i} = (n+1,n,n)$ are considered. Observations of PS model shows that the case of $n=0$, $n_{li} = n_{di} = (1,0,0)$ will be the simplest realization. To decrease the FN charges of these fermions from the GUT invariant FN charges $n_{qi} = (3,2,0)$, we utilize the partial compositeness. In this picture, the hierarchies of Yukawa matrices are a consequence of mixings between massless chiral fermions $f_{L}, f'_{R}$ and massive vector fermions $F_{L,R}, F'_{L,R}$. This is induced by the linear mixing terms $λ^{f} \bar f_{L} F_{R}$ and $λ^{f'} \bar F'_{L} f'_{R}$. As a result of the partial compositeness, the decreases of FN charges require fine-tunings between mass and Yukawa matrices either for the increases of $λ^{f, f'}$ or for the decreases of $M_{F,F'}$. Therefore, the case for $n=2$ and $n_{di} = n_{li} = (3,2,2)$, which requires only increases of FN charges will be appropriate to build a natural model.

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