arXiv subjects

Yusuke Shimizu

Publications and source records attributed to Yusuke Shimizu.

At least 19 recordsLinked to original sources

arXiv2026

Robust estimation via $\gamma$-divergence for diffusion processes

This paper deals with the problem of outliers in high frequency observation data from diffusion processes. Robust estimation methods are needed because the inclusion of outliers can lead to incorrect statistical inference even in the diffusion process. To construct a robust estimator, we first approximate the transition density of the diffusion process to the Gaussian density by using Kessler's approach and then employ two types of minimum robust divergence estimation methods. In this paper, we provide the asymptotic properties of the robust estimator using $\gamma$-divergence. Furthermore, we derive the conditional influence functions of the estimation using divergences and discuss its boundness.

stat.ME↗

arXiv2025

Revisiting Flavor Model and Leptogenesis

We revisit a supersymmetric flavor model based on the symmetries $SU(2)_L \times A_4 \times Z_3 \times U(1)_R$, which extends the original Altarelli and Feruglio construction by introducing flavon and driving superfields responsible for the spontaneous breaking of the flavor symmetry in order to obtain non-zero reactor angle. The vacuum alignments of flavon fields are achieved through the minimization of the scalar potential derived from the superpotential. This setup leads to specific mass matrices for the charged leptons and neutrinos that are consistent with current experimental data, including the measured values of the lepton mixing angles and neutrino mass squared differences. We investigate whether the model can simultaneously accommodate successful thermal leptogenesis. In particular, we analyze the CP asymmetry generated in the decay of heavy Majorana neutrinos, the resulting lepton asymmetry, and its conversion to the baryon asymmetry through the electroweak sphalerons. However the CP asymmetry is zero, since the Dirac neutrino mass matrix is simple texture in the leading order for our model. Then we consider the next-to-leading order in Yukawa interactions of the Dirac neutrinos. Therefore, we can realize the baryon asymmetry of the universe at the present universe. By numerically scanning the parameter space, we identify the regions consistent with both neutrino oscillation data and the observed baryon asymmetry. In the specific case such that one of the couplings for the right-handed Majorana neutrinos is real parameter, the predicted lightest neutrino mass is at least $5$ meV and $15$ meV for the normal and inverted neutrino mass hierarchies, respectively. In addition, the range of the Majorana phases may be tested in future experiments.

hep-ph↗

arXiv2024

Flavino Dark Matter in a Non-Abelian Discrete Flavor Model

We study a relic density of the flavino dark matter in modified Altarelli and Feruglio $A_4$ model which is respecting the $SU(2)_L\times A_4\times Z_3\times U(1)_R$ symmetry. We calculate the Lagrangian from the superpotential in the model. In estimating relic density, we consider the relevant interactions from the Lagrangian that realize the vacuum expectation value alignments and charged lepton masses where we assume that the supersymmetry breaking effects are small for flavon sector. As a result, we find the degenerate masses between the lightest ``flavon'' and ``flavino'', and only two parameters in the potential determines the relic density. Then allowed parameter space of these parameters are estimated from relic density calculation taking a constraint from lepton flavor violation into account. We also briefly discuss other dark matter physics such as direct detection, indirect detection and collider search.

hep-ph↗

arXiv2023

$W$ Boson Mass and Grand Unification via the Type-$\rm{I\hspace{-.01em}I}$ Seesaw-like Mechanism

We propose an SU(5) GUT model extended with two additional pairs of $\mathbf{10}$ representation vector-like fermions. The CDF collaboration $W$ boson mass anomaly is explained by using the VEV of a real $\mathrm{SU(2)_L}$ triplet scalar coming from the $\mathbf{24}$ representation Higgs. The vector-like fermions are decomposed partly into vector-like quark doublets. Those vector-like quark doublets acquire mass from two sources; through the Yukawa interaction with the real $\mathrm{SU(2)_L}$ triplet via a type-$\rm{I\hspace{-.01em}I}$ seesaw-like mechanism. And, they acquire mass from the $\mathbf{24}$ representation Higgs. We assume that the mass for the vector-like quark doublets is expressed in terms of the real triplets mass. By combining the constraints on the vector-like quark masses with those on the heavy Higgs boson masses, we can obtain the narrow allowed mass ranges for the vector-like quark doublet and the real triplet. Therefore, our model can be tested in searches for these particles in the near future. In addition, the two additional pairs of vector-like fermions allow the SM gauge couplings to unify successfully at $M_{\mathrm{GUT}}\thickapprox5.1\times10^{15}$~GeV. Our model is also testable by the future Hyper-Kamiokande experiment via the proton decay lifetime $τ_p(p\toπ^0{e^+})<1.0\times10^{35}$~years.

hep-ph↗

arXiv2023

Non-SUSY Lepton Flavor Model with 3HDM

We propose a simple non-supersymmetric lepton flavor model with $A_4$ symmetry. The $A_4$ group is a minimal one which includes triplet irreducible representation. We introduce three Higgs doublets which are assigned as triplet of the $A_4$ symmetry. It is natural that there are three generations of the Higgs fields as same as the standard model fermions. We study the potential analysis and we get the vacuum expectation values for the local minimum. In the vacuum expectation values, we obtain the charged lepton, Dirac neutrino, and right-handed Majorana neutrino mass matrices. By using type-I seesaw mechanism, we get the left-handed Majorana neutrino mass matrix. In the NuFIT 5.1 data, we predict the Dirac CP phase and the Majorana phases for the only inverted neutrino mass hierarchy. Especially, the Dirac CP phase and lepton mixing angle $θ_{23}$ are strongly correlated. If the $θ_{23}$ is more precise measured, the Dirac CP phase is more precise predicted, and vice versa. We also predict the effective mass for neutrino-less double beta decay $m_{ee}\simeq 47.1~[\mathrm{meV}]$ and the lightest neutrino mass $m_3\simeq 0.789$~-~$1.43~[\mathrm{meV}]$. It is testable for our model in the near future neutrino experiments.

hep-ph↗

arXiv2023

Mass Relations, Unification, and Proton Decay in the Mirror GUT Model

We propose an SU(5)$\times $U(1)$_\text{X}\times$U(1)$_\text{PQ}$ model without SUSY because the SUSY particles have not been observed yet. The $\mathrm{U(1)_{X}}$ gauge symmetry is the generalization of the $\mathrm{U(1)_{B-L}}$ gauge symmetry and $\mathrm{U(1)_{PQ}}$ symmetry is the global Peccei-Quinn symmetry. We introduce three mirror families in order to unify the SM gauge couplings and avoid the restriction of proton lifetime. In order to obtain the difference of the masses for the down-type quarks and charged leptons, we also introduce the $\mathbf{45}$ representation Higgs in addition to the $\mathbf{5}$ representation one. In this paper, we discuss the mass relations between the SM and mirror particles and identify the mass scales of the mirror particles. Since the new particles exist in the intermediate energy scale and contribute to the renormalization group equation, the SM gauge couplings unify successfully at high energy. Our model can be tested by the future proton decay search, e.g., the Hyper-Kamiokande experiment expected as $τ_p(p\toπ^0{e^+})<1.0\times10^{35}$ years. Also, by using the mass relations between the active and mirror neutrinos, we estimate the lower bound of the heavy neutrino masses.

hep-ph↗

arXiv2022

Determination of Majorana type-phases from the time evolution of lepton numbers

We have investigated an approach for determining the Majorana type-phases using the time evolution of lepton family numbers. We show how the second-order time derivative of the expectation values for the lepton family numbers depends on the sum of the Majorana type-phases. Furthermore, others have connected the Majorana type-phases to the orientation of unitary triangles for the PMNS matrix, and the usual Majorana phases. Theoretically,this allows for the extraction of the orientation of the triangles and the Majorana phases from lepton family numbers. We study three example situations. First, how to extract the Majorana type-phases and the lightest neutrino mass for three massive neutrinos, and when a neutrino is massless. Second,the determination of the Majorana phase and the lightest neutrino mass for a two generation toy model. Third, simplified realizations of the type I seesaw model with two gauge singlet neutrinos and two families of lepton doublets. We calculate how the Majorana phases and Majorana type-phases are related to CP violation for leptogenesis at high energies. At first,the effective Majorana mass matrix is parametrized with real and positive diagonal elements. In this basis, the phase of the off-diagonal elements are related to the CP violating phases in the PMNS matrix. We explicitly show the relation between the single Majorana phase and the phase of the effective Majorana mass matrix for the toy model with two generations of active neutrinos. Then for the model with two gauge singlet neutrinos and two families of lepton doublets, we study the effective Majorana mass matrix generated by the seesaw model. In that model, we can show how the Majorana phase at low energy is related to the two CP violating phases of the seesaw matrix. That relation between the phases depends on the lepton number asymmetries of the heavy Majorana neutrinos decays for the toy models.

hep-ph↗

arXiv2022

Effective theory for universal seesaw model and FCNC

We study the quark sector of the universal seesaw model with SU(2)$_L$ $\times$ SU(2)$_R$ $\times$ $U(1)$.The model incorporates the seesaw mechanism with the vector-like quarks (VLQs). The purpose of this work is to study the model with the effective theory. After integrating the heavy five VLQs, we derive the effective theory with four up-type quark and three down type quark. In this work, the FCNC of Z boson for top quark and top$^\prime$ quark is derived.

hep-ph↗

arXiv2022

Renormalization group effects for a rank degenerate Yukawa matrix and the fate of the massless neutrino

The Type-I seesaw model is a common extension to the Standard Model that describes neutrino masses. The Type-I seesaw introduces heavy right-handed neutrinos with Majorana mass that transform as Standard Model electroweak gauge singlets. We initially study a case with two right-handed neutrinos called the 3-2 model. At an energy scale above the right-handed neutrinos, the effective neutrino mass matrix is rank degenerate implying the lightest neutrino is massless. After considering renormalization effects below the two right-handed neutrinos, the effective neutrino mass matrix remains rank degenerate. Next, we study a model with three right-handed neutrinos called the 3-3 model. Above the energy scale of the three right-handed neutrinos, we construct the effective neutrino mass matrix to be rank degenerate. After solving for the renormalization effects to energies below the three right-handed neutrinos, we find the rank of the effective neutrino mass matrix depends on the kernel solutions of the renormalization group equations. We prove for the simplest kernel solutions the effective neutrino mass matrix remains rank degenerate.

hep-ph↗

arXiv2021

Modulus $τ$ linking leptonic CP violation to baryon asymmetry in $A_4$ modular invariant flavor model

We propose an $A_4$ modular invariant flavor model of leptons, in which both CP and modular symmetries are broken spontaneously by the vacuum expectation value of the modulus $τ$. The value of the modulus $τ$ is restricted by the observed lepton mixing angles and lepton masses for the normal hierarchy of neutrino masses at $3σ$ confidence level. The predictive Dirac CP phase $δ_{CP}$ is in the ranges $[0^\circ,50^\circ]$, $[170^\circ,175^\circ]$ and $[280^\circ,360^\circ]$ for ${\rm Re}\, [τ]<0$, and $[0^\circ,80^\circ]$, $[185^\circ,190^\circ]$ and $[310^\circ,360^\circ]$ for ${\rm Re}\,[τ]>0$ at $3σ$ confidence level. The sum of three neutrino masses is predicted in $[60, 84]$ meV, and the effective mass for the $0νββ$ decay is in [0.003, 3] meV. On the other hand, there is no allowed region of the modulus $τ$ for the inverted hierarchy of neutrino masses at $3σ$ confidence level. The modulus $τ$ links the Dirac CP phase to the cosmological baryon asymmetry (BAU) via the leptogenesis. Due to the strong wash-out effect, the predictive baryon asymmetry $Y_B$ can be at most the same order of the observed value. Then, the lightest right-handed neutrino mass is restricted in the range of $M_1 =[1.5,\,6.5] \times 10^{13}$ GeV. We find the correlation between the predictive $Y_B$ and the Dirac CP phase $δ_{CP}$. Only two predictive $δ_{CP}$ ranges, $[5^\circ,40^\circ]$ (${\rm Re}\,[τ]>0$) and $[320^\circ,355^\circ]$ (${\rm Re}\,[τ]<0$) are consistent with the BAU.

hep-ph↗

arXiv2021

Spacetime evolution of lepton number densities and wave packet-like effects for neutrino flavor and chiral oscillations in quantum field theory

We present a formulation of lepton family numbers, based on quantum field theory, for neutrino oscillation phenomenology that can be applied to nonrelativistic and relativistic energies for neutrinos. It is formulated for both types of neutrinos, Dirac and Majorana. The formulation is constructed as the time evolution of a lepton family number density operator. Then, the time evolution of the lepton family number density operator becomes dependent on the mass and new features appear. The expectation value of the density operator is evaluated for the initial state with a Gaussian distribution for the momentum amplitude. This enables us to study wave packet-like decoherence effects. We show in the nonrelativistic regime, the type of neutrino mass are distinguishable even under the presence of wave packet-like decoherence effects.

hep-ph↗

arXiv2021

Lepton family numbers and non-relativistic Majorana neutrinos

In this talk, we have reviewed the recent development on the time evolution of lepton family number carried by Majorana neutrinos \cite{Adam:2021qiq}. This article focuses on the subtle points of the derivation of the lepton family numbers and their time evolution. We also show how the time evolution is sensitive to $m_{ee}$ and $m_{eμ}$ components of the effective Majorana mass matrix by applying the formula to the two family case. The dependence on the Majorana phase is clarified and the implication on CNB (cosmic neutrino background) is also discussed.

hep-ph↗

arXiv2021

Time Evolution of Lepton Number Carried by Majorana Neutrinos

We revisit the time evolution of the lepton family number for a SU(2) doublet consisting of a neutrino and a charged lepton. The lepton family number is defined through the weak basis of the SU(2) doublet, where the charged lepton mass matrix is real and diagonal. The lepton family number carried by the neutrino is defined by the left-handed current of the neutrino family. For this work we assume the neutrinos have Majorana mass. This Majorana mass term is switched on at time $t=0$ and the lepton family number is evolved. Since the operator in the flavor eigenstate is continuously connected to that of the mass eigenstate, the creation and annihilation operators for the two eigenstates are related to each other. We compute the time evolution of all lepton family numbers by choosing a specific initial flavor eigenstate for a neutrino. The evolution is studied for relativistic and nonrelativistic neutrinos. The nonrelativistic region is of particular interest for the Cosmic Neutrino Background predicted from big bang models. In that region we find the lepton family numbers are sensitive to Majorana and Dirac phases, the absolute mass, and mass hierarchy of neutrinos.

hep-ph↗

arXiv2020

Lepton number violation in a unified framework

We study the time evolution of lepton family number for neutrino which forms SU(2) doublet with charged lepton. The lepton family number is defined through a weak basis of SU(2) doublet in which the charged lepton mass matrix is a real and diagonal one. The lepton family number carried by the neutrino is defined with a left-handed current of the neutrino family. We study the time evolution of the lepton family number operator for Majorana neutrino. To be definite, we introduce the mass term at $t=0$ and study the time evolution of the lepton family number for the later time. Since the operator in flavor eigenstate is continuously connected to that of the mass eigenstate, the creation and annihilation operators for flavor eigenstates are related to those of mass eigenstates. The total lepton number of the Majorana neutrino is conserved. By choosing a specific flavor eigenstate of neutrino as an initial state, we compute the time evolution of all lepton family numbers. They are sensitive to Majorana and Dirac phases and also are sensitive to the absolute mass and mass hierarchy of neutrinos.

hep-ph↗

arXiv2020

$CP$ violation in modular invariant flavor models

We study the spontaneous $CP$ violation through the stabilization of the modulus $τ$ in modular invariant flavor models. The $CP$-invaraiant potentential has the minimum only at ${\rm Re}[τ] = 0$ or 1/2. From this prediction, we study $CP$ violation in modular invariant flavor models. The physical $CP$ phase is vanishing. The important point for the $CP$ conservation is the $T$ transformation in the modular symmetry. One needs the violation of $T$ symmetry to realize the spontaneous $CP$ violation.

hep-ph↗

arXiv2020

Modular $S_3$ invariant flavor model in SU(5) GUT

We present a flavor model with the $S_3$ modular invariance in the framework of SU(5) GUT. The $S_3$ modular forms of weights $2$ and $4$ give the quark and lepton mass matrices with a common complex parameter, the modulus $τ$. The GUT relation of down-type quarks and charged leptons is imposed by the VEV of adjoint 24-dimensional Higgs multiplet in addition to the VEVs of $5$ and $\bar 5$ Higgs multiples of SU(5). The observed CKM and PMNS mixing parameters as well as the mass eigenvalues are reproduced properly. We discuss the leptonic CP phase and the effective mass of the neutrinoless double beta decay with the sum of neutrino masses.

hep-ph↗

arXiv2020

$A_4$ lepton flavor model and modulus stabilization from $S_4$ modular symmetry

We study the modulus stabilization in an $A_4$ model whose $A_4$ flavor symmetry is originated from the $S_4$ modular symmetry. We can stabilize the modulus so that the $A_4$ invariant superpotential leads to the realistic lepton masses and mixing angles. We also discuss the phenomenological aspect of the present model as a consequence of the modulus stabilization.

hep-ph↗

arXiv2020

New $A_4$ lepton flavor model from $S_4$ modular symmetry

We study a flavor model with $A_4$ symmetry which originates from $S_4$ modular group. In $S_4$ symmetry, $Z_2$ subgroup can be anomalous, and then $S_4$ can be violated to $A_4$. Starting with a $S_4$ symmetric Lagrangian at the tree level, the Lagrangian at the quantum level has only $A_4$ symmetry when $Z_2$ in $S_4$ is anomalous. We obtain modular forms of two singlets and a triplet representations of $A_4$ by decomposing $S_4$ modular forms into $A_4$ representations. We propose a new $A_4$ flavor model of leptons by using those $A_4$ modular forms. We succeed in constructing a viable neutrino mass matrix through the Weinberg operator for both normal hierarchy (NH) and inverted hierarchy (IH) of neutrino masses. Our predictions of the CP violating Dirac phase $δ_{CP}$ and the mixing $\sin^2θ_{23}$ depend on the sum of neutrino masses for NH.

hep-ph↗