arXiv subjects

Morimitsu Tanimoto

Publications and source records attributed to Morimitsu Tanimoto.

At least 19 recordsLinked to original sources

arXiv2026

Textures of dimension-six operators in the SMEFT with non-invertible selection rules

We investigate the flavor structures of dimension-six operators in the Standard Model Effective Field Theory (SMEFT) subject to non-invertible selection rules. In particular, we classify the flavor textures of all baryon-number-conserving dimension-six SMEFT operators and determine the resulting constraints on their Wilson coefficients. The selection rules determine not only the texture zeros but also the allowed tensor structures of the Wilson coefficients, which can be expressed analytically in terms of a reduced number of independent parameters. We also find that the flavor structures of higher-dimensional operators are not necessarily aligned with those of the Yukawa couplings, in contrast to the Minimal Flavor Violation hypothesis, in which the Yukawa couplings govern the flavor structure of higher-dimensional operators. It turns out that the resulting flavor and chirality patterns differ from those typically obtained in SMEFT with conventional flavor symmetries, providing characteristic predictions for $B$-meson observables and charged-lepton-flavor-violating radiative decays.

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arXiv2025

GUT-motivated non-invertible symmetry as a solution to the strong CP problem and the neutrino CP-violating phase

The unsuppressed CP violation in QCD is a problem in the standard model. If we have some mechanism to guarantee real determinants of the quark mass matrices, the vanishing physical vacuum angle $\bar \theta$ indicates the CP invariance at the fundamental level. Thus, the small ${\bar \theta}$ is technically natural, since we have an enhanced CP symmetry in the limit of the vanishing $\bar \theta =0$. In fact, it was proved that the vacuum angle is never renormalized up to the four-loop level once it is fixed at 0 value at some high energy scale. The purpose of this paper is to construct a model which guarantees the real determinants of the quark mass matrices assuming a non-invertible symmetry.

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arXiv2025

Lepton mass textures from non-invertible multiplication rules

We study the lepton mass textures, which are derived by $\mathbb{Z}_2$ gauging of $\mathbb{Z}_M$ symmetries. We can obtain various textures for the Yukawa couplings in the charged lepton sector, but the patterns of neutrino mass matrices are limited. All the obtained textures can not be realized by group-theoretical symmetries, and certain textures can lead to realistic results.

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arXiv2025

Axionless Solution to the Strong CP Problem -- two-zeros textures of the quark and lepton mass matrices and neutrino CP violation --

CP invariance is a very attractive solution to the strong CP problem in QCD. This solution requires the vanishing ${\rm arg}\,[{\rm det}\, M_d\, {\rm det} M_u]$, where the $M_d$ and $M_u$ are the mass matrices for the down- and up-type quarks. It happens if we have several zeros in the quark mass matrices. We proceed a systematic construction, in this paper, of two zeros textures for the down-type quark mass matrix while the mass matrix for the up-type quarks is always diagonal. We find only three types of the mass matrices can explain the observed CKM matrix, the masses of the quarks and the charged leptons and the small enough vacuum angle $\theta < 10^{-10}$. We extend the mass construction to the neutrino sector and derive predictions on the CP violating parameter $\delta_{CP}$ in the neutrino oscillation and the mass parameter $m_{\beta\beta}$. It is extremely remarkable that the normal (NH) and inverted (IH) hierarchies in the neutrino masses are equally possible in the case where we introduce only two right-handed neutrinos $N$s. Furthermore, we have a strict prediction on the $\delta_{CP} \simeq 200^\circ$ or $250^\circ$ in the NH case. If it is the case we can naturally explain the positive sign of the baryon asymmetry in the present universe.

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arXiv2025

More about quark Yukawa textures from selection rules without group actions

We study the coupling selection rules associated with non-group symmetries, i.e., $\mathbb{Z}_2$ gauging of $\mathbb{Z}_M$ symmetries. We clarify which Yukawa textures can be derived by our selection rules for $M=3, 4$, and 5, and obtain various textures including the the nearest neighbor interaction type and its extension. Some of them cannot be realized by a conventional group-like symmetry. They lead to interesting phenomenology such as a solution to the strong CP problem without axion.

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arXiv2024

Prediction of the CP Phase $\delta_{CP}$ in the Neutrino Oscillation and an Axion-less Solution to the Strong CP Problem

A model of the axion-less solution to the strong CP problem has been recently constructed based on the $\bf T^2/\mathbb{Z}_3$ orbifold in the six dimensional space-time. We extend, in this paper, the model to include the lepton sector with three right-handed neutrinos. A crucial point in the extended model is that we have only one CP-violating phase and thus the CP phase in the neutrino oscillation can be predicted by the CP phase in the CKM matrix. The CP phase $\delta_{CP}$ in the PMNS matrix is predicted as $\delta_{CP}\simeq 192^\circ - 195^\circ$ which can be tested in the near future experiments. We also discuss the effective mass $m_{\beta\beta}$ responsible for the neutrino-less double beta decay of nucleus, which is predicted as $m_{\beta\beta} \simeq 8-11$\,meV. We consider the leptogenesis and confirm that our model generates the right sign of the baryon asymmetry if the first family right-handed neutrino is the lightest among the heavy right-handed neutrinos.

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arXiv2024

Yukawa textures from non-invertible symmetries

Phenomenological aspects of non-invertible symmetries, in particular the flavor structure of quarks and leptons, are studied. We start with a $\mathbb{Z}_M$ discrete symmetry and gauge $\mathbb{Z}_2$ so as to obtain a non-invertible symmetry. We study which Yukawa textures can be derived from the non-invertible symmetries. Various textures can be realized and some of them cannot be realized by a conventional symmetry. For example, the nearest neighbor interaction texture as well as other interesting textures of quarks and leptons are obtained.

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arXiv2024

Leptonic dipole operator with $\Gamma_2$ modular invariance in light of Muon $(g-2)_\mu$

We have studied the leptonic EDM and the LFV decays relating with the recent data of anomalous magnetic moment of muon, $(g-2)_{\mu}$ in the leptonic dipole operator. We have adopted the successful $\Gamma_2$ modular invariant model by Meloni-Parriciatu as the flavor symmetry of leptons. Suppose the anomaly of $(g-2)_{\mu}$, $\Delta a_{\mu}$ to be evidence of New Physics (NP), we have related it with the anomalous magnetic moment of the electron $\Delta a_e$, the electron EDM $d_e$ and the $\mu\to e \gamma$ decay. We found that the NP contributions to $\Delta a_{e(\mu)}$ are proportional to the lepton masses squared likewise the naive scaling $\Delta a_\ell \propto m^2_\ell$. The experimental constraint of $|d_e|$ is much tight compared with the one from the branching ratio $\mathcal{B} (\mu \to e \gamma)$ in our framework. Supposing the phase of our model parameter $\delta_{\alpha}$ for the electron to be of order one, we have estimated the upper-bound of $\mathcal{B}(\mu \to e \gamma)$, which is at most $10^{-21}-10^{-20}$. If some model parameters are real, leptonic EDMs vanish since the CP phase of the modular form due to modulus $\tau$ does not contribute to the EDM. However, we can obtain $\mathcal{B} (\mu \to e \gamma)\simeq 10^{-13}$ with non-vanishing $d_e$ in a specific case. The imaginary part of a parameter can lead to $d_e$ in the next-to-leading contribution. The predicted electron EDM is below $10^{-32}$e\,cm, while $\mathcal{B} (\mu \to e \gamma)$ is close to the experimental upper-bound. The branching ratios of $\tau\to e\gamma$ and $\tau\to \mu\gamma$ are also discussed.

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arXiv2023

Electron EDM and LFV decays in the light of Muon $(g-2)_\mu$ with U(2) flavor symmetry

We study the interplay of New Physics (NP) among the lepton magnetic moment, the lepton flavor violation (LFV) and the electron electric dipole moment (EDM) in light of recent data of the muon $(g-2)_\mu$. The NP is discussed in the leptonic dipole operator with the $U(2)$ flavor symmetry of the charged leptons, where possible CP violating phases of the three family space are taken into account. It is remarked that the third-family contributes significantly to the LFV decay, $\mu \to e\gamma$, and the electron EDM. The experimental upper-bound on $\mu \to e\gamma$ decay gives a severe constraint on the parameters of the flavor model. The predicted electron EDM is rather large due to the CP violating phases in the three family space. In addition, we also study $(g-2)_{e,\tau}$ of the electron and tauon, and EDMs of the muon and tauon as well as the $\tau \to e \gamma$ and $\tau \to \mu \gamma$ decays. The $\tau_R \to \mu_L \gamma$ decay is predicted to be close to the experimental upper-bound.

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arXiv2023

Modular flavor symmetric models

We review the modular flavor symmetric models of quarks and leptons focusing on our works. We present some flavor models of quarks and leptons by using finite modular groups and discuss the phenomenological implications. The modular flavor symmetry gives interesting phenomena at the fixed point of modulus. As a representative, we show the successful texture structure at the fixed point $\tau = \omega$. We also study CP violation, which occurs through the modulus stabilization. Finally, we study SMEFT with modular flavor symmetry by including higher dimensional operators.

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arXiv2022

4D modular flavor symmetric models inspired by higher dimensional theory

We study a scenario to derive four-dimensional modular flavor symmetric models from higher dimensional theory by assuming the compactification consistent with the modular symmetry. In our scenario, wavefunctions in extra dimensional compact space are modular forms. That leads to constraints on combinations between modular weights and $Γ_N$ ($Γ_N')$ representations of matter fields. We also present illustrating examples.

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arXiv2022

Generalized Matter Parities from Finite Modular Symmetries

We classify a supersymmetric extension of the Standard Model by discrete symmetries originating from finite modular symmetries $\Gamma_N$. Since all the couplings in supersymmetric theories of finite modular symmetries $\Gamma_N$ are described by holomorphic modular forms with even modular weights, renormalizable and non-renormalizable operators such as baryon- and/or lepton-number violating operators are severely constrained. From the modular transformation of matter multiplets with modular weight $1/M$, we find $\mathbb{Z}_{2M}$ symmetries, including the generalized baryon and lepton parities, $R$-parity, $\mathbb{Z}_3$ baryon triality and $\mathbb{Z}_6$ proton hexality. Such $\mathbb{Z}_{2M}$ symmetries are enlarged to $\mathbb{Z}_{2M} \rtimes \mathbb{Z}_2^{\text{CP}}$ symmetries together with the CP transformation.

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arXiv2022

Texture zeros of quark mass matrices at fixed point $\tau=\omega$ in modular flavor symmetry

We study systematically derivation of the specific texture zeros, that is the nearest neighbor interaction (NNI) form of the quark mass matrices at the fixed point $\tau=\omega$ in modular flavor symmetric models. We present models that the NNI forms of the quark mass matrices are simply realized at the fixed point $\tau=\omega$ in the $A_4$ modular flavor symmetry by taking account multi-Higgs fields. Such texture zero structure originates from the $ST$ charge of the residual symmetry $Z_3$ of $SL(2,Z)$. The NNI form can be realized at the fixed point $\tau = \omega$ in $A_4$ and $S_4$ modular flavor models with two pairs of Higgs fields when we assign properly modular weights to Yukawa couplings and $A_4$ and $S_4$ representations to three generations of quarks. We need four pairs of Higgs fields to realize the NNI form in $A_5$ modular flavor models.

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arXiv2022

Mass matrices with CP phase in modular flavor symmetry

We study the CP violation and the CP phase of quark mass matrices in modular flavor symmetric models. The CP symmetry remains at $τ= e^{2 πi/3}$ by a combination of the $T$-symmetry of the modular symmetry. However, the $T$-symmetry breaking may lead to the CP violation at the fixed point $τ= e^{2 πi/3}$. We study such a possibility in magnetized orbifold models as examples of modular flavor symmetric models. These models, in general, have more than one candidates for Higgs modes, while generic string compactifications also lead to several Higgs modes. These Higgs modes have different behaviors under the $T$-transformation. The light Higgs mode can be a linear combination of those modes so as to lead to realistic quark mass matrices. The CP phase of mass matrix does not appear in a certain case, which is determined by the $T$-transformation behavior. Deviation from it is important to realize the physical CP phase. We discuss an example leading to non-vanishing CP phase at the fixed point $τ= e^{2 πi/3}$.

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arXiv2022

Confronting the prediction of leptonic Dirac CP-violating phase with experiments

We update and improve past efforts to predict the leptonic Dirac CP-violating phase with models that predict perturbatively modified tribimaximal or bimaximal mixing. Simple perturbations are applied to both mixing patterns in the form of rotations between two sectors. By translating these perturbed mixing matrices to the standard parameterization for the neutrino mixing matrix we derive relations between the Dirac CP-phase and the oscillation angles. We use these relations together with current experimental results to constrain the allowed range for the CP-phase and determine its probability density. Furthermore, we elaborate on the prospects for future experiments probing on the perturbations considered in this work. We present a model with $A_4$ modular symmetry that is consistent with one of the described perturbed scenarios and successfully predicts current oscillation parameter data.

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arXiv2022

Lepton flavor violation, lepton $(g-2)_{μ,\,e}$ and electron EDM in the modular symmetry

We study the lepton flavor violation (LFV), the leptonic magnetic moments $(g-2)_{μ,\,e} $ and the electric dipole moment (EDM) of the electron in the Standard-Model Effective Field Theory with the $Γ_N$ modular flavor symmetry. We employ the stringy Ansatz on coupling structure that 4-point couplings of matter fields are written by a product of 3-point couplings of matter fields. We take the level 3 finite modular group, $Γ_3$ for the flavor symmetry, and discuss the dipole operators at nearby fixed point $τ=i$, where observed lepton masses and mixing angles are well reproduced. Suppose the anomaly of the anomalous magnetic moment of the muon to be evidence of the new physics (NP), we have related it with $(g-2)_{e}$, LFV decays, and the electron EDM. It is found that the NP contribution to $(g-2)_{e}$ is proportional to the lepton masses squared likewise the naive scaling. We also discuss the correlations among the LFV processes $μ\to eγ$, $τ\to μγ$ and $τ\to eγ$, which are testable in the future. The electron EDM requires the tiny imaginary part of the relevant Wilson coefficient in the basis of real positive charged lepton masses, which is related to the $μ\to eγ$ transition in our framework.

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arXiv2021

Modular symmetry in the SMEFT

We study the modular symmetric standard-model effective field theory. We employ the stringy Ansatz on coupling structure that 4-point couplings $y^{(4)}$ of matter fields are written by a product of 3-point couplings $y^{(3)}$ of matter fields, i.e., $y^{(4)} = y^{(3)}y^{(3)}$. In this framework, we discuss the flavor structure of bilinear fermion operators and 4-fermion operators, where the holomorphic and anti-holomorphic modular forms appear. From the Ansatz, the $A_4$ modular-invariant semileptonic four-fermion operator $[\,\bar E_R ΓE_R][\,\bar D_R ΓD_R\,]$ does not lead to the flavor changing (FC) processes since this operator would be constructed in terms of gauge couplings $g$ as $y^{(3)} \sim g$. The chirality flipped bilinear operator $[\,\bar D_R ΓD_L\,]$ also does not lead FC if the mediated mode corresponds to the Higgs boson $H_d$. In this case, the flavor structure of this operator is the exactly same as the mass matrix. On the other hand, if the flavor structure of the operator is not the exactly same as the mass matrix, the situation would change drastically. Then, we obtain the non-trivial relations of FC transitions at nearby fixed points $τ=i,\,ω\,, i\infty$, which are testable in the future. As an application, we discuss the relations of the lepton flavor violation processes $ μ\to eγ,\, τ\to μγ$ and $τ\to eγ$ at nearby $τ_e=i$, where the successful lepton mass matrix was obtained. We also study the flavor changing 4-quark operators in the $A_4$ modular symmetry of quarks. As a result, the minimal flavor violation could be realized by taking relevant specific parameter sets of order one.

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arXiv2021

Dirac Radiative Neutrino Mass with Modular Symmetry and Leptogenesis

Minimalistic Dirac radiative neutrino mass model based on modular symmetry is proposed. We predict maximum number of observables possible including neutrino mass splittings, neutrino mass scale, lepton mixing angles, and Dirac phases in the leptonic sector with minimum number of input parameters possible. Model is capable of accommodating multicomponent dark matter, thanks to the $\emph{R}-$parity and accidental scotogenic $\mathbb{Z}_2$ discrete symmetry. Furthermore, even-though neutrinos are Dirac in our model, matter-antimatter asymmetry of the Universe is achieved via neutrinogenesis mechanism. Phenomenology of the dark sector including various dark matter candidates is briefly discussed.

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