arXiv subjects

Tatsuo Kobayashi

Publications and source records attributed to Tatsuo Kobayashi.

At least 73 records · Page 4Linked to original sources

arXiv2022

Classifications of magnetized $T^4$ and $T^4/Z_2$ orbifold models

We study constructions and classifications of three-generation models based on magnetized $T^4$ and $T^4/{Z}_2$ orbifold as candidates of the compact space. We focus on chiral fermion zero-mode wave functions in the extra dimensions. Freedoms of constant gauge fields, called Scherk-Schwarz phases are taken into account. Infinite number of three-generation models are yielded, corresponding to the ways in which the magnetic flux can be turned on. We classify them in a systematic manner, clarifying the relationship between different models. The Higgs sector is also studied by analyzing possible assignments of the magnetic flux and Scherk-Schwarz phases, etc. to left- and right-handed fermions.

hep-th↗

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.

hep-ph↗

arXiv2022

Texture zeros of quark mass matrices at fixed point $τ=ω$ 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 $τ=ω$ in modular flavor symmetric models. We present models that the NNI forms of the quark mass matrices are simply realized at the fixed point $τ=ω$ 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 $τ= ω$ 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.

hep-ph↗

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 $τ= e^{2 πi/3}$.

hep-ph↗

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.

hep-ph↗

arXiv2022

Modular symmetry of soft supersymmetry breaking terms

We study the modular symmetry of soft supersymmetry breaking terms. Soft scalar masses and $A$-term coefficients are invariant under the modular symmetry when we regard $F$-term as a spurion with the modular weight $-2$. Their flavor structure is determined by the same symmetry as Yukawa couplings, i.e., fermion masses. The modular symmetric behavior of $μ$-term and $B$-term depends on how the $μ$-term is generated.

hep-ph↗

arXiv2022

Anomaly of non-Abelian discrete symmetries

We study anomalies of non-Abelian discrete symmetries; which part of non-Abelian group is anomaly free and which part can be anomalous. It is found that the anomaly-free elements of the group $G$ generate a normal subgroup $G_0$ of $G$ and the residue class group $G/G_0$, which becomes the anomalous part of $G$, is isomorphic to a single cyclic group. The derived subgroup $D(G)$ of $G$ is useful to study the anomaly structure. This structure also constrains the structure of the anomaly-free subgroup; the derived subgroup $D(G)$ should be included in the anomaly-free subgroup. We study the detail structure of the anomaly-free subgroup from the structure of the derived subgroup in various discrete groups. For example, when $G=S_n \simeq A_n \rtimes Z_2$ and $G=Δ(6n^2) \simeq Δ(3n^2) \rtimes Z_2$, in particular, $A_n$ and $Δ(3n^2)$ are at least included in the anomaly-free subgroup, respectively. This result holds in any arbitrary representations.

hep-th↗

arXiv2022

Modular symmetry anomaly and non-perturbative neutrino mass terms in magnetized orbifold models

We study the modular symmetry anomaly in magnetized orbifold models. The non-perturbative effects such as D-brane instanton effects can break tree-level symmetry. We study which part of the modular symmetry is broken explicitly by Majorana mass terms with three generations of neutrinos. The modular weight of neutrino mass terms does not match with other coupling terms in tree-level Lagrangian. In addition, the $Z_N$ symmetry of the modular flavor symmetry is broken and a certain normal subgroup of the modular flavor symmetry remains in neutrino mass terms.

hep-th↗

arXiv2022

On Stringy Origin of Minimal Flavor Violation

We study the minimal flavor violation in the context of string effective field theory. Stringy selection rules indicate that $n$-point couplings among fermionic zero-modes and lightest scalar modes in the string effective action are given by a product of Yukawa couplings which are regarded as spurion fields of stringy and geometrical symmetries. Hence, Yukawa couplings determine the dynamics of flavor and CP violations. This observation strongly supports the hypothesis of minimal flavor violation in the Standard Model effective field theory.

hep-ph↗

arXiv2022

Symplectic modular symmetry in heterotic string vacua: flavor, CP, and $R$-symmetries

We examine a common origin of four-dimensional flavor, CP, and $U(1)_R$ symmetries in the context of heterotic string theory with standard embedding. We find that flavor and $U(1)_R$ symmetries are unified into the $Sp(2h+2, \mathbb{C})$ modular symmetries of Calabi-Yau threefolds with $h$ being the number of moduli fields. Together with the $\mathbb{Z}_2^{\rm CP}$ CP symmetry, they are enhanced to $GSp(2h+2, \mathbb{C})\simeq Sp(2h+2, \mathbb{C})\rtimes \mathbb{Z}_2^{\rm CP}$ generalized symplectic modular symmetry. We exemplify the $S_3, S_4, T^\prime, S_9$ non-Abelian flavor symmetries on explicit toroidal orbifolds with and without resolutions and $\mathbb{Z}_2,S_4$ flavor symmetries on three-parameter examples of Calabi-Yau threefolds. Thus, non-trivial flavor symmetries appear in not only the exact orbifold limit but also a certain class of Calabi-Yau threefolds. These flavor symmetries are further enlarged to non-Abelian discrete groups by the CP symmetry.

hep-th↗

arXiv2021

4D effective action from non-Abelian DBI action with magnetic flux background

We study a systematic derivation of four dimensional $\mathcal{N}=1$ supersymmetric effective theory from ten dimensional non-Abelian Dirac-Born-Infeld action compactified on a six dimensional torus with magnetic fluxes on the D-branes. We find a new type of matter Kähler metric while gauge kinetic function and superpotential are consistent with previous studies. For the ten dimensional action, we use a symmetrized trace prescription and focus on the bosonic part up to $\mathcal{O}(F^4)$. In the presence of the supersymmetry, four dimensional chiral fermions can be obtained via index theorem. The new matter Kähler metric is independent of flavor but depends on the fluxes, 4D dilaton, Kähler moduli and complex structure moduli, and will be always positive definite if an induced Ramond-Ramond charge of the D-branes on which matters are living are positive. We read the superpotential from an F-term scalar quartic interaction derived from the ten dimensional action and the contribution of the new matter Kähler metric to the scalar potential which we derive turns out to be consistent with the supergravity formulation.

hep-th↗

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.

hep-ph↗

arXiv2021

Yukawa textures in modular symmetric vacuum of magnetized orbifold models

We study quark mass matrices derived from magnetized $T^2/\mathbb{Z}_2$ orbifold models. Yukawa matrices at three modular fixed points, $τ=i, e^{2πi/3}$ and $i\infty$ are invariant under $S$, $ST$ and $T$-transformations. We study these invariances on $T^2/\mathbb{Z}_2$ twisted orbifold. We find that Yukawa matrices have a kind of texture structures although ones at $τ=i\infty$ are not realistic. We classify Yukawa textures at $τ=i$ and $e^{2πi/3}$. Moreover we investigate the conditions such that quark mass matrix constructed by Yukawa textures becomes approximately rank one matrix, which is favorable to lead to hierarchical masses between the third generation and the others. It is found that realistic quark mass matrices can be obtained around the $S$-invariant vacuum and $ST$-invariant vacuum. As an illustrating example, we show the realization of the quark mass ratios and mixing based on Fritzch and Fritzch-Xing mass matrices.

hep-ph↗

arXiv2021

Modular flavor symmetries of three-generation modes on magnetized toroidal orbifolds

We study the modular symmetry on magnetized toroidal orbifolds with Scherk-Schwarz phases. In particular, we investigate finite modular flavor groups for three-generation modes on magnetized orbifolds. The three-generation modes can be the three-dimensional irreducible representations of covering groups and central extended groups of $Γ_N$ for $N=3,4,5,7,8,16$, that is, covering groups of $Δ(6(N/2)^2)$ for $N=$ even and central extensions of $PSL(2,\mathbb{Z}_{N})$ for $N=$odd with Scherk-Schwarz phases. We also study anomaly behaviors.

hep-th↗

arXiv2021

Dark matter stability at fixed points in a modular $A_4$ symmetry

We propose a new mechanism of stabilization for dark matter under fixed points of modular $A_4$ symmetry, thanks to recovering a residual symmetry for each of fixed points at $τ=ω,\ i, i\times\infty$. We find that a model at $τ=i$ successfully reproduces the neutrino oscillation data without conflict of the DM stability.

hep-ph↗

arXiv2021

Spontaneous CP violation and symplectic modular symmetry in Calabi-Yau compactifications

We explore the geometrical origin of CP and the spontaneous CP violation in Calabi-Yau compactifications. We find that the CP symmetry is identified with an outer automorphism of the symplectic modular group in the large complex structure regime of Calabi-Yau threefolds, thereby enlarging the symplectic modular group to their semidirect product group. The spontaneous CP violation is realized by the introduction of fluxes, whose effective action is invariant under CP as well as the discrete $\mathbb{Z}_2$ symmetry or $\mathbb{Z}_4$ R-symmetry. We explicitly demonstrate the spontaneous CP violation on a specific Calabi-Yau threefold.

hep-th↗

arXiv2021

Hierarchical structure of physical Yukawa couplings from matter field Kähler metric

We study the impacts of matter field Kähler metric on physical Yukawa couplings in string compactifications. Since the Kähler metric is non-trivial in general, the kinetic mixing of matter fields opens a new avenue for realizing a hierarchical structure of physical Yukawa couplings, even when holomorphic Yukawa couplings have the trivial structure. The hierarchical Yukawa couplings are demonstrated by couplings of pure untwisted modes on toroidal orbifolds and their resolutions in the context of heterotic string theory with standard embedding. Also, we study the hierarchical couplings among untwisted and twisted modes on resolved orbifolds.

hep-th↗

arXiv2021

Soft supersymmetry breaking terms and lepton flavor violations in modular flavor models

We study the soft supersymmetry (SUSY) breaking terms due to the modulus F-term in the modular flavor models of leptons. It is found that the soft SUSY breaking terms are constrained by the modular forms, and specific patterns are derived. Those phenomenological implications are discussed in such as the lepton flavor violation, $μ\rightarrow e + γ$ decay. In order to examine numerically, two modular flavor $A_4$ models are taken. The SUSY breaking scale is significantly constrained by inputting the observed upper bound of the $μ\rightarrow e + γ$ decay. The SUSY mass scale is larger than around $8$ TeV and $5$ TeV for the two $A_4$ models, respectively. Therefore, the current experimental upper bound for the $μ\to e + γ$ decay corresponds to the new physics of the SUSY particle at the $5$ -- $10$ TeV scale in the modular flavor models. The predicted branching ratio depends on a modulus $τ$ significantly. It decreases of one order at the large ${\rm Im}\,τ$. We also calculate the branching ratios of tauon decays to $e + γ$ and $μ+ γ$. Predicted ones are at most ${\cal O}(10^{-15})$, which are much below the current experimental bounds.

hep-ph↗