Kei Yamamoto

A bstract: We study lepton-number-violating interactions at dimension seven in the Standard Model effective field theory that contribute to the meson decays B → Kνν and K → πνν . Such interactions could washout the baryon asymmetry of the Universe and also contribute to the neutrinoless double beta decay, even though the interactions involve a change in down-type quark flavors. We clarify conditions under which excesses in meson decay rates over the Standard Model predictions can be successfully observed. We also show that, although these interactions contribute to neutrino masses at the two-loop level, the Weinberg operator can be introduced consistently without spoiling the scenario.

We classify a supersymmetric extension of the Standard Model by discrete symmetries originating from finite modular symmetries Γ_N. Since all the couplings in supersymmetric theories of finite modular symmetries Γ_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.

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, Γ₃ 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 → eγ, τ → μγ and τ → 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 → eγ transition in our framework.

The electric dipole moment (EDM) of electron is studied in the supersymmetric A4 modular invariant theory of flavors with CP invariance. The CP symmetry of the lepton sector is broken by fixing the modulus τ. Lepton mass matrices are completely consistent with observed lepton masses and mixing angles in our model. In this framework, a fixed τ also causes the CP violation in the soft SUSY breaking terms. The electron EDM arises from the CP non-conserved soft SUSY breaking terms. The experimental upper bound of the electron EDM excludes the SUSY mass scale below 4–6 TeV depending on five cases of the lepton mass matrices. In order to see the effect of CP phase of the modulus τ, we examine the correlation between the electron EDM and the decay rate of the μ → eγ decay, which is also predicted by the soft SUSY breaking terms. The correlations are clearly predicted in contrast to models of the conventional flavor symmetry. The branching ratio is approximately proportional to the square of |d_e/e|. The SUSY mass scale will be constrained by the future sensitivity of the electron EDM, |d_e/e| ≃ 10⁻³⁰ cm. Indeed, it could probe the SUSY mass range of 10–20 TeV in our model. Thus, the electron EDM provides a severe test of the CP violation via the modulus τ in the supersymmetric modular invariant theory of flavors.