2024/12/24 by Tetsutaro Higaki, Junichiro Kawamura, Higaki, Tetsutaro +7
Biochemistry, Genetics and Molecular Biology · Computer Science · #Fractal and DNA sequence analysis #Computability, Logic, AI Algorithms
paper · pdf · doi:10.48550/arxiv.2412.18435
We study the moduli stabilization by the radiative corrections due to the moduli dependent vector-like masses invariant under the finite modular symmetry. The radiative stabilization mechanism can stabilize the modulus τ of the finite modular symmetry ΓN (N ∈ ℕ) at Im τ≫ 1, where the shift symmetry τ→ τ+1 remains unbroken approximately. The shift symmetry can be considered as the residual ℤN symmetry which realizes the Froggatt-Nielsen mechanism with the hierarchy parameter e- 2πIm τ/N ≪ 1. In this work, we study the stabilization of multiple moduli fields, so that various hierarchical values of the modular forms coexist in a model. For example, one modulus stabilized at Im τ1 ∼ 3 is responsible for the hierarchical structure of the quarks and leptons in the Standard Model, and another modulus stabilized at Im τ2 ∼ 15 can account for the flatness of the Re τ2 direction which may be identified as the QCD axion.