Yukawa textures in modular symmetric vacuum of magnetized orbifold models

Abstract

We study quark mass matrices derived from magnetized $T^2/{\mathbb{Z}}_2$ orbifold models. Yukawa matrices at three modular fixed points, $\tau =i,e^{2\pi i/3}$ 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 $\tau =i\infty$ are not realistic. We classify Yukawa textures at $\tau =i$ and $e^{2\pi i/3}$. 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.

40 pages

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Cited by in corpus (9)

• $A_4$ Modular Flavour Model of Quark Mass Hierarchies close to the Fixed Point $\tau =\omega$
• A minimal modular invariant neutrino model
• Quark and lepton flavor structure in magnetized orbifold models at residual modular symmetric points
• Texture zeros of quark mass matrices at fixed point $\tau =\omega$ in modular flavor symmetry
• 4D modular flavor symmetric models inspired by higher dimensional theory
• Index theorem on magnetized blow-up manifold of $T^2/{\mathbb{Z}}_N$
• Classifications of magnetized $T^4$ and $T^4/Z_2$ orbifold models
• Number of zero-modes on magnetized $T^4/Z_N$ orbifolds analyzed by modular transformation
• Modular symmetry anomaly and non-perturbative neutrino mass terms in magnetized orbifold models