Gaussian Froggatt-Nielsen mechanism on magnetized orbifolds

Abstract

We study the structure of Yukawa matrices derived from the supersymmetric Yang-Mills theory on magnetized orbifolds, which can realize the observed quark and charged lepton mass ratios as well as the CKM mixing angles, even with a small number of tunable parameters and without any critical fine-tuning. As a reason behind this, we find that the obtained Yukawa matrices possess a Froggatt-Nielsen like structure with Gaussian hierarchies, which provides a suitable texture for them favored by the experimental data.Comment: 21 pages, 5 figure

Elliptic inflation: interpolating from natural inflation to R 2-inflation

“…As noted already, gauge and Yukawa interactions can be written in terms of the Jacobi theta functions in toroidal compactifications in intersecting or magnetized D-brane system [34,36,37]. Also on the magnetized orbifolds, e.g., T 6 /(Z 2 × Z 2 ) and T 2 × T 4 /Z 2 , Yukawa couplings are similarly expressed with the theta functions [53]. This type of function comes from the wave functions of the fields on the torus, which respects the periodicity, in magnetized brane models (or summation of world-sheet instantons in intersecting brane models).…”

“…We will focus on the contribution from a single torus and neglect contributions from the other tori, assuming that other moduli become heavy owing to flux compactification. One may consider T 4 /Z2 × T 2 , in which Wilson line moduli could be required to explain the smallness of the observable Higgs mass, although the moduli are not necessary to explain Yukawa textures [53]. On the other hand, ϑ3 is often used for realizing a large (top) Yukawa coupling because it contains unity and ϑ2 is used for a smaller top Yukawas; see eq.…”

Zero-modes on orbifolds: Magnetized orbifold models by modular transformation

“…In this appendix, we show computations on normalization N of wave functions and the relations (20) and (21). The computation on normalization is useful for computation of the relations (20) and (21). Now, we compute Z …”

“…(22) and (23). Then, we obtain phenomenological interesting results e.g., the realization of quark and lepton mass hierarchies and their mixing angles [20][21][22][23].…”

“…Indeed, Z 2 orbifold models have been studied on several aspects, e.g. model building [15][16][17][18][19], realization of quark and lepton masses and their mixing angles and CP phase [20][21][22][23]. In addition, it is possible to introduce some degree of freedom on orbifold fixed points, e.g.…”