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

We classify the combinations of parameters which lead three generations of quarks and leptons in the framework of magnetized twisted orbifolds on $T^2/Z_2$, $T^2/Z_3$, $T^2/Z_4$ and $T^2/Z_6$ with allowing nonzero discretized Wilson line phases and Scherk-Schwarz phases. We also analyze two actual examples with nonzero phases leading to one-pair Higgs and five-pair Higgses and discuss the difference from the results without nonzero phases studied previously.Comment: 28 pages (main body and references) + 65 pages (full list of classification), 22 tables (v1); typos corrected, problem in sentence fixed (v2

We study the CP-violating phase of the quark sector on T-2/Z(N) (N = 2, 3, 4, 6) with non-vanishing magnetic fluxes, where properties of possible origins of the CP violation are investigated minutely. In this system, a non-vanishing value is mandatory in the real part of the complex modulus parameter tau of the two-dimensional torus in order to explain the CP violation in the quark sector. On T-2 without orbifolding, underlying discrete flavor symmetries severely restrict the form of Yukawa couplings and it is very difficult to reproduce the observed pattern in the quark sector including the CP-violating phase delta(CP). When multiple Higgs doublets emerge on T-2/Z(2), the mass matrices of the zero -mode fermions can be written in the Gaussian textures by choosing appropriate configurations of vacuum expectation values of the Higgs fields. When such Gaussian textures of mass matrices are realized, we show that all of the quark profiles, which are mass hierarchies among the quarks, quark mixing angles, and delta(CP) can be simultaneously realized

Abstract:We study the flavor landscape of the visible sector of particle physics models based on a ten-dimensional super Yang-Mills theory compactified on magnetized tori preserving four-dimensional N = 1 supersymmetry. Recently, we constructed a semirealistic model which contains the minimal supersymmetric standard model (MSSM) using an ansatz of magnetic fluxes and orbifolding projections. However, we can consider more various configurations of magnetic fluxes and orbifolding projections preserving fourdimensional N = 1 supersymmetry. We research systematically such possibilities for leading to MSSM-like models and study their phenomenological aspects.

We thoroughly analyze the number of independent zero modes and their zero points on the toroidal orbifold T 2 =Z N ðN ¼ 2; 3; 4; 6Þ with magnetic flux background, inspired by the Atiyah-Singer index theorem. We first show a complete list for the number n η of orbifold zero modes belonging to Z N eigenvalue η. Since it turns out that n η quite complicatedly depends on the flux quanta M, the Scherk-Schwarz twist phase ðα 1 ; α 2 Þ, and the Z N eigenvalue η, it seems hard that n η can be universally explained in a simple formula. We, however, succeed in finding a single zero-mode counting formula n η ¼ ðM − V η Þ=N þ 1, where V η denotes the sum of winding numbers at the fixed points on the orbifold T 2 =Z N. The formula is shown to hold for any pattern.