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Yukawa Textures with Enhanced Symmetries in Heterotic Calabi-Yau Compactifications

Jun Dong, Tatsuo Kobayashi, Shuhei Miyamoto, Hajime Otsuka

Abstract

We clarify the structure of Yukawa couplings and mass matrices for matter fields in heterotic string theory on smooth Calabi-Yau threefolds with standard embedding. The topological structure of Calabi-Yau threefolds leads to interesting Yukawa textures that cannot be derived from group-theoretical symmetries, e.g., the so-called Weinberg texture in the case of two generations of matter fields. Furthermore, we find that a $U(2)$ flavor symmetry, which plays an important role in controlling higher-dimensional operators in the Standard Model effective field theory, emerges at specific loci in the moduli space of multi-Higgs fields. Small perturbations around these loci generate semi-realistic patterns of quark masses and mixings.

Yukawa Textures with Enhanced Symmetries in Heterotic Calabi-Yau Compactifications

Abstract

We clarify the structure of Yukawa couplings and mass matrices for matter fields in heterotic string theory on smooth Calabi-Yau threefolds with standard embedding. The topological structure of Calabi-Yau threefolds leads to interesting Yukawa textures that cannot be derived from group-theoretical symmetries, e.g., the so-called Weinberg texture in the case of two generations of matter fields. Furthermore, we find that a flavor symmetry, which plays an important role in controlling higher-dimensional operators in the Standard Model effective field theory, emerges at specific loci in the moduli space of multi-Higgs fields. Small perturbations around these loci generate semi-realistic patterns of quark masses and mixings.
Paper Structure (9 sections, 53 equations, 19 figures, 5 tables)

This paper contains 9 sections, 53 equations, 19 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Calabi-Yau compactifications and low energy effective field theory
  3. Yukawa textures and mass hierarchies
  4. Coupling selection rules and Yukawa textures
  5. CICYs with $h^{1,1}=2$
  6. CICYs with $h^{1,1}=3$
  7. Phenomenological implications
  8. Conclusions
  9. $h^{1,1}=3$

Figures (19)

  • Figure 1: Mass ratios for CICY 7644 as a function of the minimum volume ${\cal V}$ where all real parts of the moduli are greater than or equal to 1. The masses are ordered as $m_1 < m_2$. The left (right) panel shows the ratio $m_1/m_2$ for the first (second) Higgs. The lower curve in the left (right) panel corresponds to the region ${\rm Re}\,T^1 < {\rm Re}\,T^2$ (${\rm Re}\,T^1 >{\rm Re}\,T^2$).
  • Figure 2: Mass ratios for CICY 7643 as a function of the minimum volume ${\cal V}$ where all real parts of the moduli are greater than or equal to 1. The masses are ordered as $m_1 < m_2$. The left (right) panel shows the ratio $m_1/m_2$ for the first (second) Higgs. The lower curve in the left (right) panel corresponds to the region ${\rm Re}\,T^1 <{\rm Re}\,T^2$ (${\rm Re}\,T^1 > {\rm Re}\,T^2$).
  • Figure 3: Mass ratios for CICY 7806 as a function of the minimum volume ${\cal V}$ where all real parts of the moduli are greater than or equal to 1. The masses are ordered as $m_1 < m_2$. The left (right) panel shows the ratio $m_1/m_2$ for the first (second) Higgs. The lower curve in the right panel corresponds to the region ${\rm Re}\,T^1 <{\rm Re}\,T^2$.
  • Figure 4: Mass ratios for CICY 7884 as a function of the minimum volume ${\cal V}$ where all real parts of the moduli are greater than or equal to 1. The masses are ordered as $m_1 < m_2$. The left (right) panel shows the ratio $m_1/m_2$ for the first (second) Higgs. The lower curve in the left (right) panel corresponds to the region ${\rm Re}\,T^1 < {\rm Re}\,T^2$ (${\rm Re}\,T^1 > {\rm Re}\,T^2$).
  • Figure 5: Mass ratios for CICY 5299 as a function of the minimum volume ${\cal V}$ where all real parts of the moduli are greater than or equal to 1. The masses are ordered as $m_1 < m_2 < m_3$. The left (right) panel shows the scatter for $m_1/m_3$ ($m_2/m_3$).
  • ...and 14 more figures