One-parameter modular models predict exact high-scale mass relations m_s^5 = 2√2 m_d^3 m_b^2, m_μ^3 = √2 m_e m_τ^2 and m_s^2 m_τ = √2 m_e m_b^2 that become compatible with observed fermion masses after RG evolution and SUSY thresholds.
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In heterotic Z3 x Z3 orbifolds, the tree-level Yukawa amplitude has an exact column texture Y_lead(i,j) = c ε^{q_R[j]} with universal O(1) coefficient c across generations.
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Fermion mass relations in one-parameter modular models
One-parameter modular models predict exact high-scale mass relations m_s^5 = 2√2 m_d^3 m_b^2, m_μ^3 = √2 m_e m_τ^2 and m_s^2 m_τ = √2 m_e m_b^2 that become compatible with observed fermion masses after RG evolution and SUSY thresholds.
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The exact column texture: tree-level Yukawa universality in heterotic $Z_3 \times Z_3$ orbifolds
In heterotic Z3 x Z3 orbifolds, the tree-level Yukawa amplitude has an exact column texture Y_lead(i,j) = c ε^{q_R[j]} with universal O(1) coefficient c across generations.