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.
Quark and lepton masses at the GUT scale including SUSY threshold corrections
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abstract
We investigate the effect of supersymmetric (SUSY) threshold corrections on the values of the running quark and charged lepton masses at the GUT scale within the large $\tan\beta$ regime of the MSSM. In addition to the typically dominant SUSY QCD contributions for the quarks, we also include the electroweak contributions for quarks and leptons and show that they can have significant effects. We provide the GUT scale ranges of quark and charged lepton Yukawa couplings as well as of the ratios $m_\mu/m_s$, $m_e/m_d$, $y_\tau/y_b$ and $y_t/y_b$ for three example ranges of SUSY parameters. We discuss how the enlarged ranges due to threshold effects might open up new possibilities for constructing GUT models of fermion masses and mixings.
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2026 1verdicts
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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.