Supersymmetric Grand Unified Theories: Two Loop Evolution of Gauge and Yukawa Couplings

Abstract

We make a numerical study of gauge and Yukawa unification in supersymmetric grand unified models and examine the quantitative implications of fermion mass ansätze at the grand unified scale. Integrating the renormalization group equations with ${\alpha }_1(M_Z)$ and ${\alpha }_2(M_Z)$ as inputs, we find ${\alpha }_3(M_Z)\simeq 0.111(0.122)$ for $M_{SUSY}^{}=m_t$ and ${\alpha }_3(M_Z)\simeq 0.106(0.116)$ for $M_{SUSY}^{}=1$ TeV at one-loop (two-loop) order. Including $b$ and $\tau$ Yukawa couplings in the evolution, we find an upper limit $m_t\ltap 200$ GeV from Yukawa unification. For given $m_t\ltap 175$ GeV, there are two solutions for $\beta$, one with $\tan \beta >m_t/m_b$, and one with $\sin \beta \simeq 0.78(m_t/150\mathrm{GeV})$. Taking a popular ansatz for the mass matrices at the unified scale, we obtain a lower limit on the top quark mass of $m_t\gtap 150 (115)$ GeV for ${\alpha }_3(M_Z)=0.11(0.12)$ and an upper limit on the supersymmetry parameter $\tan β\ltap 50$ if ${\alpha }_3(M_Z)=0.11$. The evolution of the quark mixing matrix elements is also evaluated.

46 pages + 11 figures not included (available on request), MAD/PH/711

References in corpus (8)

• Testing the Higgs Sector of the Minimal Supersymmetric Standard Model at Large Hadron Colliders
• Mass and mixing angle patterns in the Standard Model and its Minimal Supersymmetric Extension
• A new ansatz for quark and lepton mass matrices
• Test of the Dimopouos-Hall-Raby Ansatz for Fermion Mass Matrices
• Constraints From Gauge Coupling Unification On The Scale Of Supersymmetry Breaking
• Collider discovery limits for supersymmetric Higgs bosons
• Model of the Quark Mixing Matrix
• Predictions for neutral K and B meson physics

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