Supersymmetric grand unified theories: Two loop evolution of gauge and Yukawa couplings

Sep, 1992
57 pages
Published in:
  • Phys.Rev.D 47 (1993) 1093-1113
e-Print:
Report number:
  • MAD-PH-711

Citations per year

199320012009201720240204060
Abstract:
We make a numerical study of gauge and Yukawa unification in supersymmetric grand unified models and examine the quantitative implications of fermion mass ans\"{a}tze at the grand unified scale. Integrating the renormalization group equations with α1(MZ)\alpha _1(M_Z) and α2(MZ)\alpha _2(M_Z) as inputs, we find α3(MZ)0.111(0.122)\alpha _3(M_Z)\simeq 0.111 (0.122) for MSUSY =mtM_{SUSY}~{}=m_t and α3(MZ)0.106(0.116)\alpha _3(M_Z)\simeq 0.106 (0.116) for MSUSY =1M_{SUSY}~{}=1 TeV at one-loop (two-loop) order. Including bb and τ\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 β\beta, one with tanβ>mt/mb\tan \beta > m_t/m_b, and one with sinβ0.78(mt/150  GeV)\sin \beta \simeq 0.78(m_t/150\;{\rm 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 α3(MZ)=0.11(0.12)\alpha _3(M_Z)=0.11 (0.12) and an upper limit on the supersymmetry parameter \tan \beta \ltap 50 if α3(MZ)=0.11\alpha _3(M_Z)=0.11. The evolution of the quark mixing matrix elements is also evaluated.
  • supersymmetry
  • grand unified theory
  • fermion: mass
  • mass: fermion
  • coupling: Yukawa
  • Yukawa: coupling
  • renormalization group
  • CKM matrix matrix
  • numerical calculations: interpretation of experiments