Unitarity constraints on grand unified models

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Abstract

We present a simplified method for the calculation of low-energy unitarity constraints on grand unified broken-supersymmetric models based on the Goldstone-boson equivalence theorem for high-energy scattering in gauge theories, the fermion-boson equivalence theorem for supersymmetric theories, and the evolution of couplings under the renormalization group. We apply the method to the "flipped" SU(5)\ifmmode\times\else\texttimes\fi{}U(1) superstring model, obtain high-energy unitarity constraints at the grand unified scale ${M}_{G}=4\ifmmode\times\else\texttimes\fi{}{10}^{16}$ GeV, and then use the renormalization-group equations to evolve the constraints to the low-energy mass scale ${M}_{W}$. We investigate the peculiarities of the renormalization-group flow and the existence of critical surfaces at which the scalar superpotential couplings diverge at ${M}_{G}$. We find upper bounds on the superpotential couplings at low energies and use these to establish absolute upper bounds on the top-quark mass, ${m}_{t}\ensuremath{\lesssim}200$ GeV, and on the lightest neutral-Higgs-boson mass, ${M}_{{H}_{1}^{0}}\ensuremath{\lesssim}155$ GeV in the SU(5)\ifmmode\times\else\texttimes\fi{}U(1) model. We also obtain an upper bound on ${M}_{{H}_{1}^{0}}$ as a function of ${m}_{t}$ which shows that ${M}_{{H}_{1}^{0}}\ensuremath{\lesssim}125$ GeV for favored values of the ratios of Higgs vacuum expectation values.

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