Geometric hierarchy

We present one approach for solving the gauge hierarchy problem in a grand unified supersymmetric theory. Supersymmetry is broken at a scale of order 10¹² GeV. Both the grand scale (～10¹⁹ GeV) and the weak scale are generated via radiative corrections. The main phenomenological features of the model are: (i) the proton decays into $\text{K}{}^0\text{μ}{}^{\mathrm{+}}\text{and}\text{K}{}^{\mathrm{+}}\text{ν}{}_{\mathrm{\mu }}$ and the neutron decays into $\text{K}{}^0\text{ν}{}_{\mathrm{\mu }}$; (ii) the strong GP problem is solved with an invisible axion; (iii) the superpartners of quarks, leptons, gauge and Higgs bosons have masses ～ 50–100 GeV; and (iv) the lightest superpartner is stable.