Structure of split supersymmetry and simple models

We derive in detail a condition on the Higgs mass parameters that is necessary for the recently proposed ``split supersymmetry'' (split SUSY) scenario to provide a realistic magnitude of $\tan \beta$. The nature of this condition can be understood by showing how the Higgs sector of the minimal supersymmetric Standard Model reduces to that of the Standard Model in the heavy limit of the soft supersymmetry breaking Higgs mass parameters. Based on this condition, we present some simple supersymmetry breaking models that each provides a realistic split-SUSY mass spectrum, in accordance with the scale of the gravitino mass ($m_{3/2}$) in relation to those of the soft scalar mass ($\tilde{m}$) and the gaugino mass ($M_{1/2}$) employed in each, namely $m_{3/2} \geq \tilde{m}$, $\tilde{m} \geq m_{3/2} \geq M_{1/2}$ and $M_{1/2} \geq m_{3/2}$, respectively, with the relation $\tilde{m} \gg M_{1/2}$ of the split-SUSY mass spectrum.Comment: 11 page