Minimal four-family supergravity model

In this work, we investigate the phenomenology of minimal four-family MSSM supergravity theories containing an additional general (t′,b′,τ′,ν′) of heavy fermions along with their superpartners. We constrain the models by demanding gauge coupling constant unification at high energy scales, perturbative values for all Yukawa couplings for energy scales up to the grand-unification scale, radiative electroweak (EW) symmetry breaking via renormalization group evolution down from the grand-unification scale, a neutral LSP, and consistency with constraints from direct searches for new particles and precision electroweak data. The perturbative constraints imply a rather light fourth-family quark and lepton spectrum, and tan β≲3. The lightest CP-even Higgs boson mass receives fourth-family loop corrections that can result in as much as a 30% increase over the corresponding three-family mass value. Significant fourth-family Yukawa coupling contributions to the evolution of scalar masses lead to unexpected mass hierarchies among the sparticles. For example, the τ̃ ${}_1{}^{\prime }{}_{}{}^{}$ is generally the lightest slepton and the lightest squark is the b̃ ${}_1{}^{\prime }{}_{}{}^{}$. A significant lower bound is placed on the gluino mass by the simple requirement that the τ̃ ${}_1{}^{\prime }{}_{}{}^{}$ not be the LSP. Sleptons of the first two families are much more massive compared to the LSP and other neutralinos and charginos than in the three-family models; in particular, all sleptons belonging to the first three families could easily lie beyond the reach of a √s =500 GeV ${\mathit{e}}^{+}$ ${\mathit{e}}^{\mathrm{-}}$ collider.