Isospin multiplet structure in ultraheavy fermion bound states.

Abstract

The coupled Bethe-Salpeter bound state equations for a $Q\overline{Q}$ system, where $Q=(U,D)$ is a degenerate, fourth generation, superheavy quark doublet, are solved in several ladder approximation models. The exchanges of gluon, Higgs, and Goldstone modes in the standard model are calculated in the ultraheavy quark limit where weak $\ensuremath{\gamma}$, ${W}^{\ifmmode\pm\else\textpm\fi{}}$, and ${Z}^{0}$ contributions are negligible. A natural $I=0$ and $I=1$ multiplet pattern is found, with large splittings occurring between the different weak isospin states when ${M}_{Q}$, the quark masses, are larger than values in the range $0.4 \mathrm{TeV}<{M}_{Q}<0.8 \mathrm{TeV}$, depending on which model is used. Consideration of ultraheavy quark lifetime constraints and $U\ensuremath{-}D$ mass splitting constraints are reviewed to establish the plausibility of lifetime and mass degeneracy requirements assumed for this paper.