Large-N and Vacuum Alignment in Topcolor Models

Topcolor and topcolor-assisted technicolor provide examples of dynamical electroweak symmetry breaking which include top-condensation, thereby naturally incorporating a heavy top quark. In this note we discuss the roles of the Nambu-Jona-Lasinio (NJL) and large-N approximations often used in phenomenological analyses of these models. We show that, in order to provide for top-condensation but not bottom-condensation, the top-color coupling must be adjusted to equal the critical value for chiral symmetry breaking up to O(1/N) in any theory in which the isospin-violating tilting'' interaction is a U(1) gauge interaction. A consequence of these considerations is that the potentially dangerous bottom-pions’’ are naturally light. We also show that the contributions to rho-1 previously estimated are of leading-order in N, are not included in the usual NJL analysis, and are the result of ``vacuum-alignment’'.