Condensation effects beyond one loop in the top-mode standard model without gauge bosons.

We study dynamical symmetry breaking in the standard model including the next-to-leading order terms. We introduce at a high, but finite, energy scale {Lambda} a top quark condensate {ital H}={l_angle}{bar {ital t}}{ital t}{r_angle} and derive, using path integral methods, the effective potential including quadratic fluctuations in the scalar field {ital H}. We neglect the contributions of all components of the massive electroweak gauge bosons. The existence of a nontrivial minimum in the effective potential leads to the condition that the cutoff {Lambda} is limited from above, {Lambda}{approx_lt}{Lambda}{sub crit}{approx_equal}4.7{ital m}{sub {ital t}}{sup phys} (for {ital N}{sub {ital c}}=3), and to a new lower bound for the four-fermion coupling {ital a}=({ital GN}{sub {ital c}}{Lambda}{sup 2})/(8{pi}{sup 2}){approx_gt}1.60. Similar results are obtained if we demand, instead, that the next-to-leading order contributions do not shift the location {ital z}=({ital m}{sub {ital t}}{sup bare}/{Lambda}){sup 2} of the minimum drastically, e.g., by not more than a factor of 2. The results are reproduced diagrammatically, where the leading plus all the next-to-leading order diagrams in the 1/{ital N}{sub c} expansion are included. Dominant QCD effects are also included, but their impact on the numerical results is shown to be small. {copyright} {ital 1996 The American Physical Society.}