Abstract
We consider the most general renormalizable chiral Yukawa model with SU(3) color replaced by SU( N c ), SU(2) L replaced by SU( N w ) and U(1) Y replaced by U (1) N w −1 in the limit N c → ∞, N w → ∞ with the ratio ρ= N w N c ≠ 0 , ∞ held fixed. Since for N w ⩾ 3 only one renormalizable Yukawa coupling per family exists and there is no mixing between families the limit is appropriate for the description of the effects of a heavy top quark when all the other fermions are taken to be massless. The large N= N cN w expansion is expected to be no worse quantitatively in this model that in the purely scalar case and the N = ∞ limit is soluble even when the model is regularized non-perturbatively. A rough estimate of the triviality bound on the Yukawa coupling is equivalent to m t ⩽ 1 itTeV.
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