Chiral Yukawa models in the planar limit

Physics – High Energy Physics – High Energy Physics - Lattice

Scientific paper

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8p, one postscript figure appended, RU-92-20

Scientific paper

10.1016/0370-2693(92)90906-K

We consider the most general renormalizable chiral Yukawa model with $SU(3)_{\rm color}$ replaced by $SU(N_c)$, $SU(2)_{\rm L}$ replaced by $SU(N_w )$ and $U(1)_{Y}$ replaced by $U(1)^{N_w -1}$ in the limit $N_c \rightarrow\infty$, $N_w \rightarrow\infty$ with the ratio $\rho=\sqrt{{N_w}\over{N_c}} \ne 0,\infty$ held fixed. Since for $N_w \ge 3$ 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. A rough estimate of the triviality bound on the Yukawa coupling is equivalent to $m_t \le 1~TeV$.

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