Chiral Yukawa models in the planar limit

TL;DR

This paper analyzes a generalized chiral Yukawa model in the large N limit, providing insights into the triviality bounds of the top quark mass and the model's behavior with multiple fermion families.

Contribution

It introduces a large N limit for a general chiral Yukawa model with multiple families, extending previous models and estimating the triviality bound on the top quark mass.

Findings

The model describes heavy top quark effects with massless other fermions.

Estimated triviality bound on the top quark mass is approximately 1 TeV.

The large N limit simplifies the analysis of Yukawa coupling behavior.

Abstract

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 $m_t \le 1~TeV$.