Quadratic Yukawa coupling and matrix Yukawa coupling in the large N expansion

In this article, we study three types of new Yukawa couplings (the boson field is coupled to the fermion field). Two of them are quadratic Yukawa couplings (the boson field is in the form of a vector), and the other one is the matrix Yukawa coupling (the boson field is in the form of a matrix). Based on the above three couplings, we introduce the Higgs mechanism, and find out the properties of the generated mass for the fermions with multiple flavors. For the matrix boson, we introduce its coupling with non-Abelian gauge field. It turns out that the generated mass of the gauge field through the Higgs mechanism is unique. In the large N limit, using the method of auxiliary field, we study the dynamical behaviors of the quadratic Yukawa couplings, including the poles of some dressed propagators.