The chiral transition in an SU(2) gauge-Higgs-fermion theory with Yukawa couplings

We study the (zero-temperature) chiral transition in an SU(2) lattice gauge theory with I = 1 2 Higgs fields, and fermion fields with I = 1 2 and I = 0, including Yukawa couplings. Using analytic methods in the strong gauge coupling limit, we demonstrate that (i) if at least one of the Yukawa couplings is sufficiently weak, this theory undergoes a spontaneous chiral symmetry breaking phase transition; (ii) this transition is removed when the Yukawa couplings are sufficiently strong. The transition is determined to be of second order, and approximate critical point calculations are given. Some implications for the continuum limit of the SU(2) model, and for electroweak interactions, are discussed.