Strong-coupling expansions for chiral models of electroweak symmetry breaking

We consider chiral U(N) × U(N) models with fermions in the limit of infinitely large local bare Yukawa coupling. When the scalar field is subject to non-linear constraint, phase transitions in these models are seen to be identical to those in the corresponding purely bosonic ones. Relaxing the non-linear constraint, we compute the seventh-order strong-coupling series for the susceptibility in these models and analyze them numerically for the U(2) × U(2) case. We find that in four dimensions the approach to the phase transition follows to a good accuracy the mean-field critical behavior, indicating the absence of non-trivial fixed points at strong coupling and being consistent with the first-order nature of the transition. In three dimensions, the strongly-coupled bosonic U(2) × U(2) model (without gauge fields) has a first-order transition strong enough to accommodate electroweak baryogenesis only for a narrow region of the bare parameter space.