Studies of a U(1) × U(1) Yukawa model with staggered fermions

Abstract

A U(1)×U(1) Yukawa model with staggered fermions is investigated in the broken phase. Spontaneous symmetry breaking on finite lattices is studied in two ways. In the first approach, which is similar to what is done in lattice QCD studies, we work with nonzero bare-fermion masses and try to extrapolate to the massless limit. In the second method, which to date has been the more common approach in Higgs-Yukawa models, we simulate directly the zero-bare-fermion-mass theory and carry out a global rotation on the fields before taking measurements. In the m f≠0 calculations Ward identities are monitored to asses the quality of the simulations and both fermion-antifermion and purely bosonic operators are used in Goldstone boson correlation-functions. We point out differences between the fermion-antifermion channel in the current model and analogous calculations of the pion correlation-function in lattice QCD. We show that noisy estimates of the fundamental fermion propagator can also be used very effectively for meson correlations, where the fermion and antifermion annihilate into pure bosonic matter (the so called annihilation channel). Estimates for renormalized Yukawa and λφ 4 couplings obtained via the two methods, m f = 0 and m f ≠ 0, are also presented. Renormalized Yukawa-couplings are never much larger than the value obtained from the tree-level j = 0 partial wave unitarity bound for fermion-antifermion elastic scattering in a continuum theory with the appropriate number of flavors.