$\mathrm{U(1)_L \otimes U(1)_R}$ symmetric Yukawa model in the phase with spontaneously broken symmetry

The lattice regularized U(1)L ⊗ U(1)R symmetric scalar-fermion model with a mirror pair of fermion fields is investigated in the phase with spontaneously broken symmetry. The reflection positivity condition, ensuring unitarity in Minkowski space, is proven in this lattice formulation in a wide range of bare parameters. Numerical Monte Carlo calculations with dynamical fermions are performed on 43 × 8, 43 × 16 and 63 × 16 lattices at moderately strong bare Yukawa couplings and at very small and infinite bare quartic scalar coupling. It is shown that not only the lattice fermion doublers but also the mirror fermion can be made heavy, and therefore the light fermion spectrum is “chiral” as in the standard model. The “vacuum stability” bound on the Higgs-boson mass is discussed in lattice perturbation theory and non-perturbatively. It implies that for heavy mirror fermions the Higgs-boson mass has to be close to the non-perturbative upper limit