Non-perturbative numerical lattice studies of the Higgs-Yukawa sector of the standard model with exact chiral symmetry are reviewed. In particular, we discuss bounds on the Higgs boson mass at the standard model top quark mass, and in the presence of heavy fermions. We present a comprehensive study of the phase structure of the theory at weak and very strong values of the Yukawa coupling as well as at non-zero temperature.

Abstract:We study the effect of a potential fourth quark generation on the upper and lower Higgs boson mass bounds. This investigation is based on the numerical evaluation of a chirally invariant lattice Higgs-Yukawa model emulating the same Higgs-fermion coupling structure as in the Higgs sector of the electroweak Standard Model. In particular, the considered model obeys a Ginsparg-Wilson version of the underlying SU(2) L × U(1) Y symmetry, being a global symmetry here due to the neglection of gauge fields in this model. We present our results on the modification of the upper and lower Higgs boson mass bounds induced by the presence of a hypothetical very heavy fourth quark doublet. Finally, we compare these findings to the standard scenario of three fermion generations.

The Higgs boson is a central part of the electroweak theory and is crucial to generate masses for quarks, leptons and the weak gauge bosons. We use a 4-dimensional Euclidean lattice formulation of the Higgs-Yukawa sector of the electroweak model to compute physical quantities in the path integral approach which is evaluated by means of Monte Carlo simulations thus allowing for fully non perturbative calculations. The chiral symmetry of the model is incorporated by using the Neuberger overlap Dirac operator. The here considered Higgs-Yukawa model does not involve the weak gauge bosons and furthermore, only a degenerate doublet of top-and bottom quarks are incorporated. The goal of this work is to study the resonance properties of the Higgs boson and its sensitivity to the strength of the quartic self coupling.