Monte Carlo Simulations of Higgs-Fermion Systems

Abstract

To gain understanding of the Higgs-fermion sector of the standard model, we study the one-component $Z_2$ symmetric and the four-component O(4) symmetric scalar models coupled to staggered fermions using the hybrid Monte Carlo algorithm. We map out the phase diagrams, and show that the $Z_2$ model has a tree level perturbative behaviour at all points in the broken phase. The O(4) model on the other hand is shown to have two characteristically different behaviours; one for large Yukawa couplings where the fermions get infinitely heavy and decouple in the continuum limit, and one for small Yukawa couplings where the fermions remain light. For very small Yukawa couplings the fermions show the expected tree level perturbative behaviour and for larger values the influence of the fermions becomes substantial. After estimating the finite size effects at small Yukawa couplings we make relatively accurate measurements of the scalar mass and wave function renormalization constants at the point $κ=0.0$ and $y=0.85-0.95$. Even though this is not the largest value possible for the Yukawa coupling we are able to show that the bound of the Higgs mass will move up significantly, from around $600 GeV$ to around $900 GeV$, by including fermions in the model. Likewise we show that a bound can be put on the fermion mass, around $200 GeV$. The largest value of the bare Yukawa coupling is obtained at rather large negative $κ$. Due to bad convergence rates in the inversion of the fermion matrix, which is needed in the updating procedure, this region has not been possible to investigate.