Upper and lower Higgs boson mass bounds from a chirally invariant lattice Higgs-Yukawa model

Motivated by the advent of the Large Hadron Collider (LHC) the aim of the present work is the non-perturbative determination of the cutoff-dependent upper and lower mass bounds of the Standard Model Higgs boson based on first principle calculations, in particular not relying on additional information such as the triviality property of the Higgs- Yukawa sector or indirect arguments like vacuum stability considerations. For that purpose the lattice approach is employed to allow for a non-perturbative investigation of a chirally invariant lattice Higgs-Yukawa model, serving here as a reasonable simplification of the full Standard Model, containing only those fields and interactions which are most essential for the intended Higgs boson mass determination. These are the complex Higgs doublet as well as the top and bottom quark fields and their mutual interactions. To maintain the chiral character of the Standard Model Higgs-fermion coupling also on the lattice, the latter model is constructed on the basis of the Neuberger overlap operator, obeying then an exact global lattice chiral symmetry. Respecting the fermionic degrees of freedom in a fully dynamical manner by virtue of a PHMC algorithm appropriately adapted to the here intended lattice calculations, such mass bounds can indeed be established with the aforementioned approach. Supported by analytical calculations performed in the framework of the constraint effective potential, the lower bound is found to be approximately mlowH(Λ)=80 GeV at a cutoff of Λ=1000 GeV. The emergence of a lower Higgs boson mass bound is thus a manifest property of the pure Higgs-Yukawa sector that evolves directly from the Higgs-fermion interaction for a given set of Yukawa coupling constants. Its quantitative size, however, turns out to be non-universal in the sense, that it depends on the specific form, for instance, of the Higgs boson self-interaction. The upper Higgs boson mass bound is then established in the strong coupling regime of the considered Higgs-Yukawa model. After the infinite volume extrapolation it is found to be approximately mupH (Λ)=630 GeV at a cutoff of Λ=1500 GeV. The cutoff-dependence of this upper bound can also be resolved and it is found to be in agreement with the expected logarithmic decline with increasing cutoff Λ according to the triviality picture of the Higgs-Yukawa sector. Moreover, a direct comparison of the latter cutoff-dependent mass bound with corresponding results obtained in the pure Φ4-theory, neglecting all fermion contributions, is considered with the intention to identify the fermion contribution to the upper mass bound. However, higher statistics is required to draw a clear conclusion in this matter. Finally, a first account on the applicability of Luescher's method for the determination of the Higgs boson decay width in the framework of the here considered Higgs-Yukawa model is presented. At small renormalized quartic coupling constant λr the obtained decay width ΓH is in good agreement with corresponding perturbative results, the validity of which is trustworthy according to λr being small. The good agreement thus encourages to further pursue this approach in some follow-up investigations to eventually establish an upper bound also for the decay width of the Standard Model Higgs boson. (orig.)