Lower Higgs boson mass bounds from a chirally invariant lattice Higgs-Yukawa model with overlap fermions

We study the coupling parameter dependence of the Higgs boson mass in a chirally invariant lattice Higgs-Yukawa model emulating the same Yukawa coupling structure as in the Higgs-fermion sector of the Standard Model. Eventually, the aim is to establish non-perturbative upper and lower Higgs boson mass bounds derived from first principles, in particular not relying on vacuum stability considerations for the latter case. Here, we present our lattice results for the lower Higgs boson mass bound at several values of the cutoff Λ and compare them to corresponding analytical calculations based on the effective potential as obtained from lattice perturbation theory. Furthermore, we give a preliminary outlook towards the calculation of the upper Higgs boson mass bound.