Higgs Mass Bounds from Renormalization Flow for a Higgs-top-bottom model

We study a chiral Yukawa model mimicking the Higgs-top-bottom sector of the standard model. We re-analyze the conventional arguments that relate a lower bound for the Higgs mass with vacuum stability in the light of exact results for the regularized fermion determinant as well as in the framework of the functional renormalization group. In both cases, we find no indication for vacuum instability nor meta-stability induced by top-fluctuations if the cutoff is kept finite but arbitrary. A lower bound for the Higgs mass arises for the class of standard bare potentials of \phi^4 type from the requirement of a well-defined functional integral (i.e., stability of the bare potential). This consistency bound can however be relaxed considerably by more general forms of the bare potential without necessarily introducing new meta-stable minima.