Lower bound on the Higgs mass in the presence of a heavy top quark

Abstract

We demonstrate that for finite cut-off the Higgs-Yukawa model is only defined when the bare Higgs coupling λ 0 is positive. Next we argue that if we assume this theory to be trivial, the familiar fermion loop induced “vacuum instability” may not be realized. We give a scenario where there is no vacuum instability so that the lower bound on the Higgs mass can not be derived from the behavior of the effective potential. However, there still exists a lower bound on the Higgs mass for a given fermion mass due to the fact that λ 0 is positive. Finally, we discuss some important issues for establishing a physical lower bound on the Higgs mass.