Nonpolynomial Higgs interactions and vacuum stability

The possible violation of the conventional lower Higgs mass stability bound by the discovered Higgs boson has far reaching consequences within particle physics and cosmology. We discuss the possibility that nonpolynomial bare interactions seeded at some high-momentum scale can considerably diminish the lower Higgs mass bound without introducing a metastability in the Higgs effective potential. For this, we classify various deformations of the usual quartic bare potential regarding their impact on stable IR physics. We perform the analysis in a large $N_{\mathrm{f}}$ expansion, addressing the convergence of the obtained results by taking $1/N_{\mathrm{f}}$ corrections into account as well. In addition, we investigate the renormalization group flow of the scalar potential on a nonperturbative level. Within these approximations, we are able to identify bare potentials that lead to Higgs masses below stability mass bounds obtained from finite-order polynomial bare interactions without introducing a metastability in the effective potential.