Excitations of the Higgs boson

Abstract

In a simplified version of the standard model with a single quark doublet, I derive a transcendental equation for the complex Higgs boson mass. The equation involves a divergent integral which is regularized and renormalized conventionally. Setting the Higgs mass to its observed value, the decay width is narrow and within experimental limits. The mass equation has additional roots on other sheets in the complex energy plane. The first two are at 186 and 219 GeV. The lightest excitations are well defined though wider than the 125 GeV Higgs because decays to $W^{+}W^{-}$ and $ZZ$ are allowed.