Nonperturbative Higgs propagator: NLO correction in the1/Nexpansion

We derive a nonperturbative result for the Higgs propagator by calculating the NLO correction in the $1/N$ expansion of $O\left(N\right)\mathrm{}$ sigma models. For dealing with the $1/N$ expansion beyond leading order, we develop techniques to calculate certain infinite sets of multiloop Feynman diagrams. We then calculate the Higgs line shape in fermion scattering, as seen, for instance, at a muon collider. We compare with the existing two-loop perturbative results. There is a considerable discrepancy between perturbation theory and the $1/N$ expansion in LO. By including the NLO correction, this discrepancy is reduced dramatically. The results are in very good agreement with the two-loop result even for masses as high as 850 GeV. A maximum of the mass is reached at 930 GeV. For phenomenological purposes, we give a simple approximate relation between the Higgs boson mass and width.