NLO correction to Higgs boson parameters in the 1/N expansion

We present the result of a calculation of the next-to-leading correction to the Higgs propagator in the 1/N expansion, where the Higgs sector is treated as an O(N) symmetric σ-model. The results are compared with two-loop perturbation theory. The existing discrepancy between the lowest order of the 1/N expansion and perturbation theory is dramatically reduced by including the NLO in 1/N. We find a maximum effective Higgs mass of 930-980 GeV. We give an approximate relation between Higgs width and mass, which can be used for phenomenological purposes. With the discovery of the vector bosons behind us, the next major question in the phenomenology of the weak interactions is the search for the Higgs boson. Within the standard model the properties of the Higgs boson are determined when its mass is fixed, as the tree level selfcouplings are proportional to m2H . As long as the Higgs particle is light there are therefore no fundamental problems in determining its properties from perturbation theory. This perturbation theory has recently even been extended to the two-loop level [1-3]. However, when the Higgs particle becomes heavy (O(TeV)) the selfcoupling becomes large and perturbation theory becomes unreliable. Therefore one would like to find an approximation to Higgs physics which is applicable beyond perturbation theory. When one realizes that the Higgs sector of the standard model is nothing but an O(4) linear sigma-model, the expansion in 1/N of the O(N)-symmetric sigma model suggests itself. The 1/N expansion has a long history [4-13] and has also been applied to the Higgs boson of the standard model [14,15]. The results in lowest order are interesting and indicate an upper mass to the Higgs boson, with a non-perturbative width. However the situation is not satisfactory as the lowest order is very far from perturbation theory for small Higgs mass. This discrepancy has led to Address after November 1, 1997: Laboratoire de Physique Theorique ENSLAPP, LAPP, B.P. 110, F–74941 Annecy–le–Vieux, France Address after October 1, 1997: Randall Laboratory of Physics, University of Michigan, Ann Arbor, Michigan 48109–1120, USA