On the infrared behaviour of the (singlet) Higgs propagator

Abstract

We present a simple semi-perturbative argument in favour of a peculiar infrared behaviour of the (singlet) Higgs propagator. On the basis of `triviality' one expects a continuum limit with a two-point function ${\Gamma }_2(q)\to (q^2+M_h^2)$. However, this is not valid in the limit $q\to 0$ where one actually finds a singular behaviour. This is in agreement with both non-perturbative analyses of the effective potential and with lattice computations of the propagator and of the zero-momentum susceptibility in the broken phase. The singular behaviour persists in an O(N) continuous-symmetry theory, the case first pointed out by Symanzik, and supports the existence of an extremely weak $1/r$ potential that does not disappear when coupling the scalar fields to gauge bosons.

Comments: 10 pages, LaTeX