  We investigate the spectral function of the Higgs mode in a two dimensional
Bose gas, by using the effective field theory in the zero temperature limit.
Our approach explains the experimental feature that the peak of the spectral
function is a soft continuum rather than a sharp peak, broadened and vanishing
in the superfluid phase, which cannot be explained in terms of the $O(2)$
model. We also find that the scalar susceptibility is the same as the
longitudinal susceptibility.
