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, which can explain 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. This experimental feature cannot be explained in terms of the $O(2)$ model... We also find that the scalar susceptibility is the same as the longitudinal susceptibility, in contrast with the previous result based on the $O(2)$ model. (read more)