  We study the Higgs excitation in the Goldstone phase of the relativistic O(N)
model in two spatial dimensions at zero temperature. The response functions of
the order parameter, and its magnitude-squared, become universal functions of
frequency in the vicinity of the quantum critical point described by the
Wilson-Fisher fixed point, and we compute them to next-to-leading order in 1/N.
The Higgs particle has an infrared singular decay to gapless Goldstone
excitations, and its response functions are characterized by a pole in the
lower-half of the complex frequency plane. The pole acquires a non-zero real
part only at next-to-leading order in 1/N, demonstrating that the Higgs
excitation has an oscillatory component even in the scaling limit. Both the
real and imaginary parts of the pole position vanish with the correlation
length exponent \nu upon approaching the critical point. We present evidence
that the spectral density of the O(N)-invariant amplitude-squared of the order
parameter has a peak at a non-zero frequency in the scaling limit. We connect
our results to recent experimental studies of the superfluid-insulator quantum
phase transition of ultracold bosonic atoms in optical lattices.
