  We calculate the spectrum of the amplitude mode, the analog of the Higgs mode
in high energy physics, for the $d$-density wave (DDW) state proposed to
describe the pseudogap phase of the high $T_c$ cuprates. Even though the state
breaks translational symmetry by a lattice spacing and is described by a
particle-hole singlet order parameter at the wave vector $q=Q=(\pi,\pi)$,
remarkably, we find that the amplitude mode spectrum can have peaks at both
$q=(0,0)$ and $q=Q=(\pi,\pi)$; we shall lattice spacing to unity. In general,
the spectrum is non-universal, and, depending on the microscopic parameters,
can have one or two peaks in the Brillouin zone, signifying existence of two
kinds of magnetic excitations. Our theory sheds important light on how multiple
inelastic neutron peaks at different wave vectors can, in principle, arise even
with an order parameter that condenses at $Q=(\pi,\pi)$.
