  We present experimental and theoretical evidence that an interesting quantum
many-body effect -- quasi-particle breakdown -- occurs in the
quasi-one-dimensional spin-1/2 Ising-like ferromagnet CoNb$_2$O$_6$ in its
paramagnetic phase at high transverse field as a result of explicit breaking of
spin inversion symmetry. We propose a quantum spin Hamiltonian capturing the
essential one-dimensional physics of CoNb$_2$O$_6$ and determine the exchange
parameters of this model by fitting the calculated single particle dispersion
to the one observed experimentally in applied transverse magnetic fields. We
present high-resolution inelastic neutron scattering measurements of the single
particle dispersion which observe "anomalous broadening" effects over a narrow
energy range at intermediate energies. We propose that this effect originates
from the decay of the one particle mode into two-particle states. This decay
arises from (i) a finite overlap between the one-particle dispersion and the
two-particle continuum in a narrow energy-momentum range and (ii) a small
misalignment of the applied field away from the direction perpendicular to the
Ising axis in the experiments, which allows for non-zero matrix elements for
decay by breaking the $\mathbb{Z}_2$ spin inversion symmetry of the
Hamiltonian.
