  In this work, we study effects of magnon interactions in the excitation
spectrum of CoNb$_2$O$_6$ in the quantum paramagnetic phase in transverse
field, where the $1/S$ spin-wave theory exhibits unphysical divergences at the
critical field. We propose a self-consistent Hartree-Fock approach that
eliminates such unphysical singularities while preserving the integrity of the
singular threshold phenomena of magnon decay and spectrum renormalization that
are present in both theory and experiment. With the microscopic parameters
adopted from previous studies, this method yields a close quantitative
agreement with the available experimental data for CoNb$_2$O$_6$ in the
relevant regime. Insights into the general structure of the spin-anisotropic
model of CoNb$_2$O$_6$ and related zigzag chain materials are also provided and
a discussion of the effects of additional longitudinal field on the spectrum is
given.
