  The dynamic spin structure factor $\mathcal{S}(k,\omega)$ of a system of
spin-1/2 bosons is investigated at arbitrary strength of interparticle
repulsion. As a function of $\omega$ it is shown to exhibit a power-law
singularity at the threshold frequency defined by the energy of a magnon at
given $k.$ The power-law exponent is found exactly using a combination of the
Bethe Ansatz solution and an effective field theory approach.
