Dynamics of excitations in a one-dimensional Bose liquid

The dynamical structure factor $S(q,\omega)$ of interacting 1D liquid is studied. This quantity has become experimentally accessible in the recent experiments on cold atoms and neutron scattering off spin chains. We find power law non-analyticities $S(q,\omega) \propto \left(\omega - \epsilon_{1,2}(q) \right)^{-\mu(q)}$ at the kinematical thresholds characterized by the momentum dependent exponents evauated in a broad range of parameters.