  We study low-energy excitations of one-dimensional Galilean-invariant models
integrable by Bethe ansatz and characterized by nonsingular two-particle
scattering phase shifts. We prove that the curvature of the excitation spectra
is described by the recently proposed phenomenological expression for the
effective mass. Our results apply to such models as the repulsive Lieb-Liniger
model and the hyperbolic Calogero-Sutherland model.
