  Motivated by spin-wave continuum (SWC) observed in recent neutron scattering
experiments in Herbertsmithite, we use Gutzwiller-projected wave functions to
study dynamic spin structure factor $S(\mathbf{q},\omega)$ of spin liquid
states on the kagome lattice. Spin-1 excited states in spin liquids are
represented by Gutzwiller-projected two-spinon excited wave functions. We
investigate three different spin liquid candidates, spinon Fermi-surface spin
liquid (FSL), Dirac spin liquid (DSL) and random-flux spin liquid (RSL). FSL
and RSL have low energy peaks in $S(\mathbf{q},\omega)$ at $K$ points in the
extended magnetic Brillouin zone, in contrast to experiments where low energy
peaks are found at $M$ points. There is no obviuos contradiction between DSL
and neutron scattering measurements. Besides a fractionalized spin (i.e.
spin-1/2), spinons in DSL carry a fractionalized crystal momentum which is
potentially detectable in SWC in the neutron scattering measurements.
