  We present a theory for Raman scattering on 2D quantum antiferromagnets. The
microscopic Fleury-Loudon Hamiltonian is expressed in terms of an effective
$O(3)$ - model. Well within the N\'eel ordered phase, the Raman spectrum
contains a two-magnon and a two-Higgs contribution, which are calculated
diagramatically. The vertex functions for both the Higgs and magnon
contributions are determined from a numerical solution of the corresponding
Bethe-Salpeter equation. Due to the momentum dependence of the Raman vertex in
the relevant $B_{1g}+E_{2g}$ symmetry, the contribution from the Higgs mode is
strongly suppressed. Except for intermediate values of the Higgs mass, it does
not show up as separate peak in the spectrum but gives rise to a broad
continuum above the dominant contribution from two-magnon excitations. The
latter give rise to a broad, asymmetric peak at $\omega\simeq 2.44\, J$, which
is a result of magnon-magnon interactions mediated by the Higgs mode. The full
Raman spectrum is determined completely by the antiferromagnetic exchange
coupling $J$ and a dimensionless Higgs mass. Experimental Raman spectra of
undoped cuprates turn out to be in very good agreement with the theory only
with inclusion of the Higgs contribution. They thus provide a clear signature
of the presence of a Higgs mode in spin one-half 2D quantum antiferromagnets.
