  We analyze the effect of a strong Zeeman field on the spectrum of collective
excitations of monolayer transition metal dichalcogenides. The combination of
the Dresselhaus type spin orbit coupling and an external Zeeman field result in
the lifting of the valley degeneracy in the valence band of these crystals. We
show that this lifting of the valley degeneracy manifests in the appearance of
an additional plasmon mode with linear in wavenumber dispersion along with the
standard square root in wavenumber mode. Despite this novel mode being subject
to the Landau damping, it corresponds to a well defined quasiparticle peak in
the spectral function of the electron gas.
