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

Weakly damped acoustic plasmon mode in transition metal dichalcogenides with Zeeman splitting