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We investigate the excitation spectrum of the triangular-latticeantiferromagnetic $XXZ$ model using series expansions and mean field Schwingerbosons approaches. The single-magnon spectrum computed with series expansionsexhibits rotonic minima at the middle points of the edges of the Brillouinzone, for all values of the anisotropy parameter in the range $0\leqJ^z/J\leq1$. Based on the good agreement with series expansions for thesingle-magnon spectrum, we compute the full dynamical magnetic structure factorwithin the mean field Schwinger boson approach to investigate the relevance ofthe $XXZ$ model for the description of the unusual spectrum found recently in$Ba_3CoSb_2O_9$. In particular, we obtain an extended continuum above the spinwave excitations, which is further enhanced and brought closer to thoseobserved in $Ba_3CoSb_2O_9$ with the addition of a second neighbor exchangeinteraction approximately 15% of the nearest-neighbor value. Our resultssupport the idea that excitation continuum with substantial spectral-weight aregenerically present in two-dimensional frustrated spin systems andfractionalization in terms of {\it bosonic} spinons presents an efficient wayto describe them.

Magnons and Excitation Continuum in XXZ triangular antiferromagnetic model: Application to $Ba_3CoSb_2O_9$