  Graphene sheets encapsulated between hexagonal Boron Nitride (hBN) slabs
display superb electronic properties due to very limited scattering from
extrinsic disorder sources such as Coulomb impurities and corrugations. Such
samples are therefore expected to be ideal platforms for highly-tunable
low-loss plasmonics in a wide spectral range. In this Article we present a
theory of collective electron density oscillations in a graphene sheet
encapsulated between two hBN semi-infinite slabs (hBN/G/hBN). Graphene plasmons
hybridize with hBN optical phonons forming hybrid plasmon-phonon (HPP) modes.
We focus on scattering of these modes against graphene's acoustic phonons and
hBN optical phonons, two sources of scattering that are expected to play a key
role in hBN/G/hBN stacks. We find that at room temperature the scattering
against graphene's acoustic phonons is the dominant limiting factor for
hBN/G/hBN stacks, yielding theoretical inverse damping ratios of hybrid
plasmon-phonon modes of the order of $50$-$60$, with a weak dependence on
carrier density and a strong dependence on illumination frequency. We confirm
that the plasmon lifetime is not directly correlated with the mobility: in
fact, it can be anti-correlated.
