  In van der Waals heterostructures, the relative alignment of bands between
layers, and the resulting band hybridisation, are key factors in determining a
range of electronic properties. This work examines these effects for
heterostructures of transition metal dichalcogenides (TMDs) and hexagonal boron
nitride (hBN), an ubiquitous combination given the role of hBN as an
encapsulating material. By comparing results of density functional calculations
with experimental angle-resolved photoemission spectroscopy (ARPES) results, we
explore the hybridisation between the valence states of the TMD and hBN layers,
and show that it introduces avoided crossings between the TMD and hBN bands,
with umklapp processes opening `ghost' avoided crossings in individual bands.
Comparison between DFT and ARPES spectra for the MoSe$_2$/hBN heterostructure
shows that the valence bands of MoSe$_2$ and hBN are significantly further
separated in energy in experiment as compared to DFT. We then show that a novel
scissor operator can be applied to the hBN valence states in the DFT
calculations, to correct the band alignment and enable quantitative comparison
to ARPES, explaining avoided crossings and other features of band visibility in
the ARPES spectra.
