  Exciton optical transitions in transition-metal dichalcogenides offer unique
opportunities to study rich many-body physics. Recent experiments in monolayer
WSe$_2$ and WS$_2$ have shown that while the low-temperature photoluminescence
from neutral excitons and three-body complexes is suppressed in the presence of
elevated electron densities or strong photoexcitation, new dominant peaks
emerge in the low-energy side of the spectrum. I present a theory that
elucidates the nature of these optical transitions showing the role of the
intervalley Coulomb interaction. After deriving a compact dynamical form for
the Coulomb potential, I calculate the self-energy of electrons due to their
interaction with this potential. For electrons in the upper valleys of the
spin-split conduction band, the self energy includes a moderate redshift due to
exchange, and most importantly, a correlation-induced virtual state in the
band-gap. The latter sheds light on the origin of the luminescence in monolayer
WSe$_2$ and WS$_2$ in the presence of pronounced many-body interactions.
