  Low-temperature photoluminescence (PL) of hBN-encapsulated monolayer tungsten
diselenide (WSe$_2$) shows a multitude of sharp emission peaks below the bright
exciton. Some of them have been recently identified as phonon sidebands of
momentum-dark states. However, the exciton dynamics behind the emergence of
these sidebands has not been revealed yet. In this joint theory-experiment
study, we theoretically predict and experimentally observe time-resolved PL
providing microscopic insights into thermalization of hot excitons formed after
optical excitation. In good agreement between theory and experiment, we
demonstrate a spectral red-shift of phonon sidebands on a timescale of tens of
picoseconds reflecting the phonon-driven thermalization of hot excitons in
momentum-dark states. Furthermore, we predict the emergence of a transient
phonon sideband that vanishes in the stationary PL. The obtained microscopic
insights are applicable to a broad class of 2D materials with multiple exciton
valleys.
