  In single-layer WSe$_2$, a paradigmatic semiconducting transition metal
dichalcogenide, a circularly polarized laser field can selectively excite
electronic transitions in one of the inequivalent $K^{\pm}$ valleys. Such
selective valley population corresponds to a pseudospin polarization. This can
be used as a degree of freedom in a valleytronic device provided that the time
scale for its depolarization is sufficiently large. Yet, the mechanism behind
the valley depolarization still remains heavily debated. Recent time-dependent
Kerr experiments have provided an accurate way to visualize the valley dynamics
by measuring the rotation of a linearly polarized probe pulse applied after a
circularly polarized pump pulse. We present here a clear, accurate and
parameter-free description of the valley dynamics. By using an atomistic, ab
initio, approach we fully disclose the elemental mechanisms that dictate the
depolarization effects. Our results are in excellent agreement with recent
time-dependent Kerr experiments. We explain the Kerr dynamics and its
temperature dependence in terms of electron-phonon mediated processes that
induce spin-flip inter-valley transitions.
