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In monolayer Transition Metal Dichalcogenides (TMDs) the valence andconduction bands are spin split because of the strong spin-orbit interaction.In tungsten-based TMDs the spin-ordering of the conduction band is such thatthe so-called dark exciton, consisting of an electron and a hole with oppositespin orientation, has lower energy than the A exciton. A possible mechanismleading to the transition from bright to dark excitons involves the scatteringof the electrons from the upper to the lower conduction band state in K. Herewe exploit the valley selective optical selection rules and use two-colorhelicity-resolved pump-probe spectroscopy to directly measure the intravalleyspin-flip relaxation dynamics of electrons in the conduction band ofsingle-layer WS$_2$. This process occurs on a sub-ps time scale and it issignificantly dependent on the temperature, indicative of a phonon-assistedrelaxation. These experimental results are supported by time-dependentab-initio calculations which show that the intra-valley spin-flip scatteringoccurs on significantly longer time scales only exactly at the K point. In arealistic situation the occupation of states away from the minimum of theconduction band leads to a dramatic reduction of the scattering time.

Direct observation of intravalley spin relaxation in single-layer WS$_2$