  By pumping nonresonantly a MoS$_2$ monolayer at $13$ K under a circularly
polarized cw laser, we observe exciton energy redshifts that break the
degeneracy between B excitons with opposite spin. The energy splitting
increases monotonically with the laser power reaching as much as $18$ meV,
while it diminishes with the temperature. The phenomenon can be explained
theoretically by considering simultaneously the bandgap renormalization which
gives rise to the redshift and exciton-exciton Coulomb exchange interaction
which is responsible for the spin-dependent splitting. Our results offer a
simple scheme to control the valley degree of freedom in MoS$_2$ monolayer and
provide an accessible method in investigating many-body exciton exciton
interaction in such materials.
