  We investigate the magnetic-field-induced splitting of biexcitons in
monolayer WS$_2$ using polarization-resolved photoluminescence spectroscopy in
out-of-plane magnetic fields up to 30 T. The observed $g$ factor of the
biexciton amounts to $-3.89$, closely matching the $g$ factor of the neutral
exciton. The biexciton emission shows an inverted circular field-induced
polarization upon linearly polarized excitation, i.e. it exhibits preferential
emission from the high-energy peak in a magnetic field. This phenomenon is
explained by taking into account the configuration of the biexciton
constituents in momentum space and their respective energetic behavior in
magnetic fields. Our findings reveal the critical role of dark excitons in the
composition of this many-body state.
