  Strong Coulomb correlations together with multi-valley electronic bands in
the presence of spin-orbit interaction and possible new optoelectronic
applications are at the heart of studies of the rich physics of excitons in
semiconductor structures made of monolayers of transition metal dichalcogenides
(TMD). In intrinsic TMD monolayers the basic, intravalley excitons are formed
by a hole from the top of the valence band and an electron either from the
lower or upper spin-orbit-split conduction band subbands: one of these excitons
is optically active, the second one is "dark", although possibly observed under
special conditions. Here we demonstrate the s-series of Rydberg dark exciton
states in monolayer WSe$_2$, which appears in addition to a conventional bright
exciton series in photoluminescence spectra measured in high in-plane magnetic
fields. The comparison of energy ladders of bright and dark Rydberg excitons is
shown to be a method to experimentally evaluate one of the missing band
parameters in TMD monolayers: the amplitude of the spin-orbit splitting of the
conduction band.
