  We perform a theoretical study of radiative decay of dark intravalley
excitons in transition metal dichalcogenide monolayers. This decay necessarily
involves an electronic spin flip. The intrinsic decay mechanism due to
interband spin-flip dipole moment perpendicular to the monolayer plane, gives a
rate about 100--1000 times smaller than that of bright excitons. However, we
find that this mechanism also introduces an energy splitting due to a local
field effect, and the whole oscillator strength is contained in the
higher-energy component, while the lowest-energy state remains dark and needs
an extrinsic spin-flip mechanism for the decay. Rashba effect due to a
perpendicular electric field or a dielectric substrate, gives a negligible
radiative decay rate (about $10^7$ times slower than that of bright excitons).
Spin flip due to Zeeman effect in a sufficiently strong in-plane magnetic field
can give a decay rate comparable to that due to the intrinsic interband
spin-flip dipole.
