  Dark matter particles captured in the Sun would annihilate producing a
neutrino flux that could be detected at the Earth. In some channels, however,
the neutrino flux lies in the MeV range and is thus undetectable at IceCube,
namely when the dark matter particles annihilate into $e^+e^-$, $\mu^+\mu^-$ or
light quarks. On the other hand, the same interaction that mediates the
annihilations into light fermions also leads, via higher order effects, to the
production of weak gauge bosons (and in the case of quarks also gluons) that
generate a high energy neutrino flux potentially observable at IceCube. We
consider in this paper tree level annihilations into a fermion-antifermion pair
with the associated emission of one gauge boson and one loop annihilations into
two gauge bosons, and we calculate the limits on the scattering cross section
of dark matter particles with protons in scenarios where the dark matter
particle couples to electrons, muons or light quarks from the non-observation
of an excess of neutrino events in the direction of the Sun. We find that the
limits on the spin-dependent scattering cross section are, for some scenarios,
stronger than the limits from direct detection experiments.
