  We discuss the non-perturbative effects on the annihilation cross section of
an Electro-Weak Dark Matter (EWDM) particle belonging to an electroweak
multiplet when the splittings between the masses of the DM component and the
other charged or neutral component(s) of the multiplet are treated as free
parameters. Our analysis shows that EWDM exhibits not only the usual Sommerfeld
enhancement with resonance peaks but also dips where the cross section is
suppressed. Moreover, we have shown that the non-perturbative effects become
important even when the EWDM mass is below the TeV scale, provided that some of
the mass splitting are reduced to the order of a few MeV. This extends the
possibility of observing sizeable non-perturbative effects in the dark matter
annihilation to values of the dark matter mass significantly smaller than
previously considered, since only electroweak--induced mass splittings larger
than 100 MeV have been discussed in the literature so far. We have then used
the available experimental data on the cosmic antiproton flux to constrain the
EWDM parameter space. In our calculation of the expected signal we have
included the effect of the convolution of the cross section with the velocity
distribution of the dark matter particles in the Galaxy, showing that it can
alter the non--perturbative effects significantly. In the case of EWDM with
non-zero hypercharge, we have shown that the mass splitting in the Dirac dark
matter fermion can be chosen so that the inelastic cross section of the EWDM
off nuclei is allowed by present direct detection constraints and at the same
time is within the reach of future experiments.
