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Non-perturbative Effect and PAMELA Limit on Electro-Weak Dark Matter

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.