Upper bounds on signals due to WIMP self-annihilation: comments on the case of the synchrotron radiation from the galactic center and the WMAP haze

Two recent papers reconsider the possibility that the excess of microwave emission from a region within $\sim 20^0$ of the galactic center (the {\it WMAP haze}), measured by WMAP, can be due to the synchrotron emission originated by neutralino self-annihilation; on the basis of this possible occurrence, also upper bounds on the neutralino self-annihilation cross--section are suggested. In the present note, we show that in the common case of thermal WIMPs in a standard cosmological model, when the rescaling of the galactic WIMP density is duly taken into account for subdominant WIMPs, the upper bound applicable generically to {\it any} signal due to self-conjugate WIMPs is more stringent than the ones obtained from analysis of the WMAP haze. We also argue that an experimental upper bound, which can compete with our generic upper limit, can rather be derived from measurements of cosmic antiproton fluxes, for some values of the parameters of the astrophysical propagation model. Finally, we comment on the possible impact of our generic upper bound on the interpretation of the WMAP haze in terms of thermal neutralinos in a standard cosmological scheme.