It is much simpler to obtain the flux for anti-proton than that of positron. The point is that the astrophysical information is totally factorized out in H ¯ $_{p}$( E ), and no further convolu- tion operation is needed. The predicted anti-proton fluxes comparing to the background flux in Model I and Model II are plotted in Fig. 4, where the suitable astrophysical parameters have been chosen. The background anti-protons mainly arise from the collisions between the primary CR protons (produced also by supernova) and the interstellar hydrogen gas (for details, please see Ref. [41]). Taking proper astrophysics parameters in the practical calcu- lations, we find that the anti-proton excess is definitely excluded below 50 GeV (Sixteen of the PAMELA seventeen points on ¯ p/p are in this energy region [3].). In Model I for the PAMELA and FERMI data fitting, the DM particle S is very heavy about 3 TeV, and then the anti-proton flux is suppressed in all energy region below about 130 GeV. However, in Model II for the PAMELA and ATIC data fitting, the DM particle S is about 1 . 8 TeV, and then the anti-proton flux begins to exceed background above about 60 GeV. Especially, the excess is more significant as the energy increasing, which is interesting since it can be tested in the future. FIG. 4: PAMELA data fitting for ¯ p/p ratio in Model I and Model II. The anti-proton fluxes Φ ¯ p $_{⊙}$( E ) is in the unit GeV − $^{1}$m − $^{2}$s − $^{1}$sr − $^{1}$. 16 5e-006 5e-005 0.0005 10 50 100 F ERMI+P AMELA fit A TIC+PA M ELA fit B ackgroun d