In the framework of Left-Right symmetric model, we investigate an interesting scenario, in which the so-called VEV seesaw problem can be naturally solved with Z_2 symmetry. In such a scenario, we find a pair of stable weakly interacting massive particles (WIMPs), which may be the cold dark matter candidates. However, the WIMP-nucleon cross section is 3-5 orders of magnitude above the present upper bounds from the direct dark matter detection experiments for $m sim 10^2-10^4 $ GeV. As a result, the relic number density of two stable particles has to be strongly suppressed to a very small level. Nevertheless, our analysis shows that this scenario cant provide very large annihilation cross sections so as to give the desired relic abundance except for the resonance case. Only for the case if the rotation curves of disk galaxies are explained by the Modified Newtonian Dynamics (MOND), the stable WIMPs could be as the candidates of cold dark matter.
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