There are strong evidences for existence of dark matter in some experiments at present. However, the question is that we do not have a reasonable explanation for dark matter in the framework of the Standard Model(SM) of particle physics. It is necessary to extend the SM in order to explain the dark matter. According to the current possible existence conditions of dark matter, we choose $chi^0_L$ and $tilde{Y}$ as candidates for dark matter in the EBLMSSM. We study the dominant annihilation processes in detail, including $bar{chi}^0_Lchi^0_L(bar{tilde{Y}}tilde{Y})rightarrow bar{l}^Il^I$ and $bar{chi}^0_Lchi^0_L(bar{tilde{Y}}tilde{Y})rightarrow bar{ u}^I u^I$. And we calculate their annihilation cross section $sigma$ and relic density $Omega_D h^2$. Then we analyze the limitations of dark matter relic density on the parameters of the EBLMSSM.
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