Analysis of the $\Sigma_Q$ baryons in the nuclear matter with the QCD sum rules

In this article, we extend our previous work to study the $\Sigma$-type heavy baryons $\Sigma_c$ and $\Sigma_b$ in the nuclear matter using the QCD sum rules, and obtain three coupled QCD sum rules for the masses $M_{\Sigma_Q}^*$, vector self-energies $\Sigma_v$ and pole residues $\lambda^*_{\Sigma_Q}$ in the nuclear matter. Then we take into account the effects of the unequal pole residues from different spinor structures, and normalize the masses from the QCD sum rules in the vacuum to the experimental data, and obtain the mass-shifts $\delta M_{\Sigma_c}=-123\,\rm{MeV}$ and $\delta M_{\Sigma_b}=-375\,\rm{MeV}$ in the nuclear matter.