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The nuclear density dependencies of the neutron and $\Sigma$ and $\Lambda$hyperons are important inputs in the determination of the neutron star mass asthe appearance of hyperons coming from strong attractions significantly changesthe stiffness of the equation of state (EOS) at iso-spin asymmetric densenuclear matter. In-medium spectral sum rules have been analyzed for thenucleon, $\Sigma$, and $\Lambda$ hyperon to investigate their properties up toslightly above the saturation nuclear matter density by using the lineardensity approximation for the condensates. The construction scheme of theinterpolating fields without derivatives has been reviewed and used toconstruct a general interpolating field for each baryon with parametersspecifying the strength of independent interpolating fields. Optimal choicesfor the interpolating fields were obtained by requiring the sum rules to bestable against variations of the parameters and the result to be consistentwith known phenomenology. The optimized result shows that Ioffe's choice is notsuitable for the $\Lambda$ hyperon sum rules. It is found that, for the$\Lambda$ hyperon interpolating field, the up and down quark combined into thescalar diquark structure $u^T C \gamma_5 d$ should be emphasized to ensurestable sum rules. The quasi-$\Sigma$ and -$\Lambda$ hyperon energies are alwaysfound to be higher than the quasineutron energy in the region $0.5<\rho/\rho_0<1.5 $ where the linear density approximation in the sum-ruleanalysis is expected to be reliable.

QCD sum rules for the neutron, $\Sigma$, and $\Lambda$ in neutron matter