QCD sum rules for the neutron, Σ , and Λ in neutron matter

Abstract

The nuclear density dependencies of the neutron and $\Sigma$ and $\Lambda$ hyperons are important inputs in the determination of the neutron star mass as the appearance of hyperons coming from strong attractions significantly changes the stiffness of the equation of state (EOS) at iso-spin asymmetric dense nuclear matter. In-medium spectral sum rules have been analyzed for the nucleon, $\Sigma$, and $\Lambda$ hyperon to investigate their properties up to slightly above the saturation nuclear matter density by using the linear density approximation for the condensates. The construction scheme of the interpolating fields without derivatives has been reviewed and used to construct a general interpolating field for each baryon with parameters specifying the strength of independent interpolating fields. Optimal choices for the interpolating fields were obtained by requiring the sum rules to be stable against variations of the parameters and the result to be consistent with known phenomenology. The optimized result shows that Ioffe's choice is not suitable for the $\Lambda$ hyperon sum rules. It is found that, for the $\Lambda$ hyperon interpolating field, the up and down quark combined into the scalar diquark structure $u^T C \gamma_5 d$ should be emphasized to ensure stable sum rules. The quasi-$\Sigma$ and -$\Lambda$ hyperon energies are always found 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-rule analysis is expected to be reliable.