QCD sum rules for the $\Delta$ isobar in neutron matter

TL;DR

This paper uses QCD sum rules to analyze the properties of the $ riangle$ isobar in nuclear matter, revealing smaller vector repulsion compared to nucleons and weak isospin dependence, with minimal effects from the $ ext{pi}-N$ continuum.

Contribution

It introduces a QCD sum rules approach with different continuum thresholds to study the $ riangle$ isobar in medium, providing new insights into its mass and interaction characteristics.

Findings

Stable $ riangle$ masses in vacuum and medium.

Smaller vector repulsion for $ riangle$ compared to nucleons.

Weak isospin dependence of quasiparticle energy.

Abstract

We study the properties of the $\Delta$ isobar in the symmetric and asymmetric nuclear matter using the QCD sum rules approach based on the energy dispersion relation. Allowing for different continuum thresholds for the polarization tensors with different dimensions, we find stable masses for the $\Delta$ in both the vacuum and the medium. Compared to the nucleon case, we find that the vector repulsion is smaller for the $\Delta$ while the scalar attraction is similar (75 MeV vector repulsion and 150 MeV scalar attraction in the symmetric matter). The smaller vector repulsion can be understood using the Pauli principle and a constituent quark model. Also the isospin dependence of the quasiparticle energy, which mainly comes from the vector self energy, is quite weak. We also allow for an explicit $\pi -N$ continuum contribution to the polarization function, but find its effect to be minimal. Phenomenological consequences of our results are discussed.