Covariant and self consistent vertex corrections for pions and isobars in nuclear matter

TL;DR

This paper presents a covariant, self-consistent approach to calculating pion and isobar propagators in nuclear matter, highlighting the significant impact of vertex corrections on resonance properties and soft modes.

Contribution

It introduces a covariant, vertex-corrected isobar-hole model without phenomenological form factors, providing new insights into resonance shifts and pion modes in nuclear matter.

Findings

Delta resonance shifts downward by about 50 MeV at saturation density

Short-range dressing significantly affects pion and isobar properties

Pionic soft modes are less pronounced than previously thought

Abstract

We evaluate the pion and isobar propagators in cold nuclear matter self consistently applying a covariant form of the isobar-hole model. Migdal's vertex correction effects are considered systematically in the absence of phenomenological soft form factors. Saturated nuclear matter is modeled by scalar and vector mean fields for the nucleon. It is shown that the short-range dressing of the pi N Delta vertex has a significant effect on the pion and isobar properties. Using realistic parameters sets we predict a downward shift of about 50 MeV for the Delta resonance at nuclear saturation density. The pionic soft modes are much less pronounced than in previous studies.