Effects of consistent and inconsistent isobar coupling in the nuclear medium

TL;DR

This paper compares consistent and inconsistent pion-nucleon-isobar couplings, showing that consistent couplings simplify calculations and yield similar physical observables as inconsistent couplings when properly adjusted.

Contribution

It demonstrates that consistent couplings can be used effectively with simple basis choices, simplifying the isobar propagator calculations without losing physical accuracy.

Findings

Consistent coupling simplifies the isobar self energy calculations.

Proper form-factor adjustments ensure comparable physical observables.

Consistent and inconsistent couplings produce indistinguishable results when adjusted.

Abstract

We investigate effects of consistent (conserving the number of degrees of freedom) and inconsistent pion-nucleon-isobar couplings on the isobar propagator in vacuum and in nuclear medium. Using the consistent coupling in conjunction with a convenient basis leads to significant simplification of the isobar vacuum and in-medium self energy and dressed propagator compared to the case of inconsistent interaction. The higher-derivative nature of the consistent interaction requires a suitable compensation by an additional form-factor term or adjustment in the used cut-off values. This modification is straightforward to perform and assures that the physical observables connected to the spin-3/2 sector in vacuum and nuclear medium acquire values indistinguishable from the ones obtained by using an inconsistent coupling.