Effects of consistent and inconsistent isobar coupling in the nuclear medium

Abstract

We investigate effects of consistent (conserving the number of degrees of freedom) and inconsistent pionnucleon-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 higherderivative 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.

Δself-energy at finite temperature and density and theπNcross section

“…As described above, the cut-off in the form factor used here was obtained by fitting the πN cross-section. The spectral functions evaluated using this (conventional) vertex were found [41] to differ slightly with the ones calculated using the consistent coupling discussed above if the same form factor is applied in both the cases. It was further shown that this difference could be eliminated if the additional momentum factor stemming from the higher derivative nature of the consistent interaction [39] was compensated either by an additional form factor term or by adjusting the cut-off values of the original form factor.…”

Nuclear Drell-Yan effect in a covariant model

“…The contribution coming from the delta baryon in the final state is made more involved by the complicated structure of the in-medium delta propagator [14]. However, considerable simplification can be achieved by including only the two dominant contributions in the convenient relativistically covariant decomposition since the imaginary part of the other components is typically two orders of magnitude smaller at nuclear saturation density [26]. The dominant contributions come from the Q µν [11] and P µν [55] terms which were degenerate in the free delta case, but are different in the medium [14].…”