Covariant propagator of the Rarita-Schwinger field in the nuclear medium

Abstract

A formalism for representing the fully relativistic propagator of the Rarita-Schwinger field in the nuclear medium is developed. Using a convenient basis for expanding the propagator it is shown that it can be represented by 40 energy and momentum dependent quantities which can be decomposed into an 2×2 and an 6×6 matrix. In this way calculations reduce to matrix multiplication. Using the presented formalism the full relativistically covariant contribution of the pion-nucleon loop to the isobar self energy and propagator in isospin-symmetric spin-saturated nuclear medium is computed. Utilizing this propagator the photoabsorption cross-section on in-medium nucleons in the isobar region is calculated and the result compared with experimental data.

Critical density and impact ofΔ(1232)resonance formation in neutron stars

“…For instance, from analyzing the (p, π) invariant masses in the final state of heavy-ion collisions at SIS/GSI energies, indications were found for an approximately −60 MeV mass shift for ∆(1232) resonances at the freeze-out of about 1/3 the saturation density [25]. However, photo absorption data and some advanced model calculations found no evidence of significant in-medium ∆(1232) mass shift [26,27]. It is thus exciting that new proposals to experimentally study at FAIR/GSI the ∆(1232) resonance spectroscopy and interactions in neutron-rich matter are being considered by the NUSTAR Collaboration [40].…”

Nuclear Drell-Yan effect in a covariant model

“…However, using the convenient basis from Ref. [14] it turns out that a single term, namely the (on-mass-shell) positive-energy spin-3/2 contribution gives the dominant contribution and all others (some terms in the propagator are identically zero) are completely negligible. In the notation of Ref.…”

“…In the notation of Ref. [14] this is the coefficient of the projector sum Q μν [11] ≡ Q μν [11] + P μν [55] , which we denote by G (Q ) [11] (p). The pion light-cone distribution originating from the π state then can be expressed as…”

“…The parameter set (1) is 3. (Color online) Sum of the second, third, fourth, and fifth terms in Eq. (14) divided by the antiquark distribution of the free "isoscalar" nucleon. The solid line is for the pion parameter set (1) and the dashed line is for parameter set (2).…”

Fermion Resonance in Quantum Field Theory

“…They simplify essentially all calculations and clarify their physical meaning. Recall that these projection operators were successfully used in calculations of the ∆-isobar propagator both in vacuum [13,14] and media [17].…”