S-wave pion-nucleus dynamics in theσ+ωmodel

The $\sigma +\omega$ model of nuclear forces has many desirable properties, including approximate chiral symmetry (partial conservation of axial vector current) and renormalizability, and it gives a good account of nuclear structure. It is therefore a useful framework within which to explore the modification of pion-nucleon dynamics in a nuclear medium, a problem which resists the usual soft-pion current-algebra cum analyticity techniques owing to the presence of anomalous thresholds (nuclear structure effects). It is found that through order $G^4$ (for pion elastic scattering) and $G^3$ (for pion absorption or emission) the chiral invariance ensures sufficient cancellations between otherwise large terms so as to produce little renormalization of free-particle dynamics. Moreover, the pseudoscalar-coupled $\sigma +\omega$ model is equivalent in pion emission or absorption, through $O\left(G^3\right)$, to a pseudovector-coupled phenomenological model (with no $\pi -\sigma$ interaction, but with a form of partially conserved axial vector current). Thus, the question of whether one can distinguish experimentally between pseudoscalar and pseudovector $\pi \mathrm{NN}$ coupling is probably meaningless.