One loop corrections to quantum hadrodynamics with vector mesons

Abstract

The renormalized elastic \ensuremath{\pi}\ensuremath{\pi} scattering amplitude to one loop is calculated in the chiral limit in the \ensuremath{\sigma} model and in a quantum hadrodynamic model (QHD-III) with vector mesons. It is argued that QHD-III reduces to the linear \ensuremath{\sigma} model in the limit that the vector meson masses become large. The pion decay constant is also calculated to 1-loop in the \ensuremath{\sigma} model, and at tree level in QHD-III; it is shown that the coefficient of the tree level term in the scattering amplitude equals ${F}_{\ensuremath{\pi}}^{\ensuremath{-}2}.$ The 1-loop correction of ${F}_{\ensuremath{\pi}}$ in QHD-III violates strong isospin current conservation. Thus, it is concluded that QHD-III can, at best, only describe the strongly interacting nuclear sector.