NN- pi NN equations and the chiral bag model.

Abstract

The NN-\ensuremath{\pi}NN equations that describe, in a unified framework, pion production in nucleon-nucleon scattering, and pion-deuteron and nucleon-nucleon elastic scattering, have been extended to include the N(939) and \ensuremath{\Delta}(1232) on an equal footing. This extension, motivated by the quark models of hadrons, has the bare N and \ensuremath{\Delta} as three quark states with the same spacial wave function, but different spin isospin states. The final equations, referred to as the BB-\ensuremath{\pi}BB equations, are consistent with the chiral bag models to the extent that the \ensuremath{\pi}NN, \ensuremath{\pi}N\ensuremath{\Delta}, and \ensuremath{\pi}\ensuremath{\Delta}\ensuremath{\Delta} coupling constants and form factors are related, and can be taken from bag models. The resultant equations satisfy two- and three-body unitarity, and are derived by exposing the lowest unitarity cuts in the n-body Green's function. These equations retain important contributions missing from the NN-\ensuremath{\pi}NN equations. For pion production and N-N scattering they include the contribution of backward pions in the NN\ensuremath{\rightarrow}N\ensuremath{\Delta} transition potential, which may overcome the problem of small pp\ensuremath{\rightarrow}\ensuremath{\pi}d cross section as predicted by the NN-\ensuremath{\pi}NN equations. For \ensuremath{\pi}-d elastic scattering they include an additional N\ensuremath{\Delta}\ensuremath{\rightarrow}N\ensuremath{\Delta} tensor force that can influence the tensor polarization.