Off-Mass-Shell Approach to Strong Decays of Baryon Resonances

It is shown that useful sets of self-consistency conditions on baryon resonances can be obtained from off-mass-shell dispersion relations satisfied by the decay amplitudes in which baryon resonances decay into a pion and other baryon resonances. The decay amplitudes are continued off the mass shell, not only with respect to pion in terms of divergence of axial-vector current, but also regarding baryon resonances using renormalized baryon fields. Self-consistency conditions are the off-mass-shell dispersion relations, with dispersion integrals saturated in terms of the baryon resonances which share the same quantum numbers, including spin. Use of the soft-pion technique and current-commutator algebra enables us to derive an additional set of self-consistency conditions. The details of the analysis are presented in the case of nucleon resonances with both spin and isospin ½. The resulting self-consistency conditions can never be satisfied unless nucleon resonances with opposite parities are both assumed. It is shown that the self-consistency conditions are consistent with all the available experiments on four nucleons. Moreover, the self-consistency conditions imply that the decay of $N\left(1700\right)\mathrm{}$ into $N\left(1400\right)\mathrm{}$ and a pion has a decay width of ∼24 MeV, which can be tested by experiment. The self-consistency conditions are in favor of increasing the mass of $N\left(1400\right)\mathrm{}$ considerably over 1400 MeV.