High-Spin Baryons. V. Dynamical Model for Regge Recurrences of Inelastic Resonances: Numerical Results

Virtual transitions of the type πNᵢ→ρNⱼ, where Nᵢ and Nⱼ are arbitrary nucleon isobars, are considered as possible mechanisms for Regge recurrences. It is found that the largest one-pion-exchange forces coupling to (ρN₁)L=0,(ρN₂)L=0,⋯ [where N₁,N₂,⋯ have spin-parity JP of SP,(S+2)P,⋯] occur in the opposite-parity states (S+1)^-P,(S+3)^-P,⋯. The most important couplings seem to be "diagonal," i.e., Nᵢ=Nⱼ. In this case, isospin {} always dominates. If all πNᵢNᵢ couplings are of the same order of magnitude, then there are negative-parity trajectories that follow along with the positive-parity trajectories. It is found that the one-pion-exchange amplitudes lead to substantial violations of unitarity and to spectrum inversion for "off-diagonal" couplings (Nᵢ≠Nⱼ) involving large momentum transfers. To deal with this problem we introduce a one-parameter "form factor." Because of the uncertainties of coupling constants and form factor, predictions of resonance energies and branching ratios are somewhat adjustable. However, resonances occur in states having the correct quantum numbers, and the calculated widths are surprisingly good. Given the nucleon (Nᵢ⁺) and Δᵢ⁺ trajectories, we are led to the Nᵢ^- trajectory with (T,JP)=(1/2,3/2^-),(1/2,7/2^-),⋯ and the Nᵢ^'- trajectory (1/2,5/2^-),(1/2,9/2^-),⋯. In addition there is possibly another (1/2,1/2^-),(1/2,5/2^-),⋯ sequence at rather high mass. The "exothermic" reactions for which M(Nᵢ)>M(Nⱼ) lead to possible isospin-3/2 resonances (3/2,1/2^-),(3/2,5/2^-),⋯, but these calculations are not considered very reliable. The virtual-f configurations fNⱼ are also considered. These characteristically involve considerably larger momentum transfers than do the corresponding ρ-meson configurations. If the fNⱼ amplitudes are modified by the same function used to repair the ρNⱼ couplings, no resonances result from the fNⱼ mechanism. However, present methods of computing the magnitude of this high-momentum-transfer effect are unreliable. Extension of the vector-meson model to SU(3) leads to 8 and 1 trajectories with 3/2^-,7/2^-,⋯ and 8 alone for 5/2^-,9/2^-,⋯ and the doubtful companion 1/2^-,5/2^-,⋯. Generalization of the f production mechanism to a tensor nonet T₉ leads to hitherto unobserved representations. P₈→B₈→T₉+B₈ would give 8, 10*, and 1 representations with spin JP of 5/2⁺,9/2⁺,⋯, and possibly 7/2^-,11/2^-,⋯, while P₈+B₁₀→T₉+B₁₀ would give 10 and 27 representations with 7/2⁺,11/2⁺,⋯ if we have underestimated the importance of this effect. Hence present experimental evidence seems to support our conclusions about the relative importance of the vector- and tensor-meson production. The resulting baryon mass spectrum includes most of the prominent observed states. No wrong states are predicted. Some new resonances in the 2-BeV region are suggested.