HighSpin Baryons. V. Dynamical Model for Regge Recurrences of Inelastic Resonances: Numerical Results
Abstract
Virtual transitions of the type πN_{i}>ρN_{j}, where N_{i} and N_{j} are arbitrary nucleon isobars, are considered as possible mechanisms for Regge recurrences. It is found that the largest onepionexchange forces coupling to (ρN_{1})_{L=0},(ρN_{2})_{L=0},... [where N_{1},N_{2},... have spinparity J^{P} of S^{P},(S+2)^{P},...] occur in the oppositeparity states (S+1)^{P},(S+3)^{P},.... The most important couplings seem to be "diagonal," i.e., N_{i}=N_{j}. In this case, isospin 1/2 always dominates. If all πN_{i}N_{i} couplings are of the same order of magnitude, then there are negativeparity trajectories that follow along with the positiveparity trajectories. It is found that the onepionexchange amplitudes lead to substantial violations of unitarity and to spectrum inversion for "offdiagonal" couplings (N_{i}≠N_{j}) involving large momentum transfers. To deal with this problem we introduce a oneparameter "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 (N_{i}^{+}) and ∆_{i}^{+} trajectories, we are led to the N_{i}^{} trajectory with (T,J^{P})=(12,32^{}),(12,72^{}),... and the N_{i}^{'} trajectory (12,52^{}),(12,92^{}),.... In addition there is possibly another (12,12^{}),(12,52^{}),... sequence at rather high mass. The "exothermic" reactions for which M(N_{i})>M(N_{j}) lead to possible isospin32 resonances (32,12^{}),(32,52^{}),..., but these calculations are not considered very reliable. The virtualf configurations fN_{j} are also considered. These characteristically involve considerably larger momentum transfers than do the corresponding ρmeson configurations. If the fN_{j} amplitudes are modified by the same function used to repair the ρN_{j} couplings, no resonances result from the fN_{j} mechanism. However, present methods of computing the magnitude of this highmomentumtransfer effect are unreliable. Extension of the vectormeson model to SU(3) leads to 8 and 1 trajectories with 32^{},72^{},... and 8 alone for 52^{},92^{},... and the doubtful companion 12^{},52^{},.... Generalization of the f production mechanism to a tensor nonet T_{9} leads to hitherto unobserved representations. P_{8}>B_{8}>T_{9}+B_{8} would give 8, 10^{*}, and 1 representations with spin J^{P} of 52^{+},92^{+},..., and possibly 72^{},112^{},..., while P_{8}+B_{10}>T_{9}+B_{10} would give 10 and 27 representations with 72^{+},112^{+},... 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 tensormeson production. The resulting baryon mass spectrum includes most of the prominent observed states. No wrong states are predicted. Some new resonances in the 2BeV region are suggested.
 Publication:

Physical Review
 Pub Date:
 November 1967
 DOI:
 10.1103/PhysRev.163.1646
 Bibcode:
 1967PhRv..163.1646C