Summary
The possibility that the existing strongly interacting particles correspond to the simplest self-consistent solution of a dispersion-theoretic bootstrap model is considered. A generalization of the Chew reciprocal bootstrap model is applied to baryons. Three simple self-consistency requirements are postulated. It is shown that the Hermitean property of the unreduced elastic crossing matrix favors a low spin value for the ground-state baryon multiplet. Attention is then limited toSU 3-invariant schemes of particles. The physical, octet-decuplet particle set, known from several previous works to satisfy similar models, is a solution to the present model. The hypotheses that the ground-state baryon multiplet corresponds to anSU 3 singlet, triplet, or sextet do not lead to a solution involving fewer particles than the octet-decuplet solution. TheF/D interaction angle in the octet-decuplet solution is 31.8°. There is a moderately strong attraction in theP 1/2 states of the representation 10* in this solution.
Riassunto
Si considera la possibilità che le esistenti particelle con interazione forte corrispondano a semplici soluzioni autocoerenti di un modello a bootstrap in teoria della dispersione. Si applica ai barioni una generalizzazione del modello di bootstrap reciproco di Chew. Si postulano tre semplici condizioni di autocoerenza. Si dimostra che la proprietà hermitiana della matrice di incrocio elastica non ridotta favorisce un basso valore dello spin per il multipletto barionico dello stato fondamentale. Si limita quindi l’attenzione a schemi di particelle invarianti nelleSU 3. Il gruppo di particelle dell’ottetto-decupletto fisico, di cui si sa da numerosi lavori precedenti che soddisfa modelli analoghi, è una soluzione del modello qui esposto. Le ipotesi che il multipletto barionico dello stato fondamentale corrisponda ad un singoletto, tripletto o sestetto nellaSU 3 non portano a soluzioni che interessano un numero minore di particelle della soluzione dell’ottetto-decupletto. L’angolo di interazioneF/D nella soluzione di ottettodecupletto è 31.8°. In questa soluzione si ha un’attrazione moderatamente forte negli statiP 1/2 della rappresentazione 10*.
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References
R. H. Capps:Phys. Rev.,134, B 460 (1964).
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In general it is the full crossing matrix (defined in Sect. IIIA of ref. (1)), rather than the elastic crossing matrix, that satisfies the conditionC 2=1. However, in all the examples considered in this paper except that of Sect.3 4,SU 3-invariance and angular-momentum conservation forbid inelastic processes in the (i, m) representation. In these cases the elastic and inelastic parts ofC are not connected, and the conditionC 2=1 applies separately to either part.
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Capps, R.H. SU 3-Invariant solutions to a reciprocal bootstrap model. Nuovo Cim 34, 932–945 (1964). https://doi.org/10.1007/BF02812522
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DOI: https://doi.org/10.1007/BF02812522