Summary
The Lovelace-Faddeev three-particle bound-state scattering equations for a system of two pions and one baryon are used as a model where the baryons are assumed to be pion-baryon bound states. Only the case of static baryons and no ππ forces is considered. The equivalence of this model to another with physically dressed baryons is demonstrated. The equations are also solved exactly in a closed analytic form satisfying three-particle unitarity. As an illustration, the masses of theI=J nonstrange baryon sequence are calculated without using scattering data in a way indicating the possibility of self-consistency. The calculated (5/2, 5/2) mass agrees with a possible, but still doubtful, π+π+p enhancement.
Riassunto
Si usano le equazioni dello scattering dello stato legato di tre particelle di Lovelace-Faddeev per un sistema di due pioni ed un barione come un modello in cui si suppone che i barioni siano stati legati pione-barione. Si considera solo il caso di barioni statici senza forze ππ. Si dimostra l’equivalenza fra questo modello ed un altro con barioni fisicamente vestiti. Si risolvono anche esattamente le equazioni in forma analitica chiusa, che soddisfa l’unitarietà di tre particelle. Come illustrazione si calcolano le masse della sequenza di barioni non straniI=J senza far uso dei dati di scattering in un modo che indica la possibilità dell’autocoerenza. La massa calcolata (5/2, 5/2) concorda con un possibile, ma ancora dubbio, accrescimento π+π+p.
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Kronfli, N.S. Bound-state theory of particles: TheJ=I baryon resonances. Nuovo Cimento A (1965-1970) 57, 125–139 (1968). https://doi.org/10.1007/BF02824441
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DOI: https://doi.org/10.1007/BF02824441