Summary
A saturation scheme within an infinite set of states is proposed for the chiral algebra. Mesons are classified in the (35, anyL) representations ofSU 6×O 3, while the (56,L=even) and (70,L=odd) representations are chosen for baryons. A mixing operator exp [−iθZ] is proposed which transforms the axial charges of theSU 6 solution into the physical ones. The specific form we choose forZ gives rise to many predictions. All the axial couplings of the lower positive-parity meson states to π, ϱ and ω are obtained in terms of only one parameter and the results are in fair agreement with experiment. In particular, the B-meson is predicted to decay transversely, whileg 1/g0 ratio for the A1 is found to be −1/2. For the 1/2+ baryon octet, we getD/F=3/2 andG *=4/5G A (which impliesΓ Δ→Nπ=125 MeV) up to second order in the mixing angle θ. For eachSU 6×O 3 multiplet all the decays intoN+π are given in terms of only one parameter (at lowest possible order in the mixing angle) in general agreement with experiment. Finally, we are able to obtain strong restrictions on the chiral content of the 1/2+ octet, which are perfectly compatible with nature.
Riassunto
Si propone uno schema di saturazione dell'algebra chirale all'interno di un insieme infinito di stati. I mesoni sono classificati nelle rappresentazioni (35,L qualsiasi) diSU 6×O 3, mentre per i barioni si scelgono le (56,L pari) e (70,L dispari). Un operatore di mistura exp [−iθZ] viene proposto per trasformare le cariche assiali diSU 6 in quelle fisiche. La forma specifica scalta perZ dà luogo a molte predizioni. Gli accoppiamenti dei mesoni più bassi di parità positiva a π, ϱ ed ω si esprimono in termini di un solo parametro in buon accordo con i valori sperimentali. In particolare si prevede il decadimento traversale del mesone B, mentre par l'A1 il rapportog 1/g0 risulta −1/2. Per quanto concerne l'ottetto dei barioni 1/2+, otteniamo 3/2 perD/F e 4/5 perG */GA (che corrisponde a 125 MeV perΓ Δ→Nπ) sino al secondo ordine nel parametro θ. Per ciascun multipletto diSU 6×O 3 tutti i decadimenti inN+π si ottengono in termini di un solo parametro (all'ordine più basso possibile nell'angolo di mistura) in accordo generale con i dati sperimentali. Infine siamo in grado di ottenere forti restrizioni sul contenuto chirale dell'ottetto 1/2+, del tutto compatibile con la realtà fisica.
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Buccella, F., Kleinert, H., Savoy, C.A. et al. A mixing operator for theSU3×SU3 chiral algebra. Nuovo Cimento A (1965-1970) 69, 133–149 (1970). https://doi.org/10.1007/BF02728775
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DOI: https://doi.org/10.1007/BF02728775