Summary
The finite-energy sum rules derived in the preceeding article are converted into a set of integral constraints on the reaction - N N → ππ. These sum rules provide information about the first eight partial waves for this reaction. Zeros above threshold are found for almost all partial waves, as well as strong evidence for background or daughters in the lower ones (J ⩽ 3). ForJ=4 and 5, daughters are less evident. Application to Regge-residue parameters for P′ and ρ suggest that these residues «turn over» at large, positivet but do not charge sign. Values for the P′ residues indicate that theA (+) amplitude does not satisfy an unsubtracted dispersion relation.
Riassunto
Si convertono le regole di somma di energia finita dedotta nell’articolo precedente in un insieme di vincoli integrali alla reazione - N N → ππ. Queste regole di somma dànno informazioni sulle prime otto onde parziali di questa reazione. In quasi tutte le onde parziali si trovano zeri al di sopra della soglia; si trovano anche forti prove di un fondo o di figlie nelle onde parziali inferiori (J ⩽ 3). PerJ=4 e 5 le figlie sono meno evidenti. L’applicazione ai parametri dei residui di Regge per P′ e ρ suggerisce che questi residui «si rovesciano» pert grande, positivo, ma non cambiano segno. I valori dei residui di P′ indicano che l’ampiezzaA (+) non soddisfa una relazione di dispersione non sottratta.
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Supported in part by the National Science Foundation under Grant NSF GP 8748.
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Sandusky, J.C. Finite-energy sum rules on hyperbolas. — II. Nuov Cim A 6, 627–638 (1971). https://doi.org/10.1007/BF02723393
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DOI: https://doi.org/10.1007/BF02723393