Summary
Neutral pion decay is studied quantitatively with dispersion relation techniques. The process is pictured as proceeding mainly through pion disintegration into baryon pairs, the latter annihilating to produce the photons. In detail we take into account only the nucleon pair, as representative of baryon pair contributions generally. The final expression for the decay rate has a structure very different from what one obtains in perturbation theory. It turns out, however, that the numerical results are not appreciably different.
Riassunto
Si studia quantitativamente il decadimento neutro dei pioni servendosi delle relazioni di dispersione. Si immagina il processo come se si svolgesse principalmente con la disintegrazione di pioni in coppie di barioni e questi si annichilassero producendo i fotoni. Teniamo dettagliatamente conto solo della coppia di nucleoni quali rappresentanti generici dei contributi della coppia di barioni. L’espressione finale per il tasso di decadimento ha una struttura molto differente da quella che si ottiene in teoria delle perturbazioni. Risulta, tuttavia, che i risultati numerici non sono sensibilmente differenti.
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In reference (1),K(ξ) was normalized toK(-m -2 π )=√ -2 G. Here we normalize toK(-m 2 π )=1.
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Supported in part by the Air Force Office of Scientific Research, Air Research and Development Command.
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Goldberger, M.L., Treiman, S.B. Neutral pion decay. Nuovo Cim 9, 451–460 (1958). https://doi.org/10.1007/BF02725101
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DOI: https://doi.org/10.1007/BF02725101