AnSU4 unified scheme for weak interactions
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Summary
In order to unify the treatment of the purely leptonic interactions and of the leptonic decays of baryons, a general scheme is proposed including into a single isobaric state of the regular representation ofSU4 all weakly interacting fermions, both baryons and leptons. The definition of the charge operator inSU4 as an extension of the usual one inSU3 is discussed in order to obtain the best agreement with the known particles. For what concerns the interaction it is then shown that, in order to agree with the experimental evidence, one has from one side to reduce the symmetry to that of the subgroupSU2 and from the other side, to rotate the strongly interacting baryonic states in respect to the weakly interacting ones according to the Cabibbo transformation. The scheme is thus able to yield in a unified way results similar to Gatto’s theory for leptons and to Cabibbo’s theory for leptonic decays of baryons.
Riassunto
Allo scopo di unificare il trattamento delle interazioni puramente leptoniche e dei decadimenti leptonici dei barioni, viene proposto uno schema che include in un unico stato isobarico della rappresentazione regolare del gruppoSU4 tutti i fermioni interagenti debolmente, siano essi barioni o leptoni. Si discute la definizione dell’operatore di carica nell’SU4 in modo che includa la definizione usuale di esso nell’SU3 e si presti nel contempo ad interpretare le cariche delle particelle note. Per ciò che riguarda le interazioni, si fa vedere che per soddisfare le prove sperimentali, occorre da un lato ridurre la simmetria dell’SU4 all’SU2, e d’altro lato ruotare gli stati barionici interagenti fortemente rispetto a quelli interagenti debolmente mediante la trasformazione di Cabibbo. Lo schema così ottenuto permette di riottenere in modo coordinato tanto i risultati di Gatto relativi alle interazioni leptoniche quanto quelli di Cabibbo relativi ai decadimenti iperonici.
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References
- (1).R. Gatto:Nuovo Cimento,28, 567 (1963).MathSciNetCrossRefGoogle Scholar
- (2).N. Cabibbo:Phys. Rev. Lett.,10, 531 (1963);12, 62 (1964).ADSCrossRefGoogle Scholar
- (3).W. Krolikowski:Nucl. Phys.,52, 342 (1964).MathSciNetCrossRefMATHGoogle Scholar
- (4).SU 4 formalisms have been proposed by several authors, but mainly for baryons and mesons.P. Tarjanne andV. L. Teplitz:Phys. Rev. Lett.,11, 447 (1963);Y. Hara:Phys. Rev., B134, 701 (1964);Z. Maki andY. Ohnuki:Prog. Theor. Phys. (in press). The last paper is related with the Nogaya model.ADSCrossRefGoogle Scholar
- (5).A. O. Barut:Nuovo Cimento,32, 234 (1964).MathSciNetCrossRefMATHGoogle Scholar
- (6).F. Paccanoni: private communication. See, for example,L. Pontrayagin:Topological Groups (Princeton, N. J., 1958). We are indebted to ProfessorJ. M. Jauch and Dr.F. Paccanoni for valuable discussions with respect to this point.Google Scholar
- (7).T. Toyoda:Journ. of Japan Phys. Soc. (in press). The mathematical part of the present paper, the representation ofSU 4 and the relation betweenSU 4 and the complex Lorentz group, was presented by one of the authors (T.T.) at a CERN Seminar (May, 1964).Google Scholar
- (8).T. Toyoda:Nuovo Cimento,32, 1721 (1964).CrossRefMATHGoogle Scholar