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On the renormalization of the axial vector β-decay coupling

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Il Nuovo Cimento (1955-1965)

Summary

A formula expressing the ratiog A/gv in β-decay on the basis of equality of the corresponding bare coupling constants is proposed and proved in perturbation theory with cut-off, provided electromagnetic interactions are neglected. The physical background of a formula of this type is discussed and illustrated by comparison with recent work byGoldberger andTreiman on π-μ decay.

Riassunto

Si propone, e si dimostra in teoria delle perturbazioni con cut-off, una formula che dà il rapportog A/gV nel decadimento β ove si postuli l’eguaglianza delle corrispondenti costanti d’accoppiamento nude, purchè si trascurino le interazioni elettromagnetiche. Si discutono i fondamenti fisici di una formula di questo tipo e si illustrano confrontandoli con recenti lavori diGoldberger eTreiman sul decadimento π-μ.

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References

  1. Cfr.Proc. of the Annual International Conference on High Energy Physics at CERN (1958), p. 258.

  2. The author is grateful to Prof.W. Pauli for a stimulating letter in which this was pointed out. Of course, one thinks here always in terms of the first order of the weak coupling constant. It might be remarked here that higher orders are not necessarily untractable since their non-renormalizability refers to a power development also in the strong couplings.

  3. M. L. Goldberger andS. B. Treiman:Phys. Rev.,111, 354 (1958). We prefer to use in the present article the notation ofBethe, Schweber andde Hoffman:Mesons and fields, vol.1.

    Article  ADS  MATH  Google Scholar 

  4. H. J. Bremermann, R. Oehme andJ. G. Taylor:Phys. Rev.,109, 2178 (1958).

    Article  MathSciNet  ADS  Google Scholar 

  5. G. Källén:Quantum electrodynamics, in:Encyclopedia of Physics, vol.5, part I, pp. 362–363.

  6. G. Källén:Consistency problems in quantum electrodynamics, CERN 57-43, andCERN Symposium, vol.2 (1956), p. 187.

    MATH  Google Scholar 

  7. R. P. Feynman andM. Gell-Mann:Phys. Rev.,109, 193 (1958). That a divergence-free strangeness-nonconserving axial vector current is ruled out experimentally has been shown byGoldberger andTreiman (Phys. Rev.,110, 1478 (1958)).

    Article  MathSciNet  ADS  Google Scholar 

  8. P. Federbush, M. L. Goldberger andS. B. Treiman:Electromagnetic structure of the nucleon (Phys. Rev.,112, 642 (1958)).

    MathSciNet  Google Scholar 

  9. Seee.g. I. Ya. Pomerančuk, V. V. Sudokov andK. A. Ter-Martirosyan:Phys. Rev.,103, 784 (1956), and also some unpublished work byW. Thirring.

    Article  MathSciNet  ADS  Google Scholar 

  10. Y. Nambu:Nuovo Cimento,6, 1064 (1957) and9, 610 (1958);K. Symanzik:Progr. Theor. Phys.,20, 690 (1958).

    Article  MathSciNet  MATH  Google Scholar 

  11. G. F. Chew:The bare particle concept and nucleon electromagnetic structure, UCRL-8194.

  12. S. D. Drell andF. Zachariasen:Phys. Rev.,111, 1727 (1958).

    Article  MathSciNet  ADS  Google Scholar 

  13. M. L. Goldberger andS. B. Treiman:Phys. Rev.,110, 1178 (1958).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. R. E. Norton andW. K. R. Watson:Phys. Rev.,110, 996 (1958).

    Article  ADS  Google Scholar 

  15. Y. Takahashi:Nuovo Cimento,6, 371 (1957).

    Article  Google Scholar 

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Symanzik, K. On the renormalization of the axial vector β-decay coupling. Nuovo Cim 11, 269–277 (1959). https://doi.org/10.1007/BF02859720

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  • DOI: https://doi.org/10.1007/BF02859720

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