Radiative Corrections in Nucleon-β-Decay and Electromagnetic Form Factors

  • G. Källen
Conference paper
Part of the Acta Physica Austriaca book series (FEWBODY, volume 3/1966)


The calculation of the radiative corrections in ordinary β-decay is reviewed with particular emphasize on the modifications necessary because of the fact that the nucleons are not point particles but have a finite extension. The calculations are conveniently performed in a particular gauge where the field operator renormalization constants are all finite (to order e2). In this gauge one obtains a finite result when one uses a dispersion theoretic approach and neglects all intermediate states with mesons. The result contains the strong interactions only through the conventional nucleon form factors and one new set of form factors which are not experimentally known today. However, in principle they can be observed from independent experiments.


Form Factor Radiative Correction Point Particle Mass Shell Electromagnetic Form Factor 
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References and Footnotes

  1. 1.
    Cf., e.g., T. Kinoshita and A. Sirlin, Phys. Rev. 113, 1652 (1959); Google Scholar
  2. S. M. Berman, Phys. Rev. 112, 267 (1958);ADSCrossRefGoogle Scholar
  3. S. M. Berman and A. Sirlin, Ann. Phys. 20, 20 (1962);ADSCrossRefGoogle Scholar
  4. L. Durand, L. F. Landowitz, R. B. Marr, Phys. Rev. 130, 1188 (1963). These papers contain references to earlier work by various authors.Google Scholar
  5. 2.
    S. S. Gershtein, I. B. Zeldovich, Soviet Phys. JETP, 2, 576 (1956);Google Scholar
  6. R. P. Feynman, M. Gell-Mann, Phys. Rev. 109, 193 (1958).MathSciNetADSMATHCrossRefGoogle Scholar
  7. 3.
    N. Cabibbo, Phys. Rev. Lett. 10, 531 (1963).CrossRefGoogle Scholar
  8. 4.
    The corresponding problem in u-particle decay offers no serious difficulty as the radiative corrections there turn out to be finite in the limit of point particles.Google Scholar
  9. 5.
    The notation used here is the same as in G. Källén, Quantenelektrodynamik, Handbuch der Physik V1, Springer (1958).Google Scholar
  10. 6.
    To obtain this result formally one also has to symmetrize the right hand side of Eq. (18) and replace Ipe(x) Ax(x) by 2{1Pe(x),Ax(x)}.Google Scholar
  11. 7.
    Cf. ‘ref. [5], esp. p. 303, Eq. (34,6).Google Scholar
  12. 8.
    At this stage we neglect the magnetic moment of the neutron as well as its charge distribution and consider only the static charge of the particle.Google Scholar
  13. 9.
    F. M. Pipkin, Proc. of the Oxford International Conference on Elementary Particles, September 1965.Google Scholar

Copyright information

© Springer-Verlag GmbH Wien 1966

Authors and Affiliations

  • G. Källen
    • 1
  1. 1.Department of Theoretical PhysicsUniversity of LundLundSweden

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