Muon Number Nonconservation in Gauge Theories

  • Ta-Pei Cheng
  • Ling-Fong Li
Part of the Studies in the Natural Sciences book series (SNS, volume 12)

Abstract

Recent rumors of possible observation at SIN (the Swiss Institute of Nuclear Research) of the famous μ→ey process has aroused a great deal of excitement. But the experimentalists themselves have so far not made any public statements; presupposition on our part about their actual result will of course be totally inappropriate. However, regardless of the ultimate outcome of this particular experiment the question of separate conservation of muon and electron number is an interesting and important problem to investigate, especially in the context of unified gauge theories of weak and electromagnetic interactions.

Keywords

Gauge Theory Neutrino Mass Heavy Neutrino Heavy Lepton Intermediate Vector Boson 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    T. P. Cheng and L. F. Li, to be published in the Phys. Rev. Letters.Google Scholar
  2. 2.
    J. D. Bjorken and S. Weinberg, submitted to the Phys. Rev. Letters.Google Scholar
  3. 3.
    J. D. Bjorken, K. Lane and S. Weinberg, in preparation.Google Scholar
  4. 4.
    F. Wilczek and A. Zee, submitted to the Phys. Rev. Letters.Google Scholar
  5. 5.
    For a related discussion of the weak interaction models and the uey process, see the report by H. Fritzsch to this conference.Google Scholar
  6. 6.
    S. Weinberg, Phys. Rev. Letters 19, 1264 (1967);CrossRefGoogle Scholar
  7. A. Salam, Elementary Particle Theory, edited by N. Svartholm, ( Almquist, Stockholm 1968 ).Google Scholar
  8. 7.
    Such an exercise has been considered before by S. Eliezer and D. A. Ross, Phys. Rev. D 10, 3080 (1974).Google Scholar
  9. However their μ→ey calculation has a number of problems: among others it does not satisfy the requirement of (electromagnetic) current conservation and the result has incorrect mass dependences. See also, S. M. Bilenky and B. Pontecorvo, Phys. Letters 61B, 248 (1976).Google Scholar
  10. 8.
    G. Feinberg, Phys. Rev. 110, 1482 (1958).CrossRefGoogle Scholar
  11. 9.
    This cancellation only requires that the electron and muon couple to independent fields. This is reminiscent of the cancellation needed to suppress aGF amplitudes for strangeness changing neutral current effects first discussed by S. L. Glashow, J. Iliopoulos, and L. Maiani, Phys. Rev. D 2, 1285 (1970). We shall call it “leptonic GIM mechanism”.Google Scholar
  12. 10.
    By “mass-insertion” we mean either the expansion of the fermion propagator or perturbation of the symmetric theory by mass terms: mijΨiΨjGoogle Scholar
  13. 11.
    S. Parker, H. L. Anderson and C. Rey, Phys. Rev. 133B, 768 (1964).CrossRefGoogle Scholar
  14. 12.
    Similar conclusion was reached by A. K. Mann and H. Primakoff, University of Pennsylvania preprint (1976).Google Scholar
  15. 13.
    A. Halprin, P. Minkowski, H. Primakoff, and S. P. Rosen, Phys. Rev. D 13, 2567 (1976);CrossRefGoogle Scholar
  16. T. P. Cheng, Univ. of Missouri-St. Louis report, 1975 (unpublished), and Phys. Rev. D 14, 1367 (1976).CrossRefGoogle Scholar
  17. 14.
    In this theory the electron and muon neutrios are two non-orthogonal combinations of the mass eigen-states v and v’: ve = αv + βv’ and vμ= γv + δv’, with (ve · vμ) = αγ + βδ = cosøsinø) memμ(m2-m’2)/m2m’2 Thus vμ + p → e + n can take place with a very small probability. This phenomenon is distinct from the question of “neutrino oscillations” as discussed by B. Pontecorvo, Zh. Eksp. Teor. Fix. 53, 1717 (1967) [Soviet Phys. JETP 26, 934 (1968)].Google Scholar
  18. 15.
    Since our one loop result involves a small factor 6N, multiloop contributions (especially those involving virtual photons) may not be small. Preliminary calculations indicate that they are indeed negligible. In this connection we can use the theorem of G. Feinberg, P. Kabir and S. Weinberg [Phys. Rev. Letters 527 (1959)] to deduce that certain two loop diagrams which are individually large will be cancelled when all diagrams of the same order are summed.Google Scholar
  19. 16.
    K. Fujikawa, B. W. Lee and A. I. Sanda, Phys. Rev. D 6, 2923 (1972);CrossRefGoogle Scholar
  20. Y. P. Yao, Phys. Rev. D7, 1647 (1973).Google Scholar
  21. 17.
    T. P. Cheng and L. F. Li, in preparation. Details of all our calculations on μ→ey, K→eμ, p→3e and μN→eN, etc. will be given in this paper.Google Scholar
  22. 18.
    S. B. Treiman, F. Wilczek and A. Zee (in preparation), and Ref. 17; A. Pais, talk at the Symposium “Five Decades of Weak Interactions”, City College of New York, Jan. 21–22, 1977.Google Scholar
  23. 19.
    See for example, S. L. Glashow and S. Weinberg to be published in the Phys. Rev.Google Scholar
  24. 20.
    P. E. G. Baird et al. and E. N. Fortson et al. Nature 284, 528 (1976);C. Bouchiat’s talk at this conference.Google Scholar
  25. 21.
    J. D. Bjorken and C. H. Llewellyn Smith, Phys. Rev. D 7, 887 (1973); R. M. Barnett’s talk at this conference.Google Scholar
  26. 22.
    W. J. Marciano and A. I. Sanda (unpublished).Google Scholar

Copyright information

© Springer Science+Business Media New York 1977

Authors and Affiliations

  • Ta-Pei Cheng
    • 1
  • Ling-Fong Li
    • 2
  1. 1.University of Missouri-St. LouisSt. LouisUSA
  2. 2.Carnegie-Mellon UniversityPittsburghUSA

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