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.
Work supported by the National Science Foundation.
Work supported by the Energy Research and Development Administration.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
T. P. Cheng and L. F. Li, to be published in the Phys. Rev. Letters.
J. D. Bjorken and S. Weinberg, submitted to the Phys. Rev. Letters.
J. D. Bjorken, K. Lane and S. Weinberg, in preparation.
F. Wilczek and A. Zee, submitted to the Phys. Rev. Letters.
For a related discussion of the weak interaction models and the uey process, see the report by H. Fritzsch to this conference.
S. Weinberg, Phys. Rev. Letters 19, 1264 (1967);
A. Salam, Elementary Particle Theory, edited by N. Svartholm, ( Almquist, Stockholm 1968 ).
Such an exercise has been considered before by S. Eliezer and D. A. Ross, Phys. Rev. D 10, 3080 (1974).
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).
G. Feinberg, Phys. Rev. 110, 1482 (1958).
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”.
By “mass-insertion” we mean either the expansion of the fermion propagator or perturbation of the symmetric theory by mass terms: mijΨiΨj
S. Parker, H. L. Anderson and C. Rey, Phys. Rev. 133B, 768 (1964).
Similar conclusion was reached by A. K. Mann and H. Primakoff, University of Pennsylvania preprint (1976).
A. Halprin, P. Minkowski, H. Primakoff, and S. P. Rosen, Phys. Rev. D 13, 2567 (1976);
T. P. Cheng, Univ. of Missouri-St. Louis report, 1975 (unpublished), and Phys. Rev. D 14, 1367 (1976).
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)].
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.
K. Fujikawa, B. W. Lee and A. I. Sanda, Phys. Rev. D 6, 2923 (1972);
Y. P. Yao, Phys. Rev. D7, 1647 (1973).
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.
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.
See for example, S. L. Glashow and S. Weinberg to be published in the Phys. Rev.
P. E. G. Baird et al. and E. N. Fortson et al. Nature 284, 528 (1976);C. Bouchiat’s talk at this conference.
J. D. Bjorken and C. H. Llewellyn Smith, Phys. Rev. D 7, 887 (1973); R. M. Barnett’s talk at this conference.
W. J. Marciano and A. I. Sanda (unpublished).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1977 Springer Science+Business Media New York
About this chapter
Cite this chapter
Cheng, TP., Li, LF. (1977). Muon Number Nonconservation in Gauge Theories. In: Perlmutter, A., Scott, L.F. (eds) Deeper Pathways in High-Energy Physics. Studies in the Natural Sciences, vol 12. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-1565-1_25
Download citation
DOI: https://doi.org/10.1007/978-1-4757-1565-1_25
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-1567-5
Online ISBN: 978-1-4757-1565-1
eBook Packages: Springer Book Archive