Rare decay modes of the K mesons in gauge theories

M. K. Gaillard and Benjamin W. Lee
Phys. Rev. D 10, 897 – Published 1 August 1974
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Abstract

Rare decay modes of the kaons such as Kμμ¯, Kπνν¯, Kγγ, Kπγγ, and Kπee¯ are of theoretical interest since here we are observing higher-order weak and electromagnetic interactions. Recent advances in unified gauge theories of weak and electromagnetic interactions allow in principle unambiguous and finite predictions for these processes. The above processes, which are "induced" |ΔS|=1 transitions, are a good testing ground for the cancellation mechanism first invented by Glashow, Iliopoulos, and Maiani (GIM) in order to banish |ΔS|=1 neutral currents. The experimental suppression of KLμμ¯ and nonsuppression of KLγγ must find a natural explanation in the GIM mechanism which makes use of extra quark(s). The procedure we follow is the following: We deduce the effective interaction Lagrangian for λ+Nl+l¯ and λ+N¯γ+γ in the free-quark model; then the appropriate matrix elements of these operators between hadronic states are evaluated with the aid of the principles of conserved vector current and partially conserved axial-vector current. We focus our attention on the Weinberg-Salam model. In this model, Kμμ¯ is suppressed due to a fortuitous cancellation. To explain the small KLKS mass difference and nonsuppression of KLγγ, it is found necessary to assume mPmP<<1, where mP is the mass of the proton quark and mP, the mass of the charmed quark, and mP<5 GeV. We present a phenomenological argument which indicates that the average mass of charmed pseudoscalar states lies below 10 GeV. The effective interactions so constructed are then used to estimate the rates of other processes. Some of the results are the following: KSγγ is suppressed; KSπγγ proceeds at a normal rate, but KLπγγ is suppressed; KLπνν¯ is very much forbidden, and K+π+νν¯ occurs with the branching ratio of 1010; K+π+ee¯ has the branching ratio of 106, which is comparable to the presently available experimental upper bound. The predictions of other models are briefly discussed. Relevant renormalization procedures and computational details are discussed in appendixes.

  • Received 4 March 1974

DOI:https://doi.org/10.1103/PhysRevD.10.897

©1974 American Physical Society

Authors & Affiliations

M. K. Gaillard*,‡ and Benjamin W. Lee†,‡

  • National Acceleratory Laboratory, Batavia, Illinois 60510

  • *On leave of absence from Laboratoire de Physique Théorique et Particules Elémentaires, Orsay (Laboratoire associé au CNRS), France.
  • On leave of absence from the Institute for Theoretical Physics, State University of New York, Stony Brook, New York 11790.
  • Operated by Universities Research Association Inc. Under Contract with the United States Atomic Energy Commission.

Comments & Replies

Comment on calculations of the KLμμ¯ decay rate in gauge theories

M. K. Gaillard, Benjamin W. Lee, and R. E. Shrock
Phys. Rev. D 13, 2674 (1976)

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Vol. 10, Iss. 3 — 1 August 1974

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