Amelioration of Divergence Difficulties in the Theory of Weak Interactions

Phys. Rev. 179, 1518 – Published 25 March 1969
Murray Gell-Mann, Marvin L. Goldberger, Norman M. Kroll, and Francis E. Low


A new approach to the problem of the singularity of the weak interactions is presented. Its aim is to provide a theoretical interpretation of the extreme smallness of the violation of selection rules associated with the weak-vector-current operator appearing in the conventional Fermi or intermediate-vector-boson interaction Lagrangian. To illustrate what we have in mind, we note that on account of this singular character, the conventional theories have not yet yielded an understanding of the weakness of strangeness and parity violation in hadronic processes and the weakness of semileptonic neutral decays. We begin with an interaction Lagrangian in which the constituents of the conventional weak current (e.g., strangenesschanging, axial-vector, muonic, etc.) are coupled to possibly distinct local vector operators. This is done in such a way that the effective weak interaction between two currents decomposes into two parts, one having the universality of the weak interaction, the other, called diagonal, acting only between a constituent and itself. It is then possible to transfer the singularity of the weak interaction to the diagonal interaction and to impose any desired degree of symmetry upon the singular part of the diagonal interaction. Two realizations of this approach are presented. Both are intermediate-boson theories involving gradient-coupled spin-0 bosons as well as spin-1 bosons. An important consequence of these theories is that, apart from implying a lower bound, the weak interactions give no indication of the magnitude of the diagonal interactions. Thus while the scattering of μ-neutrinos by electrons should be governed by the conventional universality formula, there is no reason to expect universality to hold for the scattering of e-neutrinos by electrons.


  • Received 5 August 1968
  • Published in the issue dated March 1969

© 1969 The American Physical Society

Authors & Affiliations

Murray Gell-Mann

  • Institute for Advanced Study, Princeton, New Jersey 08540 and Physics Department, California Institute of Technology, Pasadena, California 91109

Marvin L. Goldberger

  • Institute for Advanced Study, Princeton, New Jersey 08540 and Palmer Physical Laboratory, Princeton University, Princeton, New Jersey 08540

Norman M. Kroll

  • Institute for Advanced Study, Princeton, New Jersey 08540 and Department of Physics, University of California, San Diego, La Jolla, California 92037

Francis E. Low

  • Institute for Advanced Study, Princeton, New Jersey 08540 and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

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