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Theory of Higher-Order Weak Interactions and CP-Invariance Violation. I. Leptonic Processes

Kenneth Lane* and Alan Chodos

  • Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104

  • *Present address: Department of Physics, University of California, Berkeley, Calif. 94720.
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Phys. Rev. D 6, 581 – Published 15 July, 1972

DOI: https://doi.org/10.1103/PhysRevD.6.581

Abstract

In order to cure the divergence difficulties of higher-order weak interactions, we propose a theory in which the usual current × current Lagrangian is modified by inserting the non-polynomial factor exp[fϕ†ϕ(x)], where ϕ is a charged scalar field. We show that, as a result, the usual first-order weak amplitudes are unchanged, while second-order leptonic scattering amplitudes are finite. Explicit formulas are given for lepton-lepton scattering and the logarithmically divergent lepton self-mass. A discussion of Nth order is presented, in which it is shown that the naive degree of divergence is independent of order, and the superpropagator to all orders is derived. The groundwork is laid for the discussion in a following paper of hadronic processes and the appearance of CP violation as a higher-order weak effect.

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  14. Omitted endnote

  15. Omitted endnote

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Phys. Rev. D 6, 581– Published 15 July, 1972
  • Received 2 December 1971

© 1972 American Physical Society

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