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SU(3)×SU(3), Symmetry Breaking, and Cabibbo Angle. II

J. C. Bane*

K. T. Mahanthappa†

  • University of Colorado, Boulder, Colorado 80302

  • University of Colorado, Boulder, Colorado 80302
  • Istituto di Fisica dell'Universitá, Rome, Italy

  • *Present address: Research and Development Division, E. I. du Pont de Nemours and Co., Wilmington, Del.
  • †Permanent address.
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Phys. Rev. D 3, 1446 – Published 15 March, 1971

DOI: https://doi.org/10.1103/PhysRevD.3.1446

Abstract

We construct bootstrap equations for symmetry-breaking vectors in (3¯,3)⊕(3,3¯) and (1,8)⊕(8,1) representations of the chiral SU(3)×SU(3) with both electromagnetic and nonleptonic driving terms which, being obtained from a current-current interaction with currents in (1,8)⊕(8,1) have parts belonging to both octet and 27-plet representations. Only one solution of these equations is chosen by requiring partial conservation of axial-vector current (PCAC) and the Cabibbo angle θC to have a nonzero value. It follows directly from the equations that the existence of the weak 27-plet driving term is a necessary condition to have a nonzero θC. The solution has the same form as that suggested by Gell-Mann, Oakes, and Renner for a semistrong symmetry-breaking interaction. Knowing the deviation from 2 in their work, we get θC≈0.22. The solution has both parity-conserving and parity-violating nonleptonic weak interactions in (1,8)⊕(8,1), and hence the strangeness-changing part cannot be rotated away. In our framework the electromagnetic tadpole cannot be in (3¯,3)⊕(3,3¯), but it can be in (8,1)⊕(1,8).

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Outline

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Phys. Rev. D 3, 1446– Published 15 March, 1971
  • Received 8 September 1970

© 1971 American Physical Society

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