Unitary symmetries, and their applications to high energy physics: by M. Gourdin. 303 pages, diagrams, 6 × 9 in. New York, John Wiley & Sons, and Amsterdam, North-Holland, 1967. Price $12.75

Abstract

We discuss the chiral lagrangian for JP = 12+ octet and JP = 32+ decuplet baryons in the language of the heavy particle effective theory. We show that the effective theory qualitatively reproduces the Pauli amplitudes for the nonleptonic hyperon decays, calculated recently by Trofimenkoff. We discuss the relation of our results to nonrelativistic SU(6). We argue that we can consistently classify the meson-baryon interaction terms in lowest order in the momentum expansion according to their transformation properties under nonrelativistic SU(6). Nevertheless, the theory as a whole remains explicitly Lorentz invariant. We explain why this does not run afoul of the theorems concerning interacting relativistic SU(6) theories. We use this SU(6) classification to discuss the relation between the nonleptonic Ω− decays and the nonleptonic decays of the octet baryons. We find that the Ω− decays cannot be explained by any interaction term transforming simply under SU(6) because the nonleptonic Ω− decays do not display the pronounced ΔI = 12 enhancement seen in the octet hyperon decays. Any explanation of the Ω− decays requires a fine tuning of the parameters in the effective theory. We speculate that this problem may point to a flow in the basic assumption that ΔI = 12 four-quark operators, universally enhanced by QCD, are the dominant mechanism behind the ΔS = 1 nonleptonic decays.