Prog. Theor. Phys. Vol. 46 No. 6 (1971) pp. 1805-1836
ΔI=1/2 Rule, Lee-Sugawara Relation and Cabibbo's Weak Hamiltonian
Department of Physics, Osaka City University, Sumiyoshiku, Osaka
(Received May 19, 1971)
In this paper, we treat non-leptonic decays of hyperons, explicitly using the fact that there appear only charged currents in Cabibbo's weak Hamiltonian HW. For simplicity, we consider a system consisting only of octet baryons, decuplet baryons, octet pseudoscalar mesons, octet axial vector mesons and octet vector mesons. However, we take account of all possible three-point strong interactions. Under several assumptions about strong interactions, decay amplitudes are analyzed in the order g3G(, where g(G) is the strong (weak) coupling constant), because the amplitudes in the order gG are found to be negligible.
First, S-wave amplitudes are calculated in the following tow limits, i.e., the SU(3) limit and the soft pion limit. In these limits, it is shown that special Feynman graphs exhaust all the contributions to S-wave ampliutdes. Then, using time reversal invariance of HW, we obtain amplitudes which are the same (at some points) at those found by Suzuki and Sugawara. If only one additional condition is assumed, our results become consistent with experiment. Although our amplitudes are similar to those in the K*-exchange model, it should be noticed that the latter vanish in the soft pion limit, contrary to ours.
Secondly, we calculate P-wave amplitudes in the SU(3) limit, with the help of all possible Feynman graphs for hyperon decays, and investigate under what conditions the P-wave amplitudes thus obtained can be consistent with experiment. Then, it is found that the experimental P-wave amplitudes can be obtained only when understand the co-operative mechanism among various Feynman amplitudes.
DOI : 10.1143/PTP.46.1805
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