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Prog. Theor. Phys. Vol. 38 No. 2 (1967) pp. 388-416

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On Nonleptonic Decays

— Interrelation among Various Types of Effective Weak Interactions —

Kanji Fujii, Mitsuo Imoto,* Shoichiro Kawasaki,** Shin-ya Furui*** and Tetsuya Tsuchida***

Institute for Nuclear Study, University of Tokyo, Tanashi-machi, Kitatama-gun, Tokyo
*Department of Physics, College of Science and Engineering, Nihon University, Tokyo
**Department of Physics, College of Arts and Sciences, Chiba University, Chiba
***Department of Physics, Ibaraki University, Mito

(Received December 28, 1966)

Abstract:

Interrelation among effective weak Yukawa interactions and various types of two-body weak interactions is discussed, and the refinement of the pole approximation is given. For this purpose, relations among three assumptions are investigated. Assumption I proposed by Fujii and Terazawa leads to the soft-meson theorem, owing to which one can relate the strong scattering amplitudes (the strong vertices) to the weak vertices (the effective two-body weak interactions), and octet-spurion formalism and tadpole model are derived. The decuplet-baryon-pole contributions to the hyperon decays are estimated in accordance with Assumption I and are shown to be relatively small.
Relation of the effective two-body transition defined by using appropriate neutral currents jα(7) and j5α(7) (Assumption II) to the scalar- and pseudoscalar densities is discussed. It is shown first that the effective two-body transition derived from Assumption II can be regarded as approximately proportional to the scalar- and pseudoscalar densities with appropriate SU(3)-transformation properties, and secondly that, using the F-type vector current, one can obtain favourable values for the ratios of coupling constants of the effective two-body weak transition.
In the framework of the pole approximation, when one combines Assumption I (or Assumption III–approximate Goldberger-Treiman relation) with Assumption II one can obtain the relations derived from Assumption III (or I). As a result, it is shown that the relation
AB(n) ≈d·AS(n) ≈e·AB(n)
holds for any n (decay mode) and ξ (F/D-ratio of strong meson-baryon ps(ps) interaction) ≈ (0.5 ∼0.6), where AV(n), AS(n) and AB(n) mean the S-wave hyperon decay amplitudes due to the K*-, κ-and baryon-poles, respectively, and d and e are constants. Numerical values of d and e and the scalar (pseudoscalar) spurion coupling, <κ10>0(<K10>0), depend upon the model of S-wave meson-baryon scattering. The inequality
(<κ10>0)2 ≫(<K10>0)2
holds generally, irrespective of the magnitude of S-wave damping. Without the S-wave damping one cannot reproduce the K10 →2π probability in the framework of meson-pole approximation.


URL : http://ptp.ipap.jp/link?PTP/38/388/
DOI : 10.1143/PTP.38.388

[ Full Text PDF : FREE ACCESS (1815K) ] Citation:

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  5. Progress of Theoretical Physics Vol. 40 No. 1 (1968) pp. 114-123 :
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  7. Progress of Theoretical Physics Vol. 40 No. 5 (1968) pp. 1183-1184 :
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  9. Progress of Theoretical Physics Vol. 42 No. 6 (1969) pp. 1485-1487 :
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  10. Progress of Theoretical Physics Vol. 43 No. 1 (1970) pp. 125-143 :
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  11. Progress of Theoretical Physics Vol. 43 No. 3 (1970) pp. 789-798 :
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  12. Progress of Theoretical Physics Vol. 44 No. 2 (1970) pp. 473-485 :
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  13. Progress of Theoretical Physics Vol. 45 No. 3 (1971) pp. 833-853 :
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  14. Progress of Theoretical Physics Vol. 45 No. 6 (1971) pp. 1944-1954 :
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  15. Progress of Theoretical Physics Vol. 47 No. 1 (1972) pp. 332-333 :
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  16. Progress of Theoretical Physics Vol. 47 No. 4 (1972) pp. 1430-1432 :
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  17. Progress of Theoretical Physics Vol. 51 No. 6 (1974) pp. 1971-1972 :
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  18. Progress of Theoretical Physics Vol. 55 No. 5 (1976) pp. 1582-1590 :
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  19. Progress of Theoretical Physics Vol. 58 No. 6 (1977) pp. 1849-1858 :
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  20. Progress of Theoretical Physics Vol. 59 No. 5 (1978) pp. 1600-1612 :
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