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-dody weak interactions), and octet-spurion formalism and tadpole model are derived. The decupletbaryon-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 ia< 7 ) and j 5 a< 7 > (Assumption II) to the scalar-and psuedoscalar 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 HI--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 Av(n) """'d·A 8 (n) """'e·AB (n) holds for any n (decay mode) and ~ (F/D-ratio of strong meson-baryon ps(ps) interaction) ""'"'(0.5""--'0.6), where Av(n), A 8 (n) and AB(n) mean the S-wave hyperon decay amplitudes due to the K*-, K-and baryon-poles, respectively, and d and e are constants. Numerical values of d and e and the scalar (pseudoscalar) spurion coupling,
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The opzmons e"pressea in thest columns do not necessarily reflect those of the Board of Editon. Communications should be submztted m duplicate and should be held to wtthm 100 lines (pica type) on standard stze letter paper (appro>:. 21 X 30cm.), so that each letter will be arranged into two pages when printed. Do not forget to count zn enough space for formulas, figures or tables.Recently Puppi et aUJ have pointed out a discrepancy between the dispersion relation for the n--p scattering amplitude and the experiments. In this note we reinvestigate the dispersion relation for the ( 3, 3) Pwave amplitude with new data available • now and show that there is a certain discrepancy similar to Puppi' s case.For this purpose we follow the analysis by Cini et al. 2 l in their determination of the coupling constant using the Chew-Low equation, since the P-wave dispersion re-lations3J are reduced to the Chew-Low equation with the point source in the static limit. Cini's analysis involves only those data at energies higher than 100Mev (meson kinetic energy in lab. sys.) and . we can now avail ourselves of some data at energies lower than that energy. According .to Cini the dispersion relation for the (3,3) amplitude is approximated to the relation with X(w ) = L_ P J" _dwr,and where q and lOq are the momentum ancf the energy of the meson in the center ofmass system. r is the rationalized renormalized coupling constant. If we restrict ourselves below the resonance energy, eq.(1) holds with great accuracy. We can. check the consistency if we substitute the empirical data for the l.h.s. of eq. ( 1) . In calculating X ( lOq) we use Anderson's. empirical formula tan as1=0.2375l/(l+0.75p2) (1.95-w,,) (4) for the energy less than 300 Mev. The numerical calculations are done with great care, because there is a principal integral in X ( wq) . The results are shown in Figs. 1 and 2. In Figs. 3 and 4 we plot the-at University of Hawaii, PBRC, Kewalo Marine Lab.
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