Saturation of Superconvergence Relations for Meson-Baryon Scattering
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概要
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The superconvergence relations are assumed to hold for the meson(P)-baryon(B) forward scattering amplitudes subtracted by the Regge asymptotic terms. The consequences of the assumption that the imaginary parts of the amplitudes at low energy are approximately saturated by the 1/2^+ octet (B) and the 3/2^+ decuplet (D) pole contributions are investigated in the framework of the exact SU(3) symmetry. The amplitudes at high energy are assumed to be dominated by the contributions from the exchanges of the Pomeranchuk, tensor octet (T) and vector octet (V) trajectories. Under these assumptions, the consideration of the amplitudes B^<(+)>(ν) and M^<(-)>(ν) leads to a set of seven algebraic relations (sum rules) between eight coupling parameters, which can be solved in terms of the BBP coupling constant. Therefore if the experimental values of g^2_<NNπ> and the degenerate masses (mean masses) of D, B and P are employed, the remaining parameters are completely determined. The results for the BBP and the DBP coupling constants agree with the characteristic features of experiments and some part of them just reduces to the SU(6) predictions in an appropriate limit. However, most of the results for high energy parameters are in bad agreement with experiment. On the other hand, it is pointed out that the superconvergence relations for the amplitudes M^<(+)>(ν)/ν in the same approximation lead to a set of four algebraic relations which has no nontrivial solution provided that the values of M^<(+)>(0) are approximately given by Adler's consistency condition. It should be noted that we do not take into account the Regge pole exchange contyibution to the imaginary part of the amplitude at low energy. In connection with this point, the way of decomposing the amplitude into the direct pole term and the Regge asymptotic term is discussed in the light of the superconvergence relations.
- 理論物理学刊行会の論文
- 1968-01-25
著者
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Miyamura Osamu
Department Of Applied Mathematics Faculty Of Engineering Science Osaka University
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Takagi Fujio
Department Of Basic Sciences Ishinomaki Senshu University
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Takagi Fujio
Department Of Physics Tohoku University
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