A Solution to the Yamaguchi Paradox : Particles and Fields
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概要
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From the point of view the S-matrix, Yamaguchi has studied unstable particles by the weak interaction (like K_s→ππ). He reaches the unconventional conclusion that the decay amplitudes are solely given by the weak interaction, without final state strong interaction (FSI) phases. His conclusions are based on the hypothesis that a good approximation would be to consider only, among the eigenvalues of the S-matrix, a single resonant phase shift dominated by the weak interaction. We analyse his arguments and solve the paradox by studying the behaviour of eigenvalues and eigenvectors of a typical resonant S-matrix. We find that, in general, when the FSI phases are not small, one cannot isolate a single resonant eigenphase shift. All eigenphase shifts have a rapid jump at the resonance energy and can therefore affect the resonance behaviour. We find the result that the decay amplitudes must be affected, in the usual way, by the FSI strong phases. We discuss further the situation in which all the FSI are small, where Yamaguchi's hypothesis seems more plausible. There is then indeed a single resonant phase shift and the rest of the phase shifts are rapidly varying but small. We find that their effect is indeed negligible, but the effect of the FSI phases appears due to the quick rotation, near the resonant energy, of the S-matrix eigenstate. Lastly, we show that it is possible to construct an ad hoc S-matrix satisfying Yamaguchi's Ansatz, that is, however, rather unphysical.
- 理論物理学刊行会の論文
- 1993-07-25
著者
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Oliver L.
Laboratoire De Physique Theorique Et Hautes Energies Universite De Paris-sud
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YAOUANC A.Le
Laboratoire de Physique Theorique et Hautes Energies Universite de Paris-Sud
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RAYNAL J.-C.
Laboratoire de Physique Theorique et Hautes Energies Universite de Paris-Sud