Low-Energy Behaviors of the T=0, S-Wave, π-π Scattering Phase Shift and a Possible Scalar Meson Nonet

概要

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All the possible low-energy behaviors of the T=0, S-wave π-π phase shift δ(k) are investigated using the effective range formula. It is found that there exists a case satisfying the conditions (1) that the phase shift δ(k) rises through π/2 at about the p-meson mass without any appreciable bump in the cross section around this point and (2) that the scattering length is small, say 0.5m^<-1>_π or smaller. The values of the scattering length a and the effective range r are severely restricted by the above two conditions (1) and (2), that is, a≈-r≈ 0.5m^<-1>_π, which is compatible with the recent result of Weinberg both in sign and in magnitude. If we allow a broad enhancement in the lower energy region or if we take a larger value for the position of the phase shift passing through π/2, then we can get a smaller scattering length. A possible scalar meson nonet associated with this phenomenon is proposed.
理論物理学刊行会の論文
1967-02-25