ar X iv : h ep - p h / 98 02 27 2 v 1 9 F eb 1 99 8 1 Reply to the criticism raised by Pennington on our ππ - Production Amplitudes

A recent criticism raised by M.R.Pennington on our ππ-production amplitudes seems to be due to his misunderstanding on our description, and is not right. Essential point of the relation between our scattering and production amplitudes is, in connection to the unitarity and the final state interaction theorem, briefly explained. Recently, we had analyzed the ππ-scattering phase shift 2), 3) *) and the ππ-production processes, pp-central collision 8), 9), 10) and J/Ψ → ωππ-decay, 11) and shown the evidence for existence of the long-sought σ-particle 12), 13). These results were reported in detail 14), 15), 16), 17), 18) in the international conference HADRON'97 at Brookhaven National Laboratory in August 1997. However, our description of ππ-production processes was criticized by M. R. Pennington in Ref. 1), " The production model of Ishida et al. and unitarity " : It was argued that in our description any production amplitude has a spurious zero at the same position of energy as that in the scattering amplitude. Here we explain briefly that his criticism is unfortunately based on his misunderstanding on our description and is not right. There are two general problems in treating scattering and production amplitudes: the ππ-scattering amplitude T must satisfy the unitarity relation, and the ππ-production amplitude F must satisfy, in cases with no initial phases, the final state interaction(FSI) theorem, that is, F must have the same phase 19) as that of T. In order to obtain T and F satisfying the unitarity and the FSI condition, respectively, we start from a simple field-theoretical model 20), 21), 22), 14), 18) : In the NJL-type model 23) as a low energy effective theory of QCD, (and in the linear σ model, LσM, 24) obtained as its local limit), or in the constituent quark model, the pion π and the resonant particles such as σ or f 0 (980) are the color-singlet q ¯ q-bound states and are treated on an equal footing. These " intrinsic quark dynamics states, " denoted as ¯ π, ¯ σ, ¯ f , are stable particles with zero widths and appear from the beginning. Actually these particles have structures and interact with one another and with a production channel " P " through the residual strong interaction: