A description is given of the K-matrix formalism. The formalism, which is normally applied to two-body scattering processes, is generalized to production of two-body channels with finalstate interactions. A multi-channel treatment of production of resonances has been worked out in the P-vector approach of Aitchison. An alternative approach, derived from the P-vector. gives the production amplitude as a product of the T-matrix for a two-body system and a vector Q specifying its production. This formulation, called Q-vector approach here, has also been worked out. Examples of practical importance are given.

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We con rm the existence of the two I G (J PC ) = 0 + (0 ++ ) resonances f 0 (1370) and f 0 (1500) reported by us in earlier analyses. The analysis presented here couples the nal states 0 0 0 , 0 0 and 0 of pp annihilation at rest. It is based on a 3 3 K{matrix. We nd masses and widths of M = (1390 30)MeV , ; = (380 80)MeV and M = (1500 10) MeV , ; = (154 30)MeV , respectively. The product branching ratios for the production and decay i n to 0 0 and of the f 0 (1500) are (1:27 0:33) 10 ;3 and (0:60 0:17) 10 ;3 , respectively.

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