Normalization of the ππ Veneziano Model Using a Multiperipheral Model with π, K, and ω Exchange
We consider a model of the Amati-Bertocchi-Fubini-Stanghellini-Tonin (ABFST) type with ω and K exchange, in addition to the usual pion exchange. Instead of using the usual formalism, we sum the ABFST ππ-->ππ graphs approximately by projecting out into crossed-channel partial waves (which can be continued to unphysical angular momenta) and constructing a diagonal Padé approximant. This satisfies unitarity exactly in the elastic region of that channel. In practice only the [1, 1] approximant was considered. The relevant graphs are then built up from ππ-->ππ, ππ-->πω, and ππ-->KK¯ input kernels, each of which is approximated by Veneziano-model resonances with a cutoff at the mass of the J=3 resonance and with off-shell effects neglected. By requiring that there be an output pole at t~=0 in the unphysical I=1, J=12ππ state and that its residue be consistent with the one predicted by the ππ Venezia-no model, we can determine the normalization coefficient β¯ of that model. We obtain β¯=0.65, which corresponds to a ρ width of 135 MeV.
Physical Review D
- Pub Date:
- March 1972