Normalization of the ππ Veneziano Model Using a Multiperipheral Model with π, K, and ω Exchange
Abstract
We consider a model of the AmatiBertocchiFubiniStanghelliniTonin (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 crossedchannel 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 Venezianomodel resonances with a cutoff at the mass of the J=3 resonance and with offshell 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 Veneziano 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.
 Publication:

Physical Review D
 Pub Date:
 March 1972
 DOI:
 10.1103/PhysRevD.5.1422
 Bibcode:
 1972PhRvD...5.1422B