Relativistic three-pion dynamics in the ω channel

Abstract

An extensive numerical study is made of an integral equation for the generalised isobar amplitudes (satisfying two-body unitarity and analyticity) in the I^GJ^P=0^-1^-( omega ) channel of the 3 pi system. By systematically varying the parameters of the input l=1 pi pi amplitude, some general conclusions can be drawn about rescattering corrections to the isobar model, including, in particular, cases in which the rescatterings are strong enough to generate a 3 pi resonance. For a choice of the pi pi parameters corresponding to the physical p-wave phase-shift, it is possible to generate a 3 pi resonance at the position of the physical omega , with a width of 17 MeV; however, this result depends sensitively on one of the parameters in the pi pi amplitude which is not well determined from the pi pi phase-shift, and which is associated with short-range effects.