Faddeev fixed center approximation to $π\bar{K} K^*$ system and the $π_1(1600)$

Abstract

We investigate the three-body system of π KK * by using the fixed-center approximation to the Faddeev equation, taking the interaction between π and K, π and K * , and K and K * from the chiral unitary approach. The study is made assuming scattering of a π on a KK * cluster, which is known to generate the f 1 (1285) state. The resonant structure around 1650 MeV shows up in the modulus squared of the π-( KK * ) f 1 (1285) scattering amplitude and suggests that a π-( KK * ) f 1 (1285) state, with "exotic" quantum numbers J PC = 1 −+ , can be formed. This state can be identified as the observed π 1 (1600) resonance. We suggest that this is the origin of the present π 1 (1600) resonance and propose to look at the π f 1 (1285) mode in future experiments to clarify the issue.