Faddeev fixed center approximation to $\pi \bar{K}{K}^{\ast }$ system and the ${\pi }_1(1600)$

Abstract

We investigate the three-body system of $\pi \bar{K}{K}^{\ast }$ by using the fixed-center approximation to the Faddeev equation, taking the interaction between $\pi$ and $\bar{K}$, $\pi$ and $K^{\ast }$, and $\bar{K}$ and $K^{\ast }$ from the chiral unitary approach. The study is made assuming scattering of a $\pi$ on a $\bar{K}{K}^{\ast }$ 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 $\pi$-$(\bar{K}{K}^{\ast }{)}_{f_1(1285)}$ scattering amplitude and suggests that a $\pi$-$(\bar{K}{K}^{\ast }{)}_{f_1(1285)}$ state, with "exotic" quantum numbers $J^{PC}=1^{-+}$, can be formed. This state can be identified as the observed ${\pi }_1(1600)$ resonance. We suggest that this is the origin of the present ${\pi }_1(1600)$ resonance and propose to look at the $\pi f_1(1285)$ mode in future experiments to clarify the issue.

Comments: 6 pages, 5 figures. To match the published version in PRD