Faddeev approach to the reaction $K^{-}d\to \pi \Sigma n$ at $p_K=1$ GeV/c

Abstract

The reaction $K^{-}d\to \pi \Sigma n$ is studied within a Faddeev-type approach, with emphasis on the specific kinematics of the E31 experiment at J-PARC, i.e. $K^{-}$ beam momentum of $p_K=1$ GeV/c and neutron angle of ${\theta }_n=0^{\circ }$. The employed Faddeev approach requires as main input amplitudes for the two-body subsystems $\bar{K}N\to \bar{K}N$ and $\bar{K}N\to \pi \Sigma$. For the latter results from recently published chiral unitary models of the $\bar{K}N$ interaction are utilized. The $\bar{K}N\to \bar{K}N$ amplitude itself, however, is taken from a recent partial-wave analysis. Due to the large incoming momentum of the $K^{-}$, the $\bar{K}N$ interaction is probed in a kinematical regime where those chiral potentials are no longer applicable. A comparison of the predicted spectrum for various $\pi \Sigma$ charge channels with preliminary data is made and reveals a remarkable agreement as far as the magnitude and the line shape in general is concerned. Noticeable differences observed in the $\pi \Sigma$ spectrum around the $\bar{K}N$ threshold, i.e. in the region of the $\Lambda$(1405) resonance, indicate a sensitivity to the details of the employed $\bar{K}N\to \pi \Sigma$ amplitudes and suggest that pertinent high-precision data could indeed provide substantial constraints on the structure of the $\Lambda$(1405).

Comments: 15 pages, 9 figures