The reaction {π}N{to}{ω}N revisited: the ω{-}N scattering length

We reinvestigate the experimental data on $\omega$--meson production in pion-nucleon collisions based on both an analytical approach and a Monte Carlo simulation. Our analysis allows us to study the kinematical peculiarities of the $\pi^-p{\to}\omega{n}$ reaction at energies close to threshold. Based on the hypothesis, that the formalism derived in ref. [1] was applied improperly, the unusually strong energy dependence claimed for the near--threshold cross section is identified as a purely kinematical effect. Based on this hypothesis, we deduce an effective ${\pi^-}p{\to}{\omega}n$ cross section that is larger by an order of magnitude compared to the one commonly used. In addition we extract a lower limit for the imaginary part $\Im a_{{\omega}N}$ of the ${\omega}N$ scattering length. We find a value of $\Im a_{{\omega}N}{=}0.24{\pm}0.05$ fm, which is significantly larger than that presently found in the literature.