Abstract

It is shown that the exchange of the $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ $J=0$, $T=0$ antibound state in the crossed channel for $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ and $\ensuremath{\pi}\ensuremath{-}N$ scattering gives a contribution similar to that due to the exchange of a scalar particle but with opposite sign of the residue. In the direct channel, this antibound state gives a large $T=0$ $s$-wave $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ scattering length, as suggested by Atkinson to explain the ABC phenomenon. The contribution of the antibound state to the physical amplitude is evaluated using dispersion relations involving the physical sheet and the second Riemann sheet.

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