Abstract
We compare the πN scattering amplitudes that underlie 2π-exchange three-nucleon forces (TBFs) with the experimental πN amplitudes in the form of partial-wave phase shifts and subthreshold invariant amplitudes. The amplitudes of the Tucson-Melbourne and Brazil TBFs when taken on-pion-mass-shell predict scattering lengths at threshold and phase shifts (slightly) above threshold which are in good agreement with the experimental amplitudes, except for the S-waves. Partial wave amplitudes from separable potentials, recently employed in a 2π-TBF calculation, were continued below threshold, summed into invariant amplitudes, and compared with the experimental amplitudes in this kinematic region, which is most relevant to the kinematics of TBFs. The separable-potential invariant amplitudes, in contrast to those of TM and Brazil TBFs, do not compare well quantitatively with the experimental amplitudes in this region but have a similar qualitative behaviour. The very small TBF effect in the triton of the separable-potential amplitude appears to be due to the πNN vertex function rather than the πN amplitude itself.
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