The real part of the πN diffraction amplitude
The real part of the invariant isospin evenπ N amplitudeC+≡A′+ at ¦t¦≲0.4 (GeV/c)2 is determined from the condition thatC+ fulfills the fixed-t dispersion relation, is compatible with this amplitude as reconstructed from phase shifts up to 1.5 GeV/c and leads to differential cross sections above 3 GeV/c in agreement with the experimental data.-The result for ReC+/ImC+ is remarkably large (−0.5 att=−0.3 (GeV/c)2 and 6 GeV/c) and up to 20 GeV/c its uncertainty is comparable with that in the upper part of the phase shift region.-Even at 40 GeV/c ReC+ is far from being asymptotic because of large energy independent low energy contributions. The deviations from our simple high energy ansatz (k>4GeV/c): ImC+(k, t)∼(k + m)exp(9t/2) are almost comparable with the experimental errors.