Determining the phase of a strong scattering amplitude from its momentum dependence to better than 1 degree: The example of kaon regeneration

We quantitatively study dispersion relations giving the phase of a strong scattering amplitude from its momentum dependence. We consider C-odd contributions to neutral kaon scattering (regeneration) where accurate measurements of both amplitudes and phases are available. We find, somewhat surprisingly, that, even including many possibly corrupting effects, the uncertainty is well below 1 degree. This allows an accurate determination of the phase φ+- in kaon decay to test CPT; conversely, assuming CPT symmetry, new phenomena can be limited