Comparison of Forward Dispersion Relations with Experiments around 10 GeV

Using the recent experimental data on the real part of the forward ${\pi }^{\pm }-p$ amplitude around 10 GeV, we have carried out a comparison of forward dispersion relations with experiments in the high-energy region. In this work we propose a new method for testing forward dispersion relations which involves no assumptions whatsoever about the unknown cross sections above 20 GeV. On account of the large systematic errors in the measured real parts, no definite conclusion can be drawn as to the validity of forward dispersion relations. In estimating the standard deviations in the dispersion integrals, a Monte Carlo method has been used.