Real parts of the pion-proton forward scattering amplitude

The most recent total-cross-section data are used to calculate real parts of the forward elastic ${\pi }^{\pm }p$ scattering amplitudes from threshold to 240 GeV/c. Using statistical and systematic uncertainties of the total cross sections and their momenta, along with uncertainties of the subtraction and coupling constants, unphysical cuts, and cross-section extrapolations, we calculate the uncertainties of the real amplitudes. Our results are compared to experimental and other theoretical determinations of the ${\pi }^{\pm }p$ forward real amplitudes.