Figure 1

(a) The fitted total cross sections ${\sigma }_{pp}$ and ${\sigma }_{\overline{p}p}$ in mb, vs $\sqrt{s}$, in GeV, using the single constraint of Eqs. (9) for the analyticity fit and (21) for the FESR fit of Table . The circles are the sieved data for $\overline{p}p$ scattering and the squares are the sieved data for $pp$ scattering for $\sqrt{s}\ge 6\mathrm{GeV}$. The short dashed curve and dot-dashed curves are the analyticity fits—the even cross section at 4 GeV was fixed—to the $\overline{p}p$ and $pp$ data, respectively. The solid curve and dotted curves are the FESR fits to the $\overline{p}p$ and $pp$ data, respectively. It should be pointed out that the FESR and analyticity curves are essentially indistinguishable numerically for energies between 4 and 20000 GeV. (b) An expanded energy scale that additionally shows the cross section data that exist [10] between 4 GeV, where ${\sigma }_{\mathrm{even}}$ was fixed, and 6 GeV, the beginning of the fitted data. It should be emphasized that none of the data between 4 and 6 GeV were used in the fits. We note that the fits go through all of the unused points, with the exception of the $\overline{p}p$ point at 4.2 GeV, which would have been excluded by the Sieve algorithm [5] because of its large $\Delta {\chi }_i^2$, had it been used.Reuse & Permissions

Figure 2

The fitted $\rho$-values, ${\rho }_{pp}$ and ${\rho }_{\overline{p}p}$, vs. $\sqrt{s}$, in GeV, using the single constraint of Eqs. (9) for the analyticity fit and (21) for the FESR fit of Table . The circles are the sieved data for $\overline{p}p$ scattering and the squares are the sieved data for $pp$ scattering for $\sqrt{s}\ge 6\mathrm{GeV}$. The short dashed curve and dot-dashed curves are the analyticity fits—the even cross section at 4 GeV was fixed—to the $\overline{p}p$ and $pp$ data, respectively. The solid curve and dotted curves are the FESR fits to the $\overline{p}p$ and $pp$ data, respectively. It should be pointed out that the FESR and analyticity curves are essentially indistinguishable numerically for energies between 4 and 20000 GeV.Reuse & Permissions