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We study the effects of curvature in the expansion of the logarithm of thedifferential elastic scattering cross section near $t=0$ as$d\sigma(s,t)/dt=d\sigma(s,0)/dt\,\times\exp(Bt+Ct^2+Dt^3\cdots)$ in an eikonalmodel for $pp$ and $\bar{p}p$ scattering, and use the results to discuss theextrapolation of measured differential cross sections and the slope parameters$B$ to $t=-q^2=0$. We find that the curvature effects represented by theparameters $C$ and $D$, while small, lead to significant changes in the forwardslope parameter relative to that determined in a purely exponential fit, and tosmaller but still significant changes in the forward elastic scattering andtotal cross sections. Curvature effects should therefore be considered infuture analyses or reanalyses of the elastic scattering data.

The slope, curvature, and higher parameters in $pp$ and $\bar{p}p$ scattering, and the extrapolation of measurements of $d\sigma(s,t)/dt$ to $t=0$