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

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

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