Duality as a Robust Constraint on the LHC Cross Section

It is well known that high energy data alone do not discriminate between asymptotic $\ln s$ and $\ln^2 s$ behavior of $pp$ and $\bar pp$ cross sections. By exploiting high quality low energy data, duality resolves this ambiguity in favor of cross sections that grow asymptotically as $\ln^2 s$. We here show that two methods for incorporating the low energy data into the high energy fits give numerically identical results, thus reinforcing the validity of duality. They yield essentially identical and tightly constrained values for the LHC cross section.