Analyticity as a robust constraint on the total cross section at the CERN large hadron collider

It is well known that high energy data alone do not discriminate between asymptotic lns and ln/sup 2/s behavior of pp and pmacronp cross sections. By exploiting high quality low energy data, analyticity resolves this ambiguity in favor of cross sections that grow asymptotically as ln/sup 2/s. We here show that two methods for incorporating the low energy data into the high energy fits give numerically identical results and yield essentially identical tightly constrained values for the LHC cross section. The agreement can be understood as a new analyticity constraint derived as an extension of a finite energy sum rule.