Sum rules for hadronic elastic scattering for the Tevatron, RHIC and LHC

Abstract

Under the assumption of total absorption and dominance of the imaginary part of the scattering amplitude, we present a sum rule for any hadronic elastic differential cross-section ${d\sigma}\over{dt}$: the dimensionless quantity ${{1}\over{2}}\int (dt)\sqrt{{{1}\over {\pi}}{{d\sigma}\over{dt}}} \to 1$, at asymptotic energies. Experimental data from ISR and Tevatron confirm a trend towards its saturation and some estimates are presented for LHC. Its universality and further consequences for the nature of absorption in QCD based models for elastic and total cross-sections are explored.