On the real part of elastic scattering amplitude

TL;DR

The paper addresses the role of the real part of the elastic scattering amplitude in high-energy hadron collisions and its compatibility with unitarity and dispersion relations. It argues that unitarity constraints and LHC data favor an imaginary-part-dominant amplitude, challenging the significance of a maximal odderon: the central-region amplitude satisfies $[\mathrm{Re}f(s,b)]^2 \le \mathrm{Im}f(s,b)[1 - \mathrm{Im}f(s,b)]$ and tends toward zero as saturation is approached. Using the unitarized form $f(s,b)=u(s,b)/(1 - i u(s,b))$ with $\mathrm{Im}\,u(s,b) \ge 0$, the work links the dominance of the imaginary part to inelastic intermediate states and shows that the real part is suppressed, with large-$b$ behavior factorizing into energy- and $b$-dependent pieces. The findings reinforce the practical neglect of the real part in many analyses, elucidate unitarity constraints on the forward amplitude, and connect the evolving hadronic picture at LHC energies (black disk to black ring) to an essentially imaginary elastic amplitude.

Abstract

We discuss dominance of imaginary part of the elastic scattering amplitude and argue in favor of approximation based on this dominance.