Leading components in forward elastic hadron scattering: Derivative dispersion relations and asymptotic uniqueness

Understand

Forward amplitude analyses constitute an important approach in the investigation of the energy dependence of the total hadronic cross-section $\sigma_{tot}$ and the $\rho$ parameter.

• The standard picture indicates for $\sigma_{tot}$ a leading log-squared dependence at the highest c.m.
• energies, in accordance with the Froissart-Lukaszuk-Martin bound.
• Beyond this log-squared (L2) leading dependence, other amplitude analyses have considered a log-raised-to-gamma form (L$\gamma$), with $\gamma$ as a real free fit parameter.