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

Abstract

Forward amplitude analyses constitute an important approach in the investigation of the energy dependence of the total hadronic cross-section [Formula: see text] and the [Formula: see text] parameter. The standard picture indicates for [Formula: see text] a leading log-squared dependence at the highest c.m. energies, in accordance with the Froissart–Lukaszuk–Martin bound and as predicted by the COMPETE Collaboration in 2002. Beyond this log-squared (L2) leading dependence, other amplitude analyses have considered a log-raised-to-gamma form [Formula: see text], with [Formula: see text] as a real free fit parameter. In this case, analytic connections with [Formula: see text] can be obtained either through dispersion relations (derivative forms), or asymptotic uniqueness (Phragmén–Lindelöff theorems). In this work, we present a detailed discussion on the similarities and mainly the differences between the Derivative Dispersion Relation (DDR) and Asymptotic Uniqueness (AU) approaches and results, with focus on the [Formula: see text] and L2 leading terms. We also develop new Regge–Gribov fits with updated dataset on [Formula: see text] and [Formula: see text] from [Formula: see text] and [Formula: see text] scattering, including all available data in the region 5 GeV–8 TeV. The recent tension between the TOTEM and ATLAS results at 7 TeV and mainly at 8 TeV is discussed and considered in the data reductions. Our main conclusions are the following: (1) all fit results present agreement with the experimental data analyzed and the goodness-of-fit is slightly better in case of the DDR approach; (2) by considering only the TOTEM data at the LHC region, the fits with L[Formula: see text] indicate [Formula: see text] (AU approach) and [Formula: see text] (DDR approach); (3) by including the ATLAS data the fits provide [Formula: see text] (AU) and [Formula: see text] (DDR); (4) in the formal and practical contexts, the DDR approach is more adequate for the energy interval investigated than the AU approach. A pedagogical and detailed review on the analytic results for [Formula: see text] and [Formula: see text] from the Regge–Gribov, DDR and AU approaches is presented. Formal and practical aspects related to forward amplitude analyses are also critically discussed.