11 de setembro de 2018 | Altas Energias, Publicações
D. A. Fagundes, M. J. Menon, P. V. R. G. Silva
International Journal of Modern Physics A, Vol. 32, No. 32, 1750184 (2017)
20/11/2017
Abstract
Forward amplitude analyses constitute an important approach in the investigation of the energy dependence of the total hadronic cross-section σtot and the ρ parameter. The standard picture indicates for σtot 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 (Lγ), with γ as a real free fit parameter. In this case, analytic connections with ρ 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 Lγ and L2 leading terms. We also develop new Regge–Gribov fits with updated dataset on σtot and ρ from pp and p̄ p 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 Lγ indicate γ∼2.0±0.2 (AU approach) and γ∼2.3±0.1 (DDR approach); (3) by including the ATLAS data the fits provide γ∼1.9±0.1 (AU) and γ∼2.2±0.2 (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 σtot and ρ from the Regge–Gribov, DDR and AU approaches is presented. Formal and practical aspects related to forward amplitude analyses are also critically discussed.