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

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.

ELECTROMAGNETIC FORWARD NEUTRINO-NEUTRINO SCATTERING IN DENSE MATTER

Using covariant methods we calculate the coherent forward amplitude for the exchange of a virtual photon between neutrinos having medium-induced electromagnetic vertices. Such a process can affect the important Mikheyev-Smirnov-Wolfenstein (MSW) mechanism in media with large neutrino asymmetries. It can be considered as a finite temperature and density (FTD) version of a two-loop contribution which gives rise to non-universal (νι-dependent) radiative corrections to the forward scattering νν → νν. Assuming no inert neutrino species, we discuss the possible importance of this contribution to the MSW effect in a supernova core and in the early Universe with large but equal neutrino asymmetries.

THE FORWARD AMPLITUDE IN LOW ENERGY $P\bar P$ SCATTERING

It is shown that the abrupt rise of around 200 MeV/c in the real-to-imaginary ratio ρ of the forward scattering amplitude in low energy [Formula: see text] scattering is not due to the [Formula: see text] threshold or approximations in the treatment of the coulomb nuclear interference. The latter breaks down below Plab≈100 MeV/c. The possibility of a potential resonance is discussed.