Preliminary Results on the Empirical Applicability of the Tsallis Distribution in Elastic Hadron Scattering

We show that the proton-proton elastic differential cross section data at dip position and beyond can be quite well described by a parametrization based on the Tsallis distribution, with only five free fit parameters. Extrapolation of the results obtained at 7 TeV to large momentum transfer, suggests that hadrons may not behave as a black-disk at the asymptotic energy region.Comment: 3 pages, 1 figure, version matching proceedings style, XII Hadron Physics, 2012, AIP Proc. Con

Asymptotic Scenarios for the Proton's Central Opacity: An Empirical Study

We present a model-independent analysis of the experimental data on the ratio $X$ between the elastic and total cross-sections from $pp$ and $\bar{p}p$ scattering in the c.m. energy interval 5 GeV - 8 TeV. Using a novel empirical parametrization for that ratio as a function of the energy and based on theoretical and empirical arguments, we investigate three distinct asymptotic scenarios: either the black-disk (BD) limit or scenarios above and below that limit. Our analysis favors a scenario below the BD, with asymptotic ratio $X = 0.36 \pm 0.08$.Comment: 5 pages, 1 figure added, extended text, matchs proceedings (Diffraction 2014

On the rise of proton-proton cross-sections at high energies

The rise of the total, elastic and inelastic hadronic cross sections at high energies is investigated by means of an analytical parametrization, with the exponent of the leading logarithm contribution as a free fit parameter. Using derivative dispersion relations with one subtraction, two different fits to proton-proton and antiproton-proton total cross section and rho parameter data are developed, reproducing well the experimental information in the energy region 5 GeV - 7 TeV. The parametrization for the total cross sections is then extended to fit the elastic (integrated) cross section data in the same energy region, with satisfactory results. From these empirical results we extract the energy dependence of several physical quantities: inelastic cross section, ratios elastic/total, inelastic/total cross sections, ratio total-cross-section/elastic-slope, elastic slope and optical point. All data, fitted and predicted, are quite well described. We find a statistically consistent solution indicating: (1) an increase of the hadronic cross sections with the energy faster than the log-squared bound by Froissart and Martin; (2) asymptotic limits 1/3 and 2/3 for the ratios elastic/total and inelastic/total cross sections, respectively, a result in agreement with unitarity. These indications corroborate recent theoretical arguments by Ya. I. Azimov on the rise of the total cross section.Comment: 35 pages, 12 figures, discussions improved with further clarifications, references added and updated, one note added, results and conclusions unchanged. Version to be published in J. Phys. G: Nucl. Part. Phy

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

FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESPForward 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 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 (L gamma), with gamma as a real free fit parameter. In this case, analytic connections with rho can be obtained either through dispersion relations (derivative forms), or asymptotic uniqueness (Phragmen-Lindeloff 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 L gamma and L2 leading terms. We also develop new Regge-Gribov fits with updated dataset on sigma(tot) and rho from pp and (p) over barp 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 gamma indicate gamma similar to 2.0 +/- 0.2 (AU approach) and gamma similar to 2.3 +/- 0.1 (DDR approach); (3) by including the ATLAS data the fits provide gamma similar to 1.9 +/- 0.1 (AU) and gamma similar to 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 sigma(tot) and rho from the Regge-Gribov, DDR and AU approaches is presented. Formal and practical aspects related to forward amplitude analyses are also critically discussed.3232150FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESPFUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP2013/27060-

Bounds on the rise of total cross section from LHC7 and LHC8 data

FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESPRecent measurements of the proton proton total cross section sigma(tot) at 7 and 8 TeV by the TOTEM and ATLAS Collaborations are characterized by some discrepant values: the TOTEM data suggest a rise of the cross section with the energy faster than the ATLAS data. Attempting to quantify these different behaviors, we develop new analytical fits to sigma(tot) and rho data from (p) over barp and pp scattering in the energy region 5 GeV-8 TeV. The dataset comprises all the accelerator data below 7 TeV and we consider three ensembles by adding: either only the TOTEM data (T), or only the ATLAS data (A), or both sets (T + A). For the purposes, we use our previous RRPL gamma parametrization for sigma(tot) (s), consisting of two Reggeons (RR), one critical Pomeron (P) and a leading log-raised-to-gamma (L gamma) contribution (with gamma as a free fit parameter), analytically connected to rho(s) through singly-subtracted derivative dispersion relations and energy scale fixed at the physical threshold. The data reductions with ensembles T and A present good agreement with the experimental data analyzed and cannot be distinguished on statistical grounds. The quality of the fit is not as good with ensemble T + A. The fit results provide gamma similar to 2.3 +/- 0.1 (T), 2.0 +/- 0.1 (A), 2.2 +/- 0.2 (T + A), with x(2)/DOF similar to 1.07 (T), 1.09 (A), 1.14 (T + A), suggesting extrema bounds for gamma given by 1.9 and 2.4. Fits with gamma = 2 (fixed) are also developed and discussed.966185196FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESPFUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP2013/27060-