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Register a new userElastic Hadron Scattering in Various Pomeron Models
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In this work the process of elastic hadron scattering is discussed. In particular, scattering amplitudes for the various Pomeron models are compared. In addition, differential elastic cross section as a function of the scattered proton transverse momentum for unpolarised and polarised protons is presented. Finally, an implementation of the elastic scattering amplitudes into the GenEx Monte Carlo generator is discussed.
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Recent data from LHC13 by the TOTEM Collaboration have indicated an unexpected decrease in the value of the $rho$ parameter and a $sigma_{tot}$ value in agreement with the trend of previous measurements at 7 and 8 TeV. These data at 13 TeV are not simultaneously described by the predictions from Pomeron models selected by the COMPETE Collaboration, but show agreement with the maximal Odderon dominance, as recently demonstrated by Martynov and Nicolescu. Here we present a detailed analysis on the applicability of Pomeron dominance by means of a general class of forward scattering amplitude, consisting of even-under-crossing leading contributions associated with single, double and triple poles in the complex angular momentum plane. We carry out fits to $pp$ and $bar{p}p$ data in the interval 5 GeV - 13 TeV. The data set comprises all the accelerator data below 7 TeV and we consider two independent ensembles by adding either only the TOTEM data or TOTEM and ATLAS data at the LHC energy region. In the data reductions to each ensemble the uncertainty regions are evaluated with both one and two standard deviation ($sim$ 68 % and $sim$ 95 % CL, respectively). Besides the general analytic model, we investigate four particular cases of interest, three of them typical of outstanding models in the literature. We conclude that, within the experimental and theoretical uncertainties and both ensembles, the general model and three particular cases are not able to describe the $sigma_{tot}$ and $rho$ data at 13 TeV simultaneously. However, if the discrepancies between the TOTEM and ATLAS data are not resolved, one Pomeron model, associated with double and triple poles and with only 7 free parameters, seems not to be excluded by the complete set of experimental information presently available.
In this paper we prove a new optimal bound on the logarithmic slope of the elastic slope when: elastic cross section and differential cross sections in forward and backward directions are known from experimental data. The results on the experimental tests of this new optimal bound are presented in Sect. 3 for the principal meson-nucleon elastic scatterings: pion-nucleon, kaon-nucleon at all available energies. Then we have shown that the saturation of this optimal bound is observed with high accuracy practically at all available energies in meson-nucleon scattering.
We study elastic pion-pion scattering in global linear moose models and apply the results to a variety of Higgsless models in flat and AdS space using the Equivalence Theorem. In order to connect the global moose to Higgsless models, we first introduce a block-spin transformation which corresponds, in the continuum, to the freedom to perform coordinate transformations in the Higgsless model. We show that it is possible to make an f-flat deconstruction in which all of the f-constants f_j of the linear moose model are identical; the phenomenologically relevant f-flat models are those in which the coupling constants of the groups at either end of the moose are small - corresponding to the global linear moose. In studying pion-pion scattering, we derive various sum rules, including one analogous to the KSRF relation, and use them in evaluating the low-energy and high-energy forms of the leading elastic partial wave scattering amplitudes. We obtain elastic unitarity bounds as a function of the mass of the lightest KK mode and discuss their physical significance.
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. 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 $bar{p}p$ scattering, in the region 5 GeV-8 TeV. The recent tension between the TOTEM and ATLAS results at 7 TeV and mainly 8 TeV is considered in the data reductions. Our main conclusions are: (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 $gammasim 2.0pm 0.2$ (AU) and $gammasim 2.3pm 0.1$ (DDR); (3) by including the ATLAS data the fits provide $gammasim 1.9pm 0.1$ (AU) and $gammasim 2.2pm 0.2$ (DDR); (4) in the formal and practical contexts, the DDR approach is more adequate for the energy interval investigated than the AU approach. A review on the analytic results for $sigma_{tot}$ and $rho$ from the Regge-Gribov, DDR and AU approaches is presented.
Starting from a short range expansion of the inelastic overlap function, capable of describing quite well the elastic pp and $bar{p}p$ scattering data, we obtain extensions to the inelastic channel, through unitarity and an impact parameter approach. Based on geometrical arguments we infer some characteristics of the elementary hadronic process and this allows an excellent description of the inclusive multiplicity distributions in $pp$ and $bar{p}p$ collisions. With this approach we quantitatively correlate the violations of both geometrical and KNO scaling in an analytical way. The physical picture from both channels is that the geometrical evolution of the hadronic constituents is principally reponsible for the energy dependence of the physical quantities rather than the dynamical (elementary) interaction itself.
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