Starting from a short range expansion of the inelastic overlap function, capable of describing quite well the elastic pp and pp 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 pp 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.
The unitarity of the S-matrix requires that the absorptive part of the elastic scattering amplitude receives contributions from both the inelastic and the elastic channels. We explore this unitarity condition in order to describe, in a connected way, hadron-hadron observables like the total and elastic differential cross sections, the ratio of the real to imaginary part of the forward scattering amplitude and the inclusive multiplicity distributions in full phase space, over a large range of energies. We introduce non-perturbative QCD effects in the forward scattering amplitude by using the infrared QCD effective charge dependent on the dynamical gluon mass. In our analysis we pay special attention to the theoretical uncertainties in the predictions due to this mass scale variation. We also present quantitative predictions for the H q moments at high energies. Our results reproduce the moment oscillations observed in experimental data, and are consistent with the behavior predicted by QCD.
We generalize an existing geometrical approach for multiparticle production in hadronic interactions, in which the overall multiplicity distribution is given by summing contributions coming from each impact parameter b of the incident hadronic system. In the previous work, the process occurring at a fixed impact parameter b was interpreted as due to an elementary collision with formation of an object similar to the one in e − e + annihilations. Here, we extend the model allowing the possibility of formation of more than just one string. The output seems to be more consistent with data.
We have applied a geometrical approach to study pp / pp inelastic scattering over the range of center mass energies from 44.5 to 900 GeV. The multiplicity distributions are described by multiple parton-parton collisions without free parameters. The output seems to be consistent with data and the results are discussed. Exploring the possible connection between impact parameter representation of the multiplicity distribution and that of the eikonal function, the range of impact parameters for multiple collisions of partons are estimated. The energy dependence of i parton-parton collisions probability is studied and the average multiplicity is related to hadron opacity at each impact parameter.
We study the impact parameter dependence of inelasticity in the framework of an updated geometrical model for multiplicity distribution. A formula in which the inelasticity is related to the eikonal is obtained. This framework permits a calculation of the multiplicity distributions as well as the inelasticity once the eikonal function is given. Adopting a QCD inspired parametrization for the eikonal, in which the gluon-gluon contribution dominates at high energy and determines the asymptotic behavior of the cross sections, we find that the inelasticity decreases as collision energy is increased. Our results predict the KNO scaling violation observed at LHC energies by CMS Collaboration.
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