Cross sections, multiplicity and moment distributions at the LHC

Abstract

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.

Empirical Equation Using GMDH Methodology for the Charged Particles Multiplicity Distribution in Hadronic Positron-Electron Annihilation

“…The produced gluon depends on the center of mass energy. Based on the GMDH, the general form empirical equation can be represented by a system of particle description using some type of order polynomial such as, linear, equations, quadratic equations and cubic equations (see equations (8) and (9)). …”

“…Based on the obtained equations (eqs. (8) and (9)), the values of energy dependence of the average charged multiplicity in e interactions, up to 206 GeV has been calculated to be n . When compared to other models, the value calculated is consistent with the evolution predicted by GMD method [21][22][23][24].…”

“…The normal method of studying the charged-particle multiplicity distribution and its shape, is to calculate its moments. The common behaviors of the charged-particle multiplicity distribution are obtained using low-order moments, such as the mean, n , the dispersion, D, which estimates the width of the distribution, the skewness, S, which measures how symmetric the distribution is, and the kurtosis, K, which measures how sharply peaked the distribution is [8]. The multiplicity distribution are treated experimentally (see e.g.…”

“…We shall study the distribution of the number of charged particles produced in positron-electron hadronic annihilation i. e. the charged multiplicity distribution and the average multiplicity (first order moment). The probability of producing a given number of charged prongs in an inelastic collision can be written as [1,8]:…”

Proton-proton forward scattering at the LHC

“…This Letter revisits this issue by investigating the behavior of the forward quantities σ tot and ρ, from pp and pp (antiproton-proton) scattering, through an eikonal QCD-based model with a scattering amplitude dominated asymptotically by only single crossing-even amplitudes [7,17,18]. We consider a model in which the bridge between the parton dynamics, described by QCD, and the dynamics of observable hadron systems is provided by the QCD parton model using updated sets of quark and gluon distribution functions, standard QCD cross sections for parton-parton processes and physically motivated cutoffs that restrict the parton-level dynamics to the semihard sector.…”