Violation of Feynman scaling and energy dependence of multiplicity for high energy hadron interactions

Abstract

We have analysed the momentum spectra of the secondary particles in pp interactions predicted by different models, comparing them with accelerator data from 19.7 GeV to 1.8 TeV (CMS). All models predicting asymptotic behaviour of secondary spectra with Feynman scaling in the fragmentation region lead to a rather slow increase of multiplicity in contradiction to the accelerator data. It is shown that the pure phenomenological model, which is based on the semi-inclusive spectra from ISR and FNAL collider experiments at 19.7 GeV, and extrapolated to higher energies by assuming violated Feynman scaling in the entire phase space, describes the data well in the whole accelerator range. This model is also relevant for application in the study of cosmic rays at high energies.

Quantum Statistical Parton Distributions and the Spin Crisis

“…As a consequence of this analysis, the Pauli principle seems to play a fundamental role in the DIS phenomena. Thus, in this framework it is natural to assume Fermi-Dirac distributions in the variable x for the quark partons [4,5]…”

“…In fact, the most divergent part of distributions is expected on general grounds to be equal for the different partons, at least in the limit of flavour symmetry, and hence it does not contribute to the sum rules, but affects other DIS observables. In order to disentangle, this divergent term from the total distribution function we add a liquid unpolarized component for the light quark-partons (u, d and their antiparticles) [5] f…”

“…Remarkably, one obtains a satisfactory description of the experimental data of DIS in terms of few free parameters [4]. The analysis has then been improved [5] by adding an extra contribution to the statistical term of parton distributions, dominating in the small x region, the so called liquid component, with Pomeron-like quantum numbers.…”

“…In this respect, it would be helpful to know the small x behaviour of g p 1 (x) − g n 1 (x). In the approach based on statistical functions this behaviour is given by the function f (x) [5], which is also related to F p 2 (x) − F n 2 (x) and xF 3 (x), occurring in the Gottfried and Gross Llewellyn-Smith sum rule [17], respectively. Since these quantities are measured more precisely than the g 1 's, f (x) is practically determined by the unpolarized structure functions.…”

“…Since these quantities are measured more precisely than the g 1 's, f (x) is practically determined by the unpolarized structure functions. Once f (x) and the parameterx are established [4,5], the polarized structure function g p 1 (x) − g n 1 (x) depends only on the thermodynamical potentials [4,5] of quarks with definite spin. In practice, we have only one free parameter for each quark, since the sum p ↑ (x) + p ↓ (x) is fixed by the unpolarized structure functions.…”