Percolation Effects in Very-High-Energy Cosmic Rays

Abstract

Most QCD models of high energy collisions predict that the inelasticity K is an increasing function of the energy. We argue that, due to percolation of strings, this behaviour will change and, at √ s ≃ 10 4 GeV, the inelasticity will start to decrease with the energy. This has straightforward consequences in high energy cosmic ray physics: 1) the relative depth of the shower maximum X grows faster with energy above the knee; 2) the energy measurements of ground array experiments at GZK energies could be overestimated.PACS numbers: 13.87. 12.40.Nn, 96.40.De, 96.40.Pq Most QCD-inspired models of multiparticle production predict, in hadron-hadron and nucleus-nucleus collisions at high energy, an increase with energy of the inelasticity parameter, [6,7]. These models predict large stopping power and a decrease of the momentum fraction carried by fast particles.Two aspects are essential in the String Percolation Model [8,9] that we use here: 1) At low energy (or density) leading valence strings are produced. As the energy increases, energy is drawn from the valence strings to produce, centrally in rapidity, sea strings. As in all the models mentioned above, the inelasticity increases with the energy. 2) At very high energy, above the percolation threshold, percolation leads to the formation of a large cluster of strings and to the production of faster particles. As a consequence the inelasticity starts to decrease with the energy.While the relatively low energy regime, with K increasing, is similar to the models already mentioned, the higher energy regime, with decreasing K and the regeneration of the fast particles, is new and has some straightforward consequences in cosmic ray physics.In the String Percolation Model [8, 9] for hadronhadron collisions, at low energy, valence strings are formed, forward and backward in the centre-of-mass, along the collision axis, containing most of the collision energy. As the energy increases, additional sea strings, central in rapidity, are created, taking away part of the energy carried the valence strings. In the impact parameter plane all the strings look like disks, and we have to deal with a two dimension percolation problem.The relevant parameter in percolation theory is the transverse density, η [10],where r is the transverse radius of the string, R the effective radius of the interaction area. N s , the average number of strings, depends on the density (centrality) and on the energy. The strings may overlap in the interaction area, forming clusters of N strings. If η ≪ 1, the average number of strings per cluster is < N >≃ 1. If η ≫ 1, < N >≃ N s . If n is the particle density for one string, m T the average transverse mass produced from a single string, and there are N s strings, one expects:with a colour summation reduction factor [11,12],The particle density does not increase as fast as N s (this corresponds to the saturation phenomenon [9]), and < m T > slowly increases with energy and density. These features are seen in data (see, for instance, [13]). Following [...

Long range forward–backward rapidity correlations in proton–proton collisions at LHC

“…In the naive model with just these percolating strings, if we impose energy conservation [15] we obtain N s ∼ s λ ,…”

“…But the region of x + ≃ x − ≃ 0 is the region of saturation and percolation of strings. If N s strings percolate the size in rapidity of the percolated strings is [14,15],…”

High multiplicityppevents andJ/ψproduction at energies available at the CERN Large Hadron Collider

“…The number of strings, < N s >, can be obtained from the SFM code [24], a Monte Carlo code based on the quark gluon string model, similar to the Dual Parton Model [25] or EPOS [26]. Moreover, the value of N s can also be calculated analytically [27]…”

Percolation and high energy cosmic rays above 1017eV

“…It has been argued [6,7] that other models predicting a development of the shower deeper in the atmosphere (an increase in X max ) could also explain this effect.…”

“…This scenario has been explored in [7], where a string percolation model predicting the required behaviour of the inelasticity at high energies was discussed. As it will be seen below, string percolation affects the energy dependence of K, P 0 and < n >.…”