Nonextensive critical effects in relativistic nuclear mean field models

We present a possible extension of the usual relativistic nuclear mean field models widely used to describe nuclear matter towards accounting for the influence of possible intrinsic fluctuations caused by the environment. Rather than individually identifying their particular causes we concentrate on the fact that such effects can be summarily incorporated in the changing of the statistical background used, from the usual (extensive) Boltzman-Gibbs one to the nonextensive taken in the form proposed by Tsallis with a dimensionless nonextensivity parameter $q$ responsible for the above mentioned effects (for $q \rightarrow 1$ one recovers the usual BG case). We illustrate this proposition on the example of the QCD-based Nambu - Jona-Lasinio (NJL) model of a many-body field theory describing the behavior of strongly interacting matter presenting its nonextensive version. We check the sensitivity of the usual NJL model to a departure from the BG scenario expressed by the value of $| q - 1|$, in particular in the vicinity of critical points.Comment: 7 pages, 10 figure

On the possibility of q-scaling in high energy production processes

It has been noticed recently that transverse momenta (p_T) distributions observed in high energy production processes exhibit remarkably universal scaling behaviour. This is the case when a suitable variable replaces the usual p_T. On the other hand, it is also widely known that transverse momentum distributions in general follow a power-like Tsallis distribution, rather than an exponential Boltzmann-Gibbs, with a (generally energy dependent) nonextensivity parameter q. Here we show that it is possible to choose a suitable variable such that all the data can be fitted by the same Tsallis distribution (with the same, energy independent value of the q-parameter). Thus they exhibit q-scaling.Comment: Final version, accepted by J.Phys.

Possible Implication of a Single Nonextensive pTp_T Distribution for Hadron Production in High-Energy pppp Collisions

Multiparticle production processes in $pp$ collisions at the central rapidity region are usually considered to be divided into independent "soft" and "hard" components. The first is described by exponential (thermal-like) transverse momentum spectra in the low-$p_T$ region with a scale parameter $T$ associated with the temperature of the hadronizing system. The second is governed by a power-like distributions of transverse momenta with power index $n$ at high-$p_T$ associated with the hard scattering between partons. We show that the hard-scattering integral can be approximated as a nonextensive distribution of a quasi-power-law containing a scale parameter $T$ and a power index $n=1/(q -1)$, where $q$ is the nonextensivity parameter. We demonstrate that the whole region of transverse momenta presently measurable at LHC experiments at central rapidity (in which the observed cross sections varies by $14$ orders of magnitude down to the low $p_T$ region) can be adequately described by a single nonextensive distribution. These results suggest the dominance of the hard-scattering hadron-production process and the approximate validity of a "no-hair" statistical-mechanical description of the $p_T$ spectra for the whole $p_T$ region at central rapidity for $pp$ collisions at high-energies.Comment: 10 pages, 3 figures; presented by G.Wilk at the XLIV International Symposium on Multiparticle Dynamics; 8 - 12 September 2014 - Bologna, ITAL