Sound waves in hadronic matter

We argue that recent high energy CERN LHC experiments on transverse momenta distributions of produced particles provide us new, so far unnoticed and not fully appreciated, information on the underlying production processes. To this end we concentrate on the small (but persistent) log-periodic oscillations decorating the observed $p_T$ spectra and visible in the measured ratios $R = \sigma_{data}\left( p_T\right)/\sigma_{fit}\left( p_T\right)$. Because such spectra are described by quasi-power-like formulas characterised by two parameters: the power index $n$ and scale parameter $T$ (usually identified with temperature $T$), the observed log-periodic behaviour of the ratios $R$ can originate either from suitable modifications of $n$ or $T$ (or both, but such a possibility is not discussed). In the first case $n$ becomes a complex number and this can be related to scale invariance in the system, in the second the scale parameter $T$ exhibits itself log-periodic oscillations which can be interpreted as the presence of some kind of sound waves forming in the collision system during the collision process, the wave number of which has a so-called self similar solution of the second kind. Because the first case was already widely discussed we concentrate on the second one and on its possible experimental consequences.Comment: 10 pages, 4 figures. Presented at the XLVII International Symposium on Multiparticle Dynamics (ISMD2017) held in Tlaxcala City, Mexico, during September 11-15, 201

Tsallis statistics approach to the transverse momentum distributions in p-p collisions

Transverse momentum distributions of negatively charged pions produced in p-p interactions at beam momenta 20, 31, 40, 80 and 158 GeV/c are studied using the Tsallis distribution as a parametrization. Results are compared with higher energies data and changes of parameters with energy are determined. Different Tsallis-like distributions are compared.Comment: 6 pages, 9 figure

Oscillations in counting statistics

The very large transverse momenta and large multiplicities available in present LHC experiments on pp collisions allow a much closer look at the corresponding distributions. Some time ago we discussed a possible physical meaning of apparent log-periodic oscillations showing up in p_T distributions (suggesting that the exponent of the observed power-like behavior is complex). In this talk we concentrate on another example of oscillations, this time connected with multiplicity distributions P(N). We argue that some combinations of the experimentally measured values of P(N) (satisfying the recurrence relations used in the description of cascade-stochastic processes in quantum optics) exhibit distinct oscillatory behavior, not observed in the usual Negative Binomial Distributions used to fit data. These oscillations provide yet another example of oscillations seen in counting statistics in many different, apparently very disparate branches of physics further demonstrating the universality of this phenomenon.Comment: Invited talk at ISMD2016, Seogwipo, Jeju Island, South Korea, 29.08-02.09.2016, to be published in EPJ Web of Conference

Tsallis Distribution Decorated With Log-Periodic Oscillation

In many situations, in all branches of physics, one encounters power-like behavior of some variables which are best described by a Tsallis distribution characterized by a nonextensivity parameter $q$ and scale parameter $T$. However, there exist experimental results which can be described only by a Tsallis distributions which are additionally decorated by some log-periodic oscillating factor. We argue that such a factor can originate from allowing for a complex nonextensivity parameter $q$. The possible information conveyed by such an approach (like the occurrence of complex heat capacity, the notion of complex probability or complex multiplicative noise) will also be discussed.Comment: 17 pages, 1 figure. The content of this article was presented by Z. Wlodarczyk at the SigmaPhi2014 conference at Rhodes, Greece, 7-11 July 2014. To be published in Entropy (2015

Numerical symmetrization of state of identical particles

The method of numerical symmetrization of state of identical particles proposed by us before is clarified and discussed.Comment: Talk presented by O.Utyuzh at XXXVI International Symposium on Multiparticle Dynamics, September 2-8, 2006, Paraty (RJ), Brazil; minor corrections, to be published in Braz. J. Phys. (2007

System size dependence of the log-periodic oscillations of transverse momentum spectra

Recently the inclusive transverse momentum distributions of primary charged particles were measured for different centralities in $Pb+Pb$ collisions. A strong suppression of the nuclear modification factor in central collisions around $p_T \sim 6-7$ GeV/c was seen. As a possible explanation, the hydrodynamic description of the collision process was tentatively proposed. However, such effect, (albeit much weaker) also exists in the ratio of data/fits, both in nuclear $Pb+Pb$ collisions, and in the elementary $p+p$ data in the same range of transverse momenta for which such an explanation is doubtful. As shown recently, in this case, assuming that this effect is genuine, it can be attributed to a specific modification of a quasi-power like formula usually used to describe such $p_T$ data, namely the Tsallis distribution. Following examples from other branches of physics, one simply has to allow for the power index becoming a complex number. This results in specific log-periodic oscillations dressing the usual power-like distribution, which can fit the $p+p$ data. In this presentation we demonstrate that this method can also describe $Pb+Pb$ data for different centralities. We compare it also with a two component statistical model with two Tsallis distributions recently proposed showing that data at still larger $p_T$ will be sufficient to discriminate between these two approaches.Comment: 6 pages, 8 figures. Contibution to the XLIV International Symposium on Multiparticle Dynamics proceeding