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Grzegorz Wilk

Publications and source records attributed to Grzegorz Wilk.

At least 37 records · Page 2Linked to original sources
arXiv2015

Superstatistical cluster decay

We provide an overview of Tsallis statistics, presented as a special case of superstatistics and applied to the multiparticle processes described by the statistical cluster model. This model combines Boltzman statistics applied to hadronization of clusters and superstatistics induced by fluctuations of their Lorentz factors. It results in a Tsallis-like distribution of transverse momenta with some scale, the origin of which is discussed. We show that this distribution becomes a Tsallis distribution in a special case, namely when one combines fluctuations of the Lorentz factor and temperature inside the cluster, given by beta and gamma distributions, respectively.

hep-ph↗
arXiv2015

From QCD-based hard-scattering to nonextensive statistical mechanical descriptions of transverse momentum spectra in high-energy $pp$ and $p\bar p$ collisions

Transverse spectra of both jets and hadrons obtained in high-energy $pp$ and $p\bar p $ collisions at central rapidity exhibit power-law behavior of $1/p_T^n$ at high $p_T$. The power index $n$ is 4-5 for jet production and is 6-10 for hadron production. Furthermore, the hadron spectra spanning over 14 orders of magnitude down to the lowest $p_T$ region in $pp$ collisions at LHC can be adequately described by a single nonextensive statistical mechanical distribution that is widely used in other branches of science. This suggests indirectly the possible dominance of the hard-scattering process over essentially the whole $p_T$ region at central rapidity in high-energy $pp$ and $p \bar p$ collisions. We show here direct evidences of such a dominance of the hard-scattering process by investigating the power indices of UA1 and ATLAS jet spectra over an extended $p_T$ region and the two-particle correlation data of the STAR and PHENIX Collaborations in high-energy $pp$ and $p \bar p$ collisions at central rapidity. We then study how the showering of the hard-scattering product partons alters the power index of the hadron spectra and leads to a hadron distribution that may be cast into a single-particle nonextensive statistical mechanical distribution. Because of such a connection, the nonextensive statistical mechanical distribution may be considered as a lowest-order approximation of the hard-scattering of partons followed by the subsequent process of parton showering that turns the jets into hadrons, in high energy $pp$ and $p\bar p$ collisions.

hep-ph↗
arXiv2015

Quasi-power laws in multiparticle production processes

We review the ubiquitous presence in multiparticle production processes of quasi-power law distributions (i.e., distributions following pure power laws for large values of the argument but remaining finite, usually exponential, for small values). Special emphasis is placed on the conjecture that this reflects the presence in the produced hadronic systems of some intrinsic fluctuations. If described by parameter q they form, together with the scale parameter $T$ ("temperature"), basis of Tsallis distribution, ${f(X)\sim [1 - (1-q)X/T]^{1/(1-q)}}$, frequently used to describe the relevant distributions (the X being usually a transverse momentum). We discuss the origin of such quasi-power law behavior based on our experience with the description of multiparticle production processes. In particular, we discuss Tsallis distribution with complex nonextensivity parameter q and argue that it is needed to describe log-oscillations as apparently observed in recent data on large momentum distributions in very high energy p-p collisions.

hep-ph↗
arXiv2015

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.

cond-mat.stat-mech↗
arXiv2014

Quasi-power law ensembles

Quasi-power law ensembles are discussed from the perspective of nonextensive Tsallis distributions characterized by a nonextensive parameter $q$. A number of possible sources of such distributions are presented in more detail. It is further demonstrated that data suggest that nonextensive parameters deduced from Tsallis distributions functions $f\left(p_T\right)$, $q_1$, and from multiplicity distributions (connected with Tsallis entropy), $q_2$, are not identical and that they are connected via $q_1 + q_2 = 2$. It is also shown that Tsallis distributions can be obtained directly from Shannon information entropy, provided some special constraints are imposed. They are connected with the type of dynamical processes under consideration (additive or multiplicative). Finally, it is shown how a Tsallis distribution can accommodate the log-oscillating behavior apparently seen in some multiparticle data.

cond-mat.stat-mech↗
arXiv2014

Possible Implication of a Single Nonextensive $p_T$ Distribution for Hadron Production in High-Energy $pp$ 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.

hep-ph↗
arXiv2014

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.

hep-ph↗
arXiv2014

The transverse-momenta distributions in high-energy $pp$ collisions -- A statistical-mechanical approach

We analyze LHC available data measuring the distribution probability of transverse momenta~$p_T$ in proton-proton collisions at $\sqrt{s}=0.9\,\textrm{TeV}$ (CMS, ALICE, ATLAS) and $\sqrt{s}=7\,\textrm{TeV}$ (CMS, ATLAS). A remarkably good fitting can be obtained, along fourteen decades in magnitude, by phenomenologically using $q$-statistics for a {\it single} particle of a two-dimensional relativistic ideal gas. The parameters that have been obtained by assuming $\textrm{d}N/p_T\textrm{d}p_T\textrm{d}y \propto e_q^{-E_T/T}$ at mid-rapidity are, in all cases, $q \simeq 1.1$ and $T\simeq 0.13\,\textrm{GeV}$ (which satisfactorily compares with the pion mass). This fact suggests the approximate validity of a "no-hair" statistical-mechanical description of the hard-scattering hadron-production process in which the detailed mechanisms of parton scattering, parton cascades, parton fragmentation, running coupling and other information can be subsumed under the stochastic dynamics in the lowest-order description. In addition to that basic structure, a finer analysis of the data suggests a small oscillatory structure on top of the leading $q$-exponential. The physical origin of such intriguing oscillatory behavior remains elusive, though it could be related to some sort of fractality or scale-invariance within the system.

hep-ph↗
arXiv2014

Log-periodic oscillations of transverse momentum distributions

Large p_T transverse momentum distributions exhibit apparently a power-like behavior. We argue that, under closer inspection, this behavior is in fact decorated with some log-periodic oscillations. Assuming that this is genuine effect and not experimental artefact, it suggests that either the exponent of the power-like behavior is in reality complex number or that there is a scale parameter which exhibits specific log-eriodic oscillations. This problem is discussed using Tsallis distributions with scale parameter being a temperature T. At this stage we consider both possibilities on equal footing.

hep-ph↗
arXiv2013

Self-similarity in jet events following from p-p collisions at LHC

Using a Tsallis nonextensive approach, we simultaneously analyze recent data obtained by the LHC ATLAS experiment on distributions of transverse momenta of jets, p_T^{jet}, together with distributions of transverse momenta of particles produced within these jets (defined relative to the jet's axis), p_T^{rel}, and their multiplicity distributions, P(N). The respective nonextensivity parameters for distributions of jets, q_{jet}, for distributions of particles in jets, q_{rel} and the global nonextensivity parameter obtained from P(N), q_N, were then compared with nonextensivity parameters q obtained from minimum bias pp collisions at energies corresponding to the energies of these jets. The values of the corresponding nonextensivity parameters were found to be similar, strongly indicating the existence of a common mechanism behind all these processes. We tentatively identify this as a self-similarity property known to be present there and resulting in Tsallis type distributions. If confirmed, this would considerably strengthen the nonextensive Tsallis approach.

hep-ph↗
arXiv2013

Relativistic Hard-Scattering and Tsallis Fits to pT Spectra in pp Collisions at the LHC

Motivated by the good Tsallis fits to the high-pT spectra in pp collisions at the LHC, we study the relativistic hard-scattering model and obtain an approximate analytical expression for the differential hard-scattering cross section at η~ 0. The power-law behaviour of the transverse spectra, in the form of dσ/dpT^2 \propto 1/pT^n, gives a power index n in the range of 4.5-5.5 for jet production as predicted by pQCD, after the dependencies of the structure functions and the running coupling constant are properly taken into account. The power indices for hadron production n are slightly greater than those for jet production.

hep-ph↗
arXiv2013

Tsallis Fits to pT Spectra and Multiple Hard Scattering in pp Collisions at the LHC

Phenomenological Tsallis fits to the CMS, ATLAS, and ALICE transverse momentum spectra of hadrons for pp collisions at LHC were recently found to extend over a large range of the transverse momentum. We investigate whether the few degrees of freedom in the Tsallis parametrization may arise from the relativistic parton-parton hard-scattering and related processes. The effects of the multiple hard-scattering and parton showering processes on the power law are discussed. We find empirically that whereas the transverse spectra of both hadrons and jets exhibit power-law behavior of 1/pT^n at high pT, the power indices n for hadrons are systematically greater than those for jets, for which n~4-5.

hep-ph↗
arXiv2012

Tsallis Fits to p_T Spectra for pp Collisions at LHC

Phenomenological Tsallis fits to the CMS and ATLAS transverse spectra of charged particles were found to extend for p_T from 0.5 to 181 GeV in pp collisions at LHC at \sqrt{s}=7 TeV, and for p_T from 0.5 to 31 GeV at \sqrt{s}=0.9 TeV. The simplicity of the Tsallis parametrization and the large range of the fitting transverse momentum raise questions on the physical meaning of the degrees of freedom that enter into the Tsallis distribution or q-statistics.

hep-ph↗
arXiv2012

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.

hep-ph↗
arXiv2012

Consequences of temperature fluctuations in observables measured in high energy collisions

We review the consequences of intrinsic, nonstatistical temperature fluctuations as seen in observables measured in high energy collisions. We do this from the point of view of nonextensive statistics and Tsallis distributions. Particular attention is paid to multiplicity fluctuations as a first consequence of temperature fluctuations, to the equivalence of temperature and volume fluctuations, to the generalized thermodynamic fluctuations relations allowing us to compare fluctuations observed in different parts of phase space, and to the problem of the relation between Tsallis entropy and Tsallis distributions. We also discuss the possible influence of conservation laws on these distributions and provide some examples of how one can get them without considering temperature fluctuations.

hep-ph↗
arXiv2012

Correlations from generalized thermodynamics

In order to account for possible nonstatistical fluctuations in a hadronizing system (leading to the characteristic power-like behavior of the respective single particle spectra and to the broadening of the corresponding multiparticle distributions) while using the statistical approach one has to resort to its nonextensive version. The new parameter q appearing there is directly connected to the variance of the particular variable X, q = 1+Var(X)/ ^2 (with q = 1 for the usual statistical model). We shall demonstrate here how such an approach allows us to compose fluctuations of different observables (described by their respective parameters q) leading to a characteristic sum rule connecting q's deduced from measurements of these observables, which can be verified experimentally. We shall also discuss ensembles in which all relevant quantities, namely the energy (U), temperature (T) and multiplicity (N), can fluctuate. A specific relation connecting all these fluctuating variables is proposed. It generalizes the so called Lindhard thermodynamic uncertainty relations known in the literature, by introducing, in a natural way, a possibility of correlations between the fluctuating variables considered. This point is illustrated using an example from the multiparticle production processes. We show that fluctuations from different parts of phase space (characterized by different parameters q) are correlated and that the strength of these correlations is a function of these q's, Cov(U,T) = F({q}). These correlations can be tested experimentally. Some rough first estimates, using available data, are presented.

hep-ph↗
arXiv2011

The imprints of superstatistics in multiparticle production processes

We provide an update of the overview of imprints of Tsallis nonextensive statistics seen in a multiparticle production processes. They reveal an ubiquitous presence of power law distributions of different variables characterized by the nonextensivity parameter q > 1. In nuclear collisions one additionally observes a q-dependence of the multiplicity fluctuations reflecting the finiteness of the hadronizing source. We present sum rules connecting parameters q obtained from an analysis of different observables, which allows us to combine different kinds of fluctuations seen in the data and analyze an ensemble in which the energy (E), temperature (T) and multiplicity (N) can all fluctuate. This results in a generalization of the so called Lindhard's thermodynamic uncertainty relation. Finally, based on the example of nucleus-nucleus collisions (treated as a quasi-superposition of nucleon-nucleon collisions) we demonstrate that, for the standard Tsallis entropy with degree of nonextensivity q < 1, the corresponding standard Tsallis distribution is described by q' = 2 - q > 1.

hep-ph↗