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Register a new userTransverse momentum spectra of strange hadrons within extensive and nonextensive statistics
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Using generic (non)extensive statistics, in which the underlying system autonomously manifests its extensive and nonextensive statistical nature, we extract various fit parameters from the CMS experiment and compare these to the corresponding results obtained from Tsallis and Boltzmann statistics. The present study is designed to indicate the possible variations between the three types of statistical approaches and characterizes their dependence on collision energy, multiplicity, and size of the system of interest. We analyze the transverse momentum spectra $p_T$ of the strange hadrons Kslxi produced in Pb+Pb collisions, at 2.76 TeV, in p+Pb collisions, at 5.02 TeV, and in $p+p$ collisions, at 7 TeV. From the comparison of the resulting fit parameters; temperature $T$, volume $V$, and nonextensvie parameter $d$, with calculations based on Tsallis and Boltzmann statistics, remarkable differences between the three types of statistics are determined besides a strong dependence on size and type of the colliding system. We conclude that the produced particles with large masses and large strange quantum numbers likely freeze out earlier than the ones with smaller masses and less strange quantum numbers. This conclusion seems not depending on the type of the particle or the collision but apparently manifesting transitions from chemical (larger temperature) to the kinetic freezeouts (lower temperature). For the first university (equivalent) class c=1, the decrease in the second one, $d$, with increasing energy and collision centrality highlights that the system departs from nonextensivity (non-equilibrium) and apparently approaches extensivity (equilibrium) indicating that the Boltzmann statistics becomes the proper statistical approach in describing that system. Last but not least, we present analytical expressions for the energy dependence of the various fit parameters.
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We present a study of transverse momentum ($p_{T}$) spectra of unidentified charged particles in pp collisions at RHIC and LHC energies from $sqrt{s}$ = 62.4 GeV to 13 TeV using Tsallis/Hagedorn function. The power law of Tsallis/Hagedorn form gives excellent description of the hadron spectra in $p_{T}$ range from 0.2 to 300 GeV/$c$. The power index $n$ of the $p_T$ distributions is found to follow a function of the type $a+b/sqrt {s}$ with asymptotic value $a = 5.72$. The parameter $T$ governing the soft bulk contribution to the spectra remains almost same over wide range of collision energies. We also provide a Tsallis/Hagedorn fit to the $p_{T}$ spectra of hadrons in pPb and different centralities of PbPb collisions at $sqrt{s_{NN}}$ = 5.02 TeV. The data/fit shows deviations from the Tsallis distribution which become more pronounced as the system size increases. We suggest simple modifications in the Tsallis/Hagedorn power law function and show that the above deviations can be attributed to the transverse flow in low $p_T$ region and to the in-medium energy loss in high $p_T$ region.
The data on hadron transverse momentum spectra in different centrality classes of p+Pb collisions at $sqrt{s}_{NN} = 5.02$ TeV has been analysed to extract the freezeout hypersurface within a simultaneous chemical and kinetic freezeout scenario. The freezeout hypersurface has been extracted for three different freezeout schemes that differ in the way strangeness is treated: i. unified freezeout for all hadrons in complete thermal equilibrium (1FO), ii. unified freezeout for all hadrons with an additional parameter $gamma_S$ which accounts for possible out-of-equilibrium production of strangeness (1FO$+gamma_S$), and iii. separate freezeout for hadrons with and without strangeness content (2FO). Unlike in heavy ion collisions where 2FO performs best in describing the mean hadron yields as well as the transverse momentum spectra, in p+Pb we find that 1FO$+gamma_S$ with one less parameter than 2FO performs better. This confirms expectations from previous analysis on the system size dependence in the freezeout scheme with mean hadron yields: while heavy ion collisions that are dominated by constituent interactions prefer 2FO, smaller collision systems like proton + nucleus and proton + proton collisions with lesser constituent interaction prefer a unified freezeout scheme with varying degree of strangeness equilibration.
The transverse momentum distributions of various hadrons produced in most central Pb+Pb collisions at LHC energy Root(s_NN) = 2.76 TeV have been studied using our earlier proposed unified statistical thermal freeze-out model. The calculated results are found to be in good agreement with the experimental data measured by the ALICE experiment. The model calculation fits provide the thermal freeze-out conditions in terms of the temperature and collective flow effect parameters for different particle species. Interestingly the model parameter fits reveal a strong collective flow in the system which appears to be a consequence of the increasing particle density at LHC. The model used incorporates a longitudinal as well as transverse hydrodynamic flow. The chemical potential has been assumed to be nearly equal to zero for the bulk of the matter owing to a high degree of nuclear transparency effect at such energies. The contributions from heavier decay resonances are also taken into account in our calculations.
In order to characterize the transverse momentum spectra of positive pions measured in the ALICE experiment, two thermal approaches are utilized; one is based on degeneracy of non-perfect Bose-Einstein gas and the other imposes an {it ad-hoc} finite pion-chemical potential. The inclusion of missing haron states and the out-of-chemical equilibrium greatly contribute to the excellent characterization of pion production. The excellent reproduction of the experimental data can be understood as a manifestation of not-yet-regarded anomalous pion-production, which likely contribute to the long-standing debate on the {it anomalous} proton-to-pion ratios at top RHIC and LHC energies.
We make use of a simple scalar diquark model to study the potential transverse momentum and potential angular momentum, defined as the difference between the Jaffe-Manohar and Ji notions of transverse momentum and orbital angular momentum, respectively. A non-vanishing potential angular momentum has been previously found in lattice calculations and is believed to appear due to the effects of initial/final state interactions between the spectator system and the struck quark in high energy scattering processes. Such re-scattering phenomena are similar in nature to those who are responsible for generating the Sivers shift. This motivates us to search for an estimate of the potential angular momentum in terms of the expectation value of the transverse momentum of the struck quark.
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