Tsallis Statistical Interpretation of Transverse Momentum Spectra in High-Energy pA Collisions

In Tsallis statistics, we investigate charged pion and proton production for pCu and pPb interactions at 3, 8, and 15 GeV/c. Two versions of Tsallis distribution are implemented in a multisource thermal model. A comparison with experimental data of the HARP-CDP group shows that they both can reproduce the transverse momentum spectra, but the improved form gives a better description. It is also found that the difference between q and q′ is small when the temperature T = T′ for the same incident momentum and angular interval, and the value of q is greater than q′ in most cases

On Descriptions of Particle Transverse Momentum Spectra in High Energy Collisions

The transverse momentum spectra obtained in the frame of an isotropic emission source are compared in terms of Tsallis, Boltzmann, Fermi-Dirac, and Bose-Einstein distributions and the Tsallis forms of the latter three standard distributions. It is obtained that, at a given set of parameters, the standard distributions show a narrower shape than their Tsallis forms which result in wide and/or multicomponent spectra with the Tsallis distribution in between. A comparison among the temperatures obtained from the distributions is made with a possible relation to the Boltzmann temperature. An example of the angular distributions of projectile fragments in nuclear collisions is given

Comparing Multicomponent Erlang Distribution and Lévy Distribution of Particle Transverse Momentums

The transverse momentum spectrums of final-state products produced in nucleus-nucleus and proton-proton collisions at different center-of-mass energies are analyzed by using a multicomponent Erlang distribution and the Lévy distribution. The results calculated by the two models are found in most cases to be in agreement with experimental data from the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). The multicomponent Erlang distribution that resulted from a multisource thermal model seems to give a better description as compared with the Lévy distribution. The temperature parameters of interacting system corresponding to different types of final-state products are obtained. Light particles correspond to a low temperature emission, and heavy particles correspond to a high temperature emission. Extracted temperature from central collisions is higher than that from peripheral collisions

On Two-Ridge Structure in Two-Particle Azimuthal Correlations in Proton-Lead Collisions at Large Hadron Collider Energy

Two-particle azimuthal correlations are studied in the framework of a multisource thermal model. Each source is assumed to produce many particles. Each particle pair measured in final state is considered to be produced at two emission points (subsources) in a single or two sources. The first emission point corresponds to the production of “trigger” particle and the second one corresponds to that of “associated” particle. There are oscillations and other interactions between the two emission points. In the rest frame of the “associated” particle's emission point, the oscillations and other interactions cause the momentum of the “trigger” particle to depart from the original value. The modelling results are in agreement with the experimental data of proton-lead (p-Pb) collisions at <math id="M1" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><mrow><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></mrow></msqrt></mrow></math> = 5.02 TeV, one of the Large Hadron Collider energies, measured by the ALICE and ATLAS Collaborations

Transverse Momentum and Pseudorapidity Distributions of Charged Particles and Spatial Shapes of Interacting Events in Pb-Pb Collisions at 2.76 TeV

The transverse momentum and pseudorapidity distributions of charged particles produced in Pb-Pb collisions with different centrality intervals at center-of-mass energy per nucleon pair <math id="M1" xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>2.76</mn></math>  TeV have been analyzed by using the improved multisource thermal model in which the whole interacting system and then the sources are described by the Tsallis statistics. The modelling results are in agreement with experimental data of the ALICE Collaboration. The rapidity distributions of charged particles are obtained according to the extracted parameter values. The shapes of interacting events (the dispersion plots of charged particles) are given in the momentum, rapidity, velocity, and coordinate spaces. Meanwhile, the event shapes in different spaces consisted by different transverse quantities and longitudinal quantities are presented

On Particle Production in Lead-Gold Collision and Azimuthal Anisotropy at Top SPS Energy

In a multisource thermal model, we analyze the dependence of elliptic flow <math id="M1" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math> on the transverse momentum <math id="M2" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>T</mi></mrow></msub></mrow></math> . The model results are compared with the data of <math id="M3" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>-</mo></mrow></msup></mrow></math> , <math id="M4" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msubsup></mrow></math> , <math id="M5" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi></mrow></math> , and <math id="M6" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Λ</mi></mrow></math> measured in Pb + Au collisions at top SPS energy, 17.3 GeV. It is found that the azimuthal anisotropy in the evolution process of high-energy collisions is correlated highly to the number of participant nucleons

Chemical Potentials of Quarks Extracted from Particle Transverse Momentum Distributions in Heavy Ion Collisions at RHIC Energies

In the framework of a multisource thermal model, the transverse momentum distributions of charged particles produced in nucleus-nucleus (A-A) and deuteron-nucleus (d-A) collisions at relativistic heavy ion collider (RHIC) energies are investigated by a two-component revised Boltzmann distribution. The calculated results are in agreement with the PHENIX experimental data. It is found that the source temperature increases obviously with increase of the particle mass and incident energy, but it does not show an obvious change with the collision centrality. Then, the values of chemical potentials for up, down, and strange quarks can be obtained from the antiparticle to particle yield ratios in a wide transverse momentum range. The relationship between the chemical potentials of quarks and the transverse momentum with different centralities is investigated, too

On Extraction of Chemical Potentials of Quarks from Particle Transverse Momentum Spectra in High Energy Collisions

We present two methods to extract the chemical potentials of quarks in high energy collisions. The first method is based on the ratios of negatively/positively charged particles, and the temperatures extracted from the transverse momentum spectra of related hadrons are needed. The second method is based on the chemical potentials of some particles, and we also need the transverse momentum spectra of related hadrons. To extract the quark chemical potentials, we would like to propose experimental collaborations to measure simultaneously not only the transverse momentum spectra of <math id="M1" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mover accent="true"><mrow><mi>p</mi></mrow><mo>-</mo></mover></mrow></math> , <math id="M2" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi></mrow></math> , <math id="M3" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>-</mo></mrow></msup></mrow></math> , <math id="M4" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> , <math id="M5" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>-</mo></mrow></msup></mrow></math> , and <math id="M6" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> , but also those of <math id="M7" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>-</mo></mrow></msup></mrow></math> , <math id="M8" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> , <math id="M9" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>-</mo></mrow></msup></mrow></math> , and <math id="M10" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> (even those of <math id="M11" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mrow><mi mathvariant="normal">Δ</mi></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msup></mrow></math> , <math id="M12" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mrow><mi mathvariant="normal">Δ</mi></mrow><mrow><mo>-</mo></mrow></msup></mrow></math> , and <math id="M13" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mrow><mi mathvariant="normal">Ω</mi></mrow><mrow><mo>-</mo></mrow></msup></mrow></math> ) in high energy nuclear collisions

Double-Differential Production Cross Sections of Charged Pions in Charged Pion Induced Nuclear Reactions at High Momentums

The double-differential <math id="M1" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>±</mo></mrow></msup></mrow></math> production cross sections in interactions of charged pions on targets at high momentums are analyzed by using a multicomponent Erlang distribution which is obtained in the framework of a multisource thermal model. The calculated results are compared and found to be in agreement with the experimental data at the incident momentums of 3, 5, 8, and 12 GeV/c measured by the HARP Collaboration. It is found that the source contributions to the mean momentum of charged particles and to the distribution width of particle momentums decrease with increase of the emission angle, and the source number and temperature do not show an obvious dependence on the emission angle of the considered particle

Emission of Protons and Charged Pions in p + Cu and p + Pb Collisions at 3, 8, and 15 GeV/c

We present an analysis of proton and charged pion transverse momentum spectra of <math id="M1" xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>+</mo><mtext>Cu</mtext></math> and <math id="M2" xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>+</mo><mtext>Pb</mtext></math> reactions at 3, 8, and 15 GeV/c in the framework of a multisource thermal model. The spectra are compared closely with the experimental data of HARP-CDP at all angular intervals. The result shows that the widths of the particle distributions in both <math id="M3" xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>+</mo><mtext>Cu</mtext></math> and <math id="M4" xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>+</mo><mtext>Pb</mtext></math> collisions decrease with increasing the angle for the same incident momentum