Two-component Erlang Distribution Research Articles

Centrality-Dependent Chemical Potentials of Light Hadrons and Quarks Based on pT Spectrum and Particle Yield Ratio in Au-Au Collisions at RHIC Energies

We analyze the pT spectra of π±, K±, p, and p¯ produced in different centralities’ Au-Au collisions at different collision energies from 7.7 to 62.4 GeV using a two-component Erlang distribution in the framework of a multi-source thermal model. The fitting results are consistent with the experimental data, and the yield ratios of negative to positive particles are obtained from the normalization constants. Based on the yield ratios, the chemical potentials of light hadrons (π, K, and p) and quarks (u, d, and s) are extracted. This study shows that only the yield ratios of p decrease with the increase in centrality. The logarithms of these yield ratios in the same centrality show obvious linear dependence on 1/sNN. The extracted chemical potentials (the absolute magnitude for π) of light hadrons and quarks decrease with the increase in energy. The curves of chemical potential vs. energy for all centralities derived from the linear fits of the logarithms of the yield ratio as a function of energy have their maximum (the absolute magnitude for π) at the same energy of 3.526 GeV, which is possibly the critical energy of phase transition from a liquid-like hadron state to a gas-like quark state in the collision system.

Statistical Behavior of Lepton Pair Spectrum in the Drell-Yan Process and Signal from Quark-Gluon Plasma in High-Energy Collisions

We analyze the transverse momentum ( p T ) spectra of lepton pairs ( ℓ ℓ ¯ ) generated in the Drell-Yan process, as detected in proton-nucleus (pion-nucleus) and proton-(anti)proton collisions by ten collaborations over a center-of-mass energy s N N or s if in a simplified form) range from ~ 20 GeV to above 10 TeV. Three types of probability density functions (the convolution of two Lévy-Tsallis functions, the two-component Erlang distribution, and the convolution of two Hagedorn functions) are utilized to fit and analyze the p T spectra. The fit results are approximately in agreement with the collected experimental data. Consecutively, we obtained the variation law of related parameters as a function of s and invariant mass Q . In the fit procedure, a given Lévy-Tsallis (or Hagedorn) function can be regarded as the probability density function of transverse momenta contributed by a single quark ( q ) or anti-quark ( q ¯ ). The Drell-Yan process is then described by the statistical method.

Excitation functions of parameters in Erlang distribution, Schwinger mechanism, and Tsallis statistics in RHIC BES program

Experimental results of the transverse momentum distributions of phi mesons and $\Omega$ hyperons produced in gold-gold (Au-Au) collisions with different centrality intervals, measured by the STAR Collaboration at different energies (7.7, 11.5, 19.6, 27, and 39 GeV) in the beam energy scan (BES) program at the relativistic heavy ion collider (RHIC), are approximately described by the single Erlang distribution and the two-component Schwinger mechanism. Meanwhile, the STAR experimental transverse momentum distributions of negatively charged particles, produced in Au-Au collisions at RHIC BES energies, are approximately described by the two-component Erlang distribution and the single Tsallis statistics. The excitation functions of free parameters are obtained from the fit to the experimental data. A weak softest point in the string tension in $\Omega$ hyperon spectra is observed at 7.7 GeV.

Comparing Erlang Distribution and Schwinger Mechanism on Transverse Momentum Spectra in High Energy Collisions

We study the transverse momentum spectra ofJ/ψandΥmesons by using two methods: the two-component Erlang distribution and the two-component Schwinger mechanism. The results obtained by the two methods are compared and found to be in agreement with the experimental data of proton-proton (pp), proton-lead (p-Pb), and lead-lead (Pb-Pb) collisions measured by the LHCb and ALICE Collaborations at the large hadron collider (LHC). The related parameters such as the mean transverse momentum contributed by each parton in the first (second) component in the two-component Erlang distribution and the string tension between two partons in the first (second) component in the two-component Schwinger mechanism are extracted.

Event Patterns Extracted from Transverse Momentum and Rapidity Spectra ofZBosons and Quarkonium States Produced in pp and Pb-Pb Collisions at LHC

Transverse momentum (pT) and rapidity (y) spectra ofZbosons and quarkonium states (some charmoniumcc¯mesons such asJ/ψandψ(2S)and some bottomoniumbb¯mesons such asΥ(1S),Υ(2S), andΥ(3S)) produced in proton-proton (pp) and lead-lead (Pb-Pb) collisions at the large hadron collider (LHC) are uniformly described by a hybrid model of two-component Erlang distribution forpTspectrum and two-component Gaussian distribution foryspectrum. The former distribution results from a multisource thermal model, and the latter one results from the revised Landau hydrodynamic model. The modelling results are in agreement with the experimental data measured in pp collisions at center-of-mass energiess=2.76and 7 TeV and in Pb-Pb collisions at center-of-mass energy per nucleon pairsNN=2.76 TeV. Based on the parameter values extracted frompTandyspectra, the event patterns (particle scatter plots) in two-dimensionalpT-yspace and in three-dimensional velocity space are obtained.

A Study of Transverse Momentum Distributions of Jets Produced inp-p,p-p-,d-Au, Au-Au, and Pb-Pb Collisions at High Energies

The transverse momentum distributions of jets produced inp-p,p-p-,d-Au, Au-Au, and Pb-Pb collisions at high energies with different selected conditions are analyzed by using a multisource thermal model. The multicomponent (mostly two-component) Erlang distribution used in our description is in good agreement with the experimental data measured by the STAR, D0, CDF II, ALICE, ATLAS, and CMS Collaborations. Related parameters are extracted from the transverse momentum distributions and some information on different interacting systems is obtained. In the two-component Erlang distribution, the first component has usually two or more sources which are contributed by strong scattering interactions between two quarks or more quarks and gluons, while the second component has mostly two sources which are contributed by harder head-on scattering between two quarks.

Unified description of transverse momentum spectrums contributed by soft and hard processes in high-energy nuclear collisions

The transverse momentum spectrums of π −, π +, K −, K +, $$\bar p$$ , and p produced in p-Pb collisions at √s NN = 502 TeV measured by the CMS Collaboration and in Pb-Pb collisions at √s NN = 2.76 TeV measured by the ALICE Collaboration are described by a two-component Erlang distribution. The first component corresponds to “soft” excitation process and contributes in the low transverse momentum region, which is contributed by 2–5 partons (sea quarks and gluons) with strong interactions. The second component corresponds to “hard” scattering process and contributes in the high transverse momentum region, which is contributed by 2 partons (valent quarks) with violent head-on collision. Each parton source contributes an exponential transverse momentum spectrum. Both the soft and hard processes result in an Erlang distribution. The transverse momentum spectrums of final-state charged particles are then described by the two-component Erlang distribution. The contribution ratio (30–40%) of the hard process extracted from nuclear collisions at the Large Hadron Collider is consistent with that (17–46%) obtained from other methods.