arXiv subjects

Fu-Hu Liu

Publications and source records attributed to Fu-Hu Liu.

At least 37 records · Page 2Linked to original sources

arXiv2022

Pseudorapidity dependence of the $p_T$ spectra of charged hadrons in $pp$ collisions at $\sqrt{s}$ = 0.9 and 2.36 TeV

We report the predictions of different Monte Carlo event generators including HIJING, Pythia, and QGSJETII in comparison with the experimental data measured by the CMS Collaboration at CERN in proton-proton ($pp$) collisions at center-of-mass energy $\sqrt{s}$ = 0.9 and 2.36 TeV. The CMS experimental transverse momentum ($p_T$ or $p_{\perp}$) spectra of charged hadrons were measured for pseudorapidity range 0 $\le$ $η$ $\le$ 2.4 with bin width of $η$ = 0.2 (for $p_T$ from 0.1 to 2 GeV/$c$) and a single bin of $η$ for $\lvert$$η$$\rvert$ $<$ 2.4 (for $p_T$ from 0.1 to 4 GeV/$c$). Pythia reproduced the $p_T$ spectra with reasonable agreement for most of the $p_T$ range. It depicts better results in the case of the $|η|<$ 2.4 than HIJING and QGSJETII which could reproduce the spectra in a limited $p_T$ range. Furthermore, to analyze the $p_T$ spectra of charged hadrons measured by the CMS Collaboration, we used a three component function (structured from the Boltzmann distribution) and the $q$-dual function (from the $q$-dual statistics) to extract parameter values relevant for the study of bulk properties of hadronic matter at high energy. We have also applied the two analytic functions over the model predictions. The values extracted by the functions from the HIJING and Pythia models are closer to the experimental data than the QGSJETII model. Although the models could reproduce the $p_T$ spectra of all charged particles in some of the $p_T$ range but none of them could reproduce the distributions over the entire $p_T$ range and in all the pseudorapidity regions.

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arXiv2022

Thermal freeze-out parameters and pseudo-entropy from charged hadron spectra in high energy collisions

We collected the transverse momentum (mass) spectra of charged hadrons ($π^{-}$, $π^{+}$, $K^{-}$, $K^{+}$, $\overline{p}$, and $p$) produced in collisions over a center-of-mass energy range from 2.70 to 200 GeV (per nucleon pair). The modified Tsallis--Pareto-type function (the TP-like function) with average transverse flow velocity is used to describe the contribution of participant or constituent quarks to transverse momentum of considered hadron. The experimental spectra of $π^{\mp}$ and $K^{\mp}$ (or $\overline{p}$ and $p$) are fitted by the convolution of two (or three) TP-like functions due to the fact that two (or three) constituent quarks are regarded as two (or three) energy resources in the formation of considered hadron. From the reasonable fits to the spectra, the thermal freeze-out parameters are extracted, and the pseudo-entropy is newly defined and extracted. Some parameters quickly change in the energy range of less than 7.7 GeV, and slowly change in the energy range of greater than 7.7 GeV, indicating the variation of collision mechanism at around 7.7 GeV.

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arXiv2022

Centrality-dependent chemical potentials of light hadrons and quarks based on transverse momentum spectra and particle yield ratios in Au-Au collisions

We describe the transverse momentum spectra of $π^\pm$, $K^\pm$, $p$, and $\bar{p}$ produced in different centralities gold-gold (Au-Au) collisions at different collision energies range from 7.7 to 62.4 GeV by a two-component Erlang distribution. The fitting results are consistent with the experimental data, and the centrality- and energy-dependent yield ratios of negative to positive particles are obtained from the normalization constants. Based on the yield ratios, the energy- and centrality-dependent chemical potentials of light hadrons and quarks are extracted. The study shows that the dependences of the three types of particle yield ratios on centrality are not significant, especially for $π$. The logarithms of the three yield ratios show obvious linear dependence on $1/\sqrt{s_{NN}}$ over a range from 7.7 to 62.4 GeV. The extracted chemical potentials show obvious dependence on energy, and decrease with the increase of energy. The dependences of the energy-dependent chemical potentials of light hadrons and quarks on centrality are relatively more obvious in low energy region. The derived curves of chemical potentials for all centralities, from the linear fits of the logarithms of yield ratios vs energy, have the extremum at the same energy of 3.526 GeV, which possibly is the critical energy of phase transition from a liquid-like hadron state to a gas-like quark state in the collision system. With the increase of energy, all types of chemical potentials become small and tend to zero at very high energy, which indicates that with the increase of energy, the hadronic interactions gradually fade and the partonic interactions gradually become greater.

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arXiv2022

Multi-Source Thermal Model Describing Transverse Momentum Spectra of Final-State Particles in High Energy Collisions

In this mini review article, the transverse momentum spectra of final-state particles produced in high energy hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions described by the multi-source thermal model at the quark or parton level is summarized. In the model, the participant or contributor quarks or partons are considered to contribute together to the transverse momentum distribution of final-state particles with different modes of contributions. The concrete mode of contribution is generally determined by the difference of azimuthal angles of contributor partons in their emissions.

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arXiv2022

An energy independent scaling of transverse momentum spectra of direct (prompt) photons from two-body processes in high-energy proton-proton collisions

Transverse momentum spectra of direct (prompt) photons from two-body processes in high-energy proton-proton (p+p) collisions are analyzed in this paper. We collected the experimental invariant cross-sections at mid-rapidity in p+p collisions measured by the UA6, CCOR, R806, R110, PHENIX, NA24, CMS, ALICE, and ATLAS Collaborations over a center-of-mass energy range from 24.3 GeV to 13 TeV. In fitting the data, we used different kinds of functions which include the revised Tsallis--Pareto-type function (the TP-like function) at the particle level, the convolution of two TP-like functions at the quark level, and the root-sum-of-squares of two revised Tsallis-like functions in which the quark chemical potentials $μ_i=μ_B/3$ or $μ_i=0$, where $μ_B$ is the baryon chemical potential. We have extracted the values of three main free parameters: the effective temperature $T$, power index $n_0$ (or entropy index $q$), and correction index $a_0$. After analyzing the changing trends of the parameters, we found that $T$, $q$, and $a_0$ increase and $n_0$ decreases with the increase of collision energy. Based on the analyses of transverse momentum spectra, an energy independent scaling, i.e. the $x_T$ scaling, is obtained.

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arXiv2022

Analyzing transverse momentum spectra by a new method in high-energy collisions

We analyzed the transverse momentum spectra of positively and negatively charged pions ($π^+$ and $π^-$), positively and negatively charged kaons ($K^+$ and $K^-$), protons and antiprotons ($p$ and $\bar p$), as well as $ϕ$ produced in mid-(pseudo)rapidity region in central nucleus--nucleus (AA) collisions over a center-of-mass energy range from 2.16 to 2760 GeV per nucleon pair. The transverse momentum of the considered particle is regarded as the joint contribution of two participant partons which obey the modified Tsallis-like transverse momentum distribution and have random azimuths in superposition. The calculation of transverse momentum distribution of particles is performed by the Monte Carlo method and compared with the experimental data measured by international collaborations. The excitation functions of effective temperature and other parameters are obtained in the considered energy range. With the increase of collision energy, the effective temperature parameter increases quickly and then slowly. The boundary appears at around 5 GeV, which means the change of reaction mechanism and/or generated matter.

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arXiv2021

Initial-state temperature of light meson emission source from squared momentum transfer spectra in high-energy collisions

The squared momentum transfer spectra of light mesons, $π^0$, $π^+$, $η$, and $ρ^0$, produced in high-energy virtual photon-proton ($γ^{*} p$) $\rightarrow {\rm meson + nucleon}$ process in electron-proton ($ep$) collisions measured by the CLAS Collaboration are analyzed by the Monte Carlo calculations, where the transfer undergoes from the incident $γ^*$ to emitted meson or equivalently from the target proton to emitted nucleon. In the calculations, the Erlang distribution from a multi-source thermal model is used to describe the transverse momentum spectra of emitted particles. Our results show that the average transverse momentum ($\langle p_T\rangle$) and the initial-state temperature ($T_i$) increase from lower squared photon virtuality ($Q^2$) and Bjorken variable ($x_B$) to higher one. This renders that the excitation degree of emission source, which is described by $\langle p_T\rangle$ and $T_i$, increases with increasing of $Q^2$ and $x_B$.

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arXiv2021

Energy dependent kinetic freeze-out temperature and transverse flow velocity in high energy collisions

Transverse momentum spectra of negative and positive pions produced at mid-(pseudo)rapidity in inelastic or non-single-diffractive proton-proton collisions and in central nucleus-nucleus collisions over an energy range from a few GeV to above 10 TeV are analyzed by a (two-component) blast-wave model with Boltzmann-Gibbs statistics and with Tsallis statistics respectively. The model results are in similarly well agreement with the experimental data measured by a few productive collaborations who work at the Heavy Ion Synchrotron (SIS), Super Proton Synchrotron (SPS), Relativistic Heavy Ion Collider (RHIC), and Large Hadron Collider (LHC), respectively. The energy dependent kinetic freeze-out temperature and transverse flow velocity are obtained and analyzed. Both the quantities have quick increase from the SIS to SPS, and slight increase or approximate invariability from the top RHIC to LHC. Around the energy bridge from the SPS to RHIC, the considered quantities in proton-proton collisions obtained by the blast-wave model with Boltzmann-Gibbs statistics show more complex energy dependent behavior comparing with the results in other three cases.

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arXiv2021

Initial- and final-state temperatures of emission source from differential cross-section in squared momentum transfer in high energy collisions

The differential cross-section in squared momentum transfer of $ρ$, $ρ^0$, $ω$, $ϕ$, $f_{0}(980)$, $f_{1}(1285)$, $f_{0}(1370)$, $f_{1}(1420)$, $f_{0}(1500)$, and $J/ψ$ produced in high energy virtual photon-proton ($γ$$^{*} p$), photon-proton ($γp$), and proton-proton ($pp$) collisions measured by the H1, ZEUS, and WA102 Collaborations are analyzed by the Monte Carlo calculations. In the calculations, the Erlang distribution, Tsallis distribution, and Hagedorn function are separately used to describe the transverse momentum spectra of the emitted particles. Our results show that the initial- and final-state temperatures increase from lower squared photon virtuality to higher one, and decrease with increasing of center-of-mass energy.

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arXiv2021

Analysis of multiplicity dependencies of midrapidity pt distributions of identified charged particles in p+p collisions at (s)1/2=7 TeV at the LHC

Multiplicity dependencies of midrapidity transverse momentum distributions of identified charged particles in inelastic proton-proton collisions at center-of-mass energy of 7 TeV at the Large Hadron Collider (LHC), measured by ALICE Collaboration, have been analyzed. The full abstract with important results on the established effective temperature versus energy density dependence, estimated critical energy densities for probable deconfinement phase transition in proton-proton collisions at center-of-mass energy of 7 and 13 TeV and other results is given in the manuscript file.

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arXiv2021

A systematic analysis of transverse momentum spectra of $J/ψ$ mesons in high energy collisions

We aggregate the transverse momentum spectra of $J/ψ$ mesons produced in high energy gold-gold (Au-Au), deuteron-gold ($d$-Au), lead-lead (Pb-Pb), proton-lead ($p$-Pb), and proton-(anti)proton ($p$-$p(\overline{p})$) collisions measured by several collaborations at the Relativistic Heavy Ion collider (RHIC), the Tevatron Proton-Antiproton Collider, and the Large Hadron Collider (LHC). The collision energy (the center-of-mass energy) gets involved in a large range from dozens of GeV to 13 TeV (the top LHC energy). We consider two participant or contributor partons, a charm quark and an anti-charm quark, in the production of $J/ψ$. The probability density of each quark is described by means of the modified Tsallis--Pareto-type function (the TP-like function) while considering that both quarks make suitable contributions to the $J/ψ$ transverse momentum spectrum. Therefore, the convolution of two TP-like functions is applied to represent the $J/ψ$ spectrum. We adopt the mentioned convolution function to fit the experimental data and find out the trends of the power exponent, effective temperature, and of the revised index with changing the centrality, rapidity, and collision energy. Beyond that, we capture the characteristic of $J/ψ$ spectrum, which is of great significance to better understand the production mechanism of $J/ψ$ in high energy collisions.

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arXiv2021

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

We analyze the transverse momentum ($p_{T}$) spectra of lepton pairs ($\ell\bar \ell$) 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 ($\sqrt{s_{NN}}$ or $\sqrt{s}$ if in a simplified form) range from $\sim20$ 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 $\sqrt{s}$ 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 ($\bar q$). The Drell-Yan process is then described by the statistical method.

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arXiv2021

Effects of coalescence and isospin symmetry on the freezeout of light nuclei and their anti-particles

The transverse momentum spectra of light nuclei (deuteron, triton and helion) produced in various centrality intervals in Gold-Gold (Au-Au), Lead-Lead (Pb-Pb) and proton-Lead (p-Pb) collisions, as well as in inelastic (INEL) proton-proton (pp) collisions are analyzed by the blast wave model with Boltzmann Gibbs statistics. The model results are nearly in agreement with the experimental data measured by STAR and ALICE Collaborations in special transverse momentum ranges. We extracted the bulk properties in terms of kinetic freezeout temperature, transverse flow velocity and freezeout volume. It is observed that deuteron and anti-deuteron freezeout later than triton and helion as well as their anti-particles due to its smaller mass, while helion and triton, and anti-helion and anti-triton freezeout at the same time due to isospin symmetry at higher energies. It is also observed that light nuclei freezeout earlier than their anti-nuclei due to the large coalescence of nucleons for light nuclei compared to their anti-nuclei. The kinetic freezeout temperature, transverse flow velocity and kinetic freezeout volume decrease from central to peripheral collisions. Furthermore, the transverse flow velocity depends on mass of the particle which decreases with increasing the mass of the particle.

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arXiv2021

Excitation Functions of Tsallis-like Parameters in High-Energy Nucleus-Nucleus Collisions

The transverse momentum spectra of charged pions, kaons, and protons produced at mid-rapidity in central nucleus-nucleus (AA) collisions at high energies are analyzed by considering particles to be created from two participant partons which are assumed to be contributors from the collision system. Each participant (contributor) parton is assumed to contribute to the transverse momentum by a Tsallis-like function. The contributions of the two participant partons are regarded as the two components of transverse momentum of the identified particle. The experimental data measured in high-energy AA collisions by international collaborations are studied. The excitation functions of kinetic freeze-out temperature and transverse flow velocity are extracted. The two parameters increase quickly from $\approx3$ to $\approx10$ GeV (exactly from 2.7 to 7.7 GeV) and then slowly at above 10 GeV with the increase of collision energy. In particular, there is a plateau from near 10 GeV to 200 GeV in the excitation function of kinetic freeze-out temperature.

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arXiv2021

Centrality dependence of kinetic freeze-out temperature and transverse flow velocity in high energy nuclear collisions

Centrality-dependent double-differential transverse momentum spectra of charged pions, kaons, and (anti)protons produced in mid-pseudorapidity interval in $\sqrt{s_{NN}}=200$ GeV gold-gold and deuteron-gold collisions with different centralities are analyzed by the blast-wave model with Boltzmann-Gibbs statistics. Meanwhile, the mentioned spectra in mid-rapidity interval in $\sqrt{s_{NN}}=2.76$ TeV lead-lead and $\sqrt{s_{NN}}=5.02$ TeV proton-lead collisions with different centralities are analyzed by the same model. The model results are approximately in agreement with the experimental data in special transverse momentum ranges. It is shown that with the increase of event centrality and energy, the kinetic freeze-out temperature of the emission source and the transverse flow velocity of the produced particles slightly increase in some cases but they do not give an obvious change in other cases. Meanwhile, the kinetic freeze-out temperature (transverse flow velocity) increases (decreases) with the increase of particle mass. The average transverse momentum and initial temperature increase with the increase of event centrality, collision energy, and particle mass. This work also confirms the maximum size dependent effect, which states that the main parameters such as the kinetic freeze-out temperature and transverse flow velocity are mainly determined by the heaviest nucleus from proton-nucleus to nucleus-nucleus collisions.

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arXiv2021

Dependence of related parameters on centrality and mass in a new treatment for transverse momentum spectra in high energy collisions

We collected the experimental data of transverse momentum spectra of identified particles produced in proton-proton ($p$-$p$), deuteron-gold ($d$-Au or $d$-$A$), gold-gold (Au-Au or $A$-$A$), proton-lead ($p$-Pb or $p$-$A$), and lead-lead (Pb-Pb or $A$-$A$) collisions measured by the ALICE, CMS, LHCb, NA49, NA61/SHINE, PHENIX, and STAR collaborations at different center-of mass energies. The multisource thermal model at the quark level or the participant quark model is used to describe the experimental data. The free parameters, the effective temperature $T$, entropy index-related $n$, and revised index $a_{0}$, in the revised Tsallis--Pareto-type function are extracted at the quark level. In most cases, $T$ and $n$ in central collisions are larger than those in peripheral collisions, and $a_0$ does not change in different centrality classes. With the increase in the mass of produced particle or participant quark, $T$ and $a_0$ increase, and $n$ does not change significantly. The behaviors of related parameters from $p$-$p$, $p(d)$-$A$, and $A$-$A$ collisions are similar.

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arXiv2021

An evidence of triple kinetic freezeout scenario observed in all centrality intervals in Cu-Cu, Au-Au and Pb-Pb collisions at high energies

Transverse momentum spectra of $π^+$, $K^+$, $p$, $K^0_s$, $Λ$, $Ξ$ or $\barΞ^+$ and $Ω$ or $\barΩ^+$ or $Ω+\barΩ$ in Copper-Copper (Cu-Cu), Gold-Gold (Au-Au) and Lead-Lead (Pb-Pb) collisions at 200 GeV, 62.4 GeV and 2.76 TeV respectively, are analyzed in different centrality bins by the blast wave model with Tsallis statistics. The model results are approximately in agreement with the experimental data measured by BRAHMS, STAR and ALICE Collaborations in special transverse momentum ranges. Kinetic freeze out temperature, transverse flow velocity and kinetic freezeout volume are extracted from the transverse momentum spectra of the particles. It is observed that $\barΞ^+$ and $Ω$ or $\barΩ^+$ or $Ω+\barΩ$ have larger kinetic freezeout temperature followed by $K^+$, $K^0_s$ and $Λ$ than $π^+$ and $p$ due to smaller reaction cross-sections of multi-strange and strange particles than non-strange particles. The present work reveals the scenario of triple kinetic freezeout in collisions at BRAHMS, STAR and ALICE Collaborations, however the transverse flow velocity and kinetic freezeout volume are mass dependent and they decrease with the increasing rest mass of the particle. In addition, the kinetic freezeout temperature, transverse flow velocity and kinetic freezeout volume are decreasing from central to peripheral collisions while the parameter q increase from central to peripheral collisions, indicating the approach of quick equilibrium in the central collisions. Besides, the kinetic freezeout temperature and kinetic freezeout volume are observed to be larger in larger collision system which shows its dependence on the size of the interacting system, while transverse flow velocity increase with increasing energy.

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arXiv2020

An analysis of transverse momentum spectra of various jets produced in high energy collisions

With the framework of the multi-source thermal model, we analyze the experimental transverse momentum spectra of various jets produced in different collisions at high energies. Two energy sources, a projectile participant quark and a target participant quark, are considered. Each energy source (each participant quark) is assumed to contribute to the transverse momentum distribution to be the TP-like function, i.e. a revised Tsallis--Pareto-type function. The contribution of the two participant quarks to the transverse momentum distribution is then the convolution of two TP-like functions. The model distribution can be used to fit the experimental spectra measured by different collaborations. The related parameters such as the entropy index-related, effective temperature, and revised index are then obtained. The trends of these parameters are useful to understand the characteristic of high energy collisions.

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