arXiv subjects

Fu-Hu Liu

Publications and source records attributed to Fu-Hu Liu.

At least 73 records · Page 4Linked to original sources

arXiv2018

Comparing a few distributions of transverse momenta in high energy collisions

Transverse momentum spectra of particles produced in high energy collisions are very important due to their relations to the excitation degree of interacting system. To describe the transverse momentum spectra, one can use more than one probability density functions of transverse momenta, which are simply called the functions or distributions of transverse momenta in some cases. In this paper, a few distributions of transverse momenta in high energy collisions are compared with each other in terms of plots to show some quantitative differences. Meanwhile, in the framework of Tsallis statistics, the distributions of momentum components, transverse momenta, rapidities, and pasudorapidities are obtained according to the analytical and Monte Carlo methods. These analyses are useful to understand carefully different distributions in high energy collisions.

hep-ph↗

arXiv2018

Chemical potentials of light flavor quarks from yield ratios of negative to positive particles in Au+Au collisions at RHIC

The transverse momentum spectra of $π^{-}$, $π^{+}$, $K^{-}$, $K^{+}$, $\bar{p}$, and $p$ produced in Au+Au collisions at center-of-mass energy $\sqrt{s_{NN}}=7.7$, 11.5, 19.6, 27, 39, 62.4, 130, and $200$ GeV are analyzed in the framework of a multisource thermal model. The experimental data measured at midrapidity by the STAR Collaboration are fitted by the (two-component) standard distribution. The effective temperature of emission source increases obviously with the increase of the particle mass and the collision energy. At different collision energies, the chemical potentials of up, down, and strange quarks are obtained from the antiparticle to particle yield ratios in given transverse momentum ranges available in experiments. With the increase of logarithmic collision energy, the chemical potentials of light flavor quarks decrease exponentially.

nucl-th↗

arXiv2018

Examining the model dependence of the determination of kinetic freeze-out temperature and transverse flow velocity in small collision system

The transverse momentum distributions of the identified particles produced in small collision systems at the Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) have been analyzed by four models. The first two models utilize the blast-wave model with different statistics. The last two models employ certain linear correspondences based on different distributions. The four models describe the experimental data measured by the Pioneering High Energy Nuclear Interaction eXperiment (PHENIX), Solenoidal Tracker at RHIC (STAR), and A Large Ion Collider Experiment (ALICE) cCollaborations equally well. It is found that both the kinetic freeze-out temperature and transverse flow velocity in the central collisions are comparable with those in the peripheral collisions. With the increase of collision energy from that of the RHIC to that of the LHC, the considered quantities typically do not decrease. Comparing with the central collisions, the proton-proton collisions are closer to the peripheral collisions.

nucl-th↗

arXiv2018

Event patterns from negative pion spectra in proton-proton and nucleus-nucleus collisions at SPS

Rapidity-dependent transverse momentum spectra of negatively charged pions measured at different rapidities in proton-proton collisions at the Super Proton Synchrotron (SPS) at various energies within its Beam Energy Scan (BES) program are investigated by using one- and two-component standard distributions where the chemical potential and spin property of particles are implemented. The rapidity spectra are described by a double-Gaussian distribution. At the stage of kinetic freeze-out, the event patterns are structured by the scatter plots in the three-dimensional subspaces of velocity, momentum and rapidity. The results of the studies of the rapidity-independent transverse mass spectra measured at mid-rapidity in proton-proton collisions are compared with those based on the similar transverse mass spectra measured in the most central beryllium-beryllium, argon-scandium and lead-lead collisions from the SPS at its BES energies.

nucl-th↗

arXiv2018

Kinetic freeze-out temperatures in central and peripheral collisions: Which one is larger?

The kinetic freeze-out temperatures, $T_0$, in nucleus-nucleus collisions at the Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) energies are extracted by four methods: i) the Blast-Wave model with Boltzmann-Gibbs statistics (the BGBW model), ii) the Blast-Wave model with Tsallis statistics (the TBW model), iii) the Tsallis distribution with flow effect (the improved Tsallis distribution), and iv) the intercept in $T=T_0+am_0$ (the alternative method), where $m_0$ denotes the rest mass and $T$ denotes the effective temperature which can be obtained by different distribution functions. It is found that the relative sizes of $T_0$ in central and peripheral collisions obtained by the conventional BGBW model which uses a zero or nearly zero transverse flow velocity, $β_T$, are contradictory in tendency with other methods. With a re-examination for $β_T$ in the first method in which $β_T$ is taken to be $\sim(0.40\pm0.07)c$, a recalculation presents a consistent result with others. Finally, our results show that the kinetic freeze-out temperature in central collisions is larger than that in peripheral collisions.

nucl-th↗

arXiv2018

Event patterns extracted from top quark-related spectra in proton-proton collisions at 8 TeV

We analyze the transverse momentum ($p_T$) and rapidity ($y$) spectra of top quark pairs, hadronic top quarks, and top quarks produced in proton-proton ($pp$) collisions at center-of-mass energy $\sqrt{s}=8$ TeV. For $p_T$ spectra, we use the superposition of the inverse power-law suggested by the QCD (quantum chromodynamics) calculus and the Erlang distribution resulting from a multisource thermal model. For $y$ spectra, we use the two-component Gaussian function resulting from the revised Landau hydrodynamic model. The modelling results are in agreement with the experimental data measured at the detector level, in the fiducial phase-space, and in the full phase-space by the ATLAS Collaboration at the Large Hadron Collider (LHC). Based on the parameter values extracted from $p_T$ and $y$ spectra, the event patterns in three-dimensional velocity ($β_x$-$β_y$-$β_z$), momentum ($p_x$-$p_y$-$p_z$), and rapidity ($y_1$-$y_2$-$y$) spaces are obtained, and the probability distributions of these components are also obtained.

hep-ph↗

arXiv2018

Comparing standard distribution and its Tsallis form of transverse momenta in high energy collisions

In this paper, the experimental (simulated) transverse momentum spectra of negatively charged pions produced at mid-rapidity in central nucleus-nucleus collisions at the Heavy Ion Synchrotron (SIS), Relativistic Heavy Ion Collider (RHIC), and Large Hadron Collider (LHC) energies obtained by different collaborations are selected by us to investigate, where a few simulated data are taken from the results of FOPI Collaboration who uses the IQMD transport code based on Quantum Molecular Dynamics. A two-component standard distribution and the Tsallis form of standard distribution are used to fit these data in the framework of a multisource thermal model. The excitation functions of main parameters in the two distributions are analyzed. In particular, the effective temperatures extracted from the two-component standard distribution and the Tsallis form of standard distribution are obtained, and the relation between the two types of effective temperatures is studied.

nucl-th↗

arXiv2017

Event patterns extracted from anisotropic spectra of charged particles produced in Pb-Pb collisions at 2.76 TeV

Event patterns extracted from anisotropic spectra of charged particles produced in lead-lead collisions at 2.76 TeV are investigated. We use an inverse power-law resulted from the QCD calculus to describe the transverse momentum spectrum in the hard scattering process, and a revised Erlang distribution resulted from a multisource thermal model to describe the transverse momentum spectrum and anisotropic flow in the soft excitation process. The pseudorapidity distribution is described by a three-Gaussian function which is a revision of the Landau hydrodynamic model. Thus, the event patterns at the kinetic freeze-out are displayed by the scatter plots of the considered particles in the three-dimensional velocity, momentum, and rapidity spaces.

nucl-th↗

arXiv2017

Extracting kinetic freeze-out temperature and radial flow velocity from an improved Tsallis distribution

We analyze the transverse momentum ($p_T$) spectra of identified particles ($π^{\pm}$, $K^{\pm}$, $p$, and $\bar p$) produced in gold-gold (Au-Au) and lead-lead (Pb-Pb) collisions over a $\sqrt{s_{NN}}$ (center-of-mass energy per nucleon pair) range from 14.5 GeV [one of the Relativistic Heavy Ion Collider (RHIC) energies] to 2.76 TeV [one of the Large Hadron Collider (LHC) energies]. For the spectra with a narrow $p_T$ range, an improved Tsallis distribution which is in fact the Tsallis distribution with radial flow is used. For the spectra with a wide $p_T$ range, a superposition of the improved Tsallis distribution and an inverse power-law is used. Both the extracted kinetic freeze-out temperature ($T_0$) and radial flow velocity ($β_T$) increase with the increase of $\sqrt{s_{NN}}$, which indicates a higher excitation and larger expansion of the interesting system at the LHC. Both the values of $T_0$ and $β_T$ in central collisions are slightly larger than those in peripheral collisions, and they are independent of isospin and slightly dependent on mass.

nucl-th↗

arXiv2017

Excitation functions of parameters extracted from three-source (net-)proton rapidity distributions in Au-Au and Pb-Pb collisions over an energy range from AGS to RHIC

Experimental results of the rapidity spectra of protons and net-protons (protons minus antiprotons) emitted in gold-gold (Au-Au) and lead-lead (Pb-Pb) collisions, measured by a few collaborations at the alternating gradient synchrotron (AGS), super proton synchrotron (SPS), and relativistic heavy ion collider (RHIC), are described by a three-source distribution. The values of the distribution width $σ_C$ and contribution ratio (relative contribution) $k_C$ of the central rapidity region, and the distribution width $σ_F$ and rapidity shift $Δy$ of the forward/backward rapidity regions, are then obtained. The excitation function of $σ_C$ increases generally with increase of the center-of-mass energy per nucleon pair $\sqrt{s_{NN}}$. The excitation function of $σ_F$ shows a saturation at $\sqrt{s_{NN}}=8.8$ GeV. The excitation function of $k_C$ shows a minimum at $\sqrt{s_{NN}}=8.8$ GeV and a saturation at $\sqrt{s_{NN}}\approx 17$ GeV. The excitation function of $Δy$ increase monotonously with $\ln \sqrt{s_{NN}}$ in the considered energy range.

hep-ph↗

arXiv2017

On J/psi and transverse momentum distributions in high energy collisions

The transverse momentum distributions of final-state particles are very important for high-energy collision physics. In this work, we investigate and meson distributions in the framework of a particle-production source, where Tsallis statistics are consistently integrated. The results are in good agreement with the experimental data of proton-proton ( ) and proton-lead ( -Pb) collisions at LHC energies. The temperature of the emission source and the nonequilibrium degree of the collision system are extracted.

nucl-th↗

arXiv2016

Event patterns (particle scatter plots) extracted from charged particle spectra in $pp$ and Pb-Pb collisions at 2.76 TeV

The transverse momentum ($p_T$) and pseudorapidity ($η$) spectra of charged particles produced in proton-proton ($pp$) and lead-lead (Pb-Pb) collisions at the large hadron collider (LHC) are described by a hybrid model. In the model, the $p_T$ spectrum is described by a two-component distribution which contains an inverse power-law suggested by the QCD (Quantum Chromodynamic) calculus and an Erlang distribution resulted from a multisource thermal model. The $η$ spectrum is described by a Gaussian rapidity ($y$) distribution resulted from the Landau hydrodynamic model and the two-component $p_T$ distribution, where the conversion between $y$ and $η$ is accurately considered. The modelling results are in agreement with the experimental data measured by the ATLAS Collaboration in $pp$ collisions at center-of-mass energy $\sqrt{s}=2.76$ TeV and in Pb-Pb collisions at center-of-mass energy per nucleon pair $\sqrt{s_{NN}}=2.76$ TeV. Based on the parameter values extracted from $p_T$ and $η$ or $y$ spectra, the event patterns or particle scatter plots in three-dimensional velocity and momentum spaces are obtained.

hep-ph↗

arXiv2016

Disentangling random thermal motion of particles and collective expansion of source from transverse momentum spectra in high energy collisions

In the framework of a multisource thermal model, we describe experimental results of the transverse momentum spectra of final-state light flavour particles produced in gold-gold (Au-Au), copper-copper (Cu-Cu), lead-lead (Pb-Pb), proton-lead ($p$-Pb), and proton-proton ($p$-$p$) collisions at various energies, measured by the PHENIX, STAR, ALICE, and CMS Collaborations, by using the Tsallis-standard (Tsallis form of Fermi-Dirac or Bose-Einstein), Tsallis, and two- or three-component standard distributions which can be in fact regarded as different types of "thermometers" or "thermometric scales" and "speedometers". A central parameter in the three distributions is the effective temperature which contains information on the kinetic freeze-out temperature of the emitting source and reflects the effects of random thermal motion of particles as well as collective expansion of the source. To disentangle both effects, we extract the kinetic freeze-out temperature from the intercept of the effective temperature ($T$) curve as a function of particle's rest mass ($m_0$) when plotting $T$ versus $m_0$, and the mean transverse flow velocity from the slope of the mean transverse momentum ($\langle p_T \rangle$) curve as a function of mean moving mass ($\overline{m}$) when plotting $\langle p_T \rangle$ versus $\overline{m}$.

nucl-ex↗

arXiv2016

Event patterns extracted from transverse momentum and rapidity spectra of Z bosons and quarkonium states produced in pp and Pb-Pb collisions at LHC

Transverse momentum ($p_T$) and rapidity ($y$) spectra of $Z$ bosons and quarkonium states (some charmonium $c\bar c$ mesons such as $J/ψ$ and $ψ(2S)$, and some bottomonium $b\bar b$ mesons such as $Υ(1S)$, $Υ(2S)$, and $Υ(3S)$) 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 for $p_T$ spectrum and two-component Gaussian distribution for $y$ spectrum. 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 energies $\sqrt{s}=2.76$ and 7 TeV, and in Pb-Pb collisions at center-of-mass energy per nucleon pair $\sqrt{s_{NN}}=2.76$ TeV. Based on the parameter values extracted from $p_T$ and $y$ spectra, the event patterns (particle scatter plots) in two-dimensional $p_T$-$y$ space and in three-dimensional velocity space are obtained.

hep-ph↗

arXiv2016

An Evidence of Mass Dependent Differential Kinetic Freeze-out Scenario Observed in Pb-Pb Collisions at 2.76 TeV

Transverse momentum spectra of different particles produced in mid-rapidity interval in lead-lead (Pb-Pb) collisions with different centrality intervals, measured by the ALICE Collaboration at center-of-mass energy per nucleon pair $\sqrt{s_{NN}}=2.76$ TeV, are conformably and approximately described by the Tsallis distribution. The dependences of parameters (effective temperature, entropy index, and normalization factor) on event centrality and particle rest mass are obtained. The source temperature at the kinetic freeze-out is obtained to be the intercept in the linear relation between effective temperature and particle rest mass, while the particle transverse flow velocity is approximately extracted to be the slope in the linear relation between mean transverse momentum and particle rest mass. It is shown that the source temperature increases with increase of particle rest mass, which exhibits an evidence of mass dependent differential kinetic freeze-out scenario or multiple kinetic freeze-out scenario.

nucl-th↗

arXiv2016

Productions of J/psi mesons in p-Pb collisions at 5 TeV

The rapidity distributions of $J/ψ$ mesons produced in proton-lead ($p$-Pb) collisions at center-of-mass energy per nucleon pair $\sqrt{s_{NN}}=5$ TeV are studied by using a multisource thermal model and compared with the experimental data of the LHCb and ALICE Collaborations. Correspondingly, the pseudorapidity distributions are accurately obtained from the parameters extracted from the rapidity distributions. At the same time, the transverse momentum distributions in the same experiments are described by the simplest Erlang distribution which is the folding result of two exponential distributions which are contributed by the target and projectile partons respectively.

nucl-th↗

arXiv2016

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 $Ω$ 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 $Ω$ hyperon spectra is observed at 7.7 GeV.

hep-ph↗

arXiv2016

Searching for minimum in dependence of squared speed-of-sound on collision energy

Experimental results of the rapidity distributions of negatively charged pions produced in proton-proton ($p$-$p$) and beryllium-beryllium (Be-Be) collisions at different beam momentums, measured by the NA61/SHINE Collaboration at the super proton synchrotron (SPS), are described by a revised (three-source) Landau hydrodynamic model. The squared speed-of-sound parameter $c^2_s$ is then extracted from the width of rapidity distribution. There is a local minimum (knee point) which indicates a softest point in the equation of state (EoS) appearing at about 40$A$ GeV/$c$ (or 8.8 GeV) in $c^2_s$ excitation function [the dependence of $c^2_s$ on incident beam momentum (or center-of-mass energy)]. This knee point should be related to the searching for the onset of quark deconfinement and the critical point of quark-gluon plasma (QGP) phase transition.

hep-ph↗