arXiv subjects

Feng-lan Shao

Publications and source records attributed to Feng-lan Shao.

At least 19 recordsLinked to original sources

arXiv2026

Transverse momentum dependence of $\Omega/\phi$ ratio in high energy collisions

We apply a constituent quark equal-velocity combination model to study the $p_{T}$ dependence of $\Omega/\phi$ ratio in $pp$, $p$-Pb and Pb-Pb collisions at LHC energies. We demonstrate that the relative change rate of the $\Omega/\phi$ ratio is dominated by a discrete curvature property of $p_{T}$ spectrum of strange quarks just before hadronization. Using experimental data of $\phi$ mesons after a quark number scaling operation, we extract $p_{T}$ spectrum of strange quarks just before hadronization and study its curvature property in high and low multiplicity events in $pp$ collisions at $\sqrt{s}=$ 7, 13 TeV, $p$-Pb collisions at $\sqrt{s_{NN}}$= 5.02 TeV and Pb-Pb collisions at $\sqrt{s_{NN}}$= 2.76 TeV. We apply these curvature properties of $p_{T}$ spectra of strange quarks to explain the observed $p_{T}$ dependence of $\Omega/\phi$ ratio in those collisions. We discuss the possible origin of the change of curvature property for $p_{T}$ spectra of strange quarks just before hadronization by considering the influence of strong collective flow formed in partonic stage evolution in collisions at LHC energies.

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arXiv2026

Anisotropic flows of light-flavor and charmed hadrons in Pb+Pb collisions at LHC energy

We apply a constituent quark equal-velocity combination (EVC) model to study the elliptic flow ($v_{2}$) and triangular flow ($v_{3}$) of light-flavor and single-charmed hadrons in Pb+Pb collisions at $\sqrt{s_{NN}}=$ 2.76 and 5.02 TeV. $v_{2,3}$ of hadrons in the EVC model can be expressed as a linear superposition of the $v_{2,3}$ of quarks at the same velocity as that of the hadrons. We find that available experimental data for $v_{2}$ and $v_{3}$ of $p$, $\Lambda$, $\Xi$, and $\Omega$ as the function of transverse momentum ($p_{T}$) can be consistently explained by the EVC formula using a $v_{2}$ of up/down quarks and a $v_{2}$ of strange quarks. In comparison with $v_{2}$ data of $\phi$ at $\sqrt{s_{NN}}=$2.76 TeV which can be naturally explained by $v_{2}$ of strange quarks, explanation of data of $\phi$ mesons at $\sqrt{s_{NN}}=$5.02 TeV requires an additional contribution of two-kaon coalescence, which indicates approximately 20% influence of final-state hadronic rescattering on $v_{2}$ of $\phi$ at $\sqrt{s_{NN}}=$5.02 TeV. Using $v_{2}$ and $v_{3}$ of light-flavor quarks obtained in studying light-flavor hadrons and $v_{2}$ and $v_{3}$ of charm quarks determined from $D^{0}$ meson data, we apply the EVC model to predict the anisotropic flows of $D_{s}^{+}$, $\Lambda_{c}^{+}$, $\Xi_{c}^{0}$, and $\Omega_{c}^{0}$ and compare them with the available experimental data. The preliminary data for $v_{2}$ of $D^{0}$, $D_{s}^{+}$, and $\Lambda_{c}^{+}$ at $\sqrt{s_{NN}}=$ 5.36 TeV are found to be naturally described by the EVC model.

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arXiv2025

The domain of soft hadrons in transverse momentum space in high energy collisions

By studying experimental data for invariant transverse momentum distribution $f(p_{T})$ of hadrons in high energy $pp$, $p$A and AA collisions, we find two characteristic $p_{T}$ points relating to the behavior of $\left[\ln f(p_{T})\right]^{''}$, i.e., the second derivative of the logarithm of hadronic $p_{T}$ spectrum with respect to $p_{T}$. One point is $p_{0}$ at which $\left[\ln f(p_{T})\right]^{''}$ is zero and another point is $p_{1}$ at which $\left[\ln f(p_{T})\right]^{''}$ reaches maximum. \bz{The hadronic distribution can be classified into three kinetic regions, i.e., soft region $0 p_{1}$ dominated by hadrons from high energy partonic jet, and the transition region $p_{0}<p_{T}<p_{1}$ of above two sources of hadron production.} Using rich data of hadronic $p_{T}$ spectra at RHIC and LHC, we carry out a systematical analysis for $p_{0}$ and $p_{1}$ of kaon, $K^{*}$, $\phi$ and baryons such as $p$, $\Lambda$, $\Xi$, $\Omega$ in $pp$, $p$-Pb and heavy-ion collisions, and show their dependence on hadron species, collision energy, collision centrality and/or charged-particle multiplicity. We also study the correlation between $p_{0}$ of hadrons and their average transverse momentum $\left\langle p_{T}\right\rangle $, and find a difference between $p_{0}$-$\left\langle p_{T}\right\rangle $ correlation of baryons and that of mesons which can be understood by quark combination mechanism at hadronization. The systematic comparison for $p_{0}$-$\left\langle p_{T}\right\rangle $ correlation of kaon, $\phi$, $p$ and $\Lambda$ in $pp$, $p$-Pb, Pb-Pb and Au+Au collisions at RHIC and LHC energies indicates that $p_{0}$ is a sensitive physical quantity of reflecting the production property of soft hadrons in high energy collisions.

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arXiv2025

Anisotropic flows of identified hadrons in the equal-velocity quark combination model at RHIC energy

We employ an equal-velocity quark combination model to study anisotropic flows $v_{2}$, $v_{3}$ and $v_{4}$ of identified hadrons at mid-rapidity in heavy-ion collisions at RHIC energies. Under the equal-velocity combination mechanism of constituent quarks at hadronization, we build analytical formulas of anisotropic flows of hadrons in terms of those of quarks just before hadronization. We systematically analyze the contribution of higher order flows of quarks, and show how simple formulas of $v_{2}$, $v_{3}$ and $v_{4}$ of identified hadrons with the desired precision can be obtained by neglecting the small contribution of higher order flows of quarks. We systematically test these simple formulas of hadronic flows by the experimental data of $v_{2}$, $v_{3}$ and $v_{4}$ of identified hadrons $\phi$, $\Lambda$, $\Xi^{-}$, $\Omega^{-}$, $\bar{\Lambda}$, $\bar{\Xi}^{+}$, $\bar{\Omega}^{+}$, $p$ and $\bar{p}$ in Au+Au collisions at $\sqrt{s_{NN}}=$ 19.6, 54.4 and 200 GeV, and we find that the equal-velocity quark combination model can well describe the measured $v_{2}$, $v_{3}$ and $v_{4}$ of identified hadrons in Au+Au collisions at those collision energies. We further study the obtained anisotropic flows of quarks and find two scaling properties\textcolor{red}{{} }which can be qualitatively understood by the hydrodynamic evolution of thermal quark medium produced in relativistic heavy-ion collisions.

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arXiv2023

Transverse momentum and multiplicity dependence of $\Lambda_{c}^{+}/D^{0}$ ratio in $pp$ collisions at $\sqrt{s}=13$ TeV

We apply an equal-velocity quark combination model to study the $\Lambda_{c}^{+}/D^{0}$ ratio in the range $p_{T}\lesssim10$ GeV/c in $pp$ collisions at $\sqrt{s}=13$ TeV. We decompose the ratio into four parts which are related to quark numbers, light-flavor quark $p_{T}$ spectrum, charm quark $p_{T}$ spectrum, momentum correlation between light and charm quarks, respectively. Their influence on $\Lambda_{c}^{+}/D^{0}$ ratio are individually studied. The curvature property of light-flavor quark $p_{T}$ spectrum is found to be the main reason of the non-monotonic $p_{T}$ dependence of $\Lambda_{c}^{+}/D^{0}$ ratio exhibited in high multiplicity events. Moreover, the multiplicity dependence of $\Lambda_{c}^{+}/D^{0}$ ratio as the function of $p_{T}$ is mainly because of the multiplicity dependence of light-flavor quark $p_{T}$ spectrum. Using the light-flavor quark $p_{T}$ spectrum obtained from experimental data of light-flavor hadrons and charm quark $p_{T}$ spectrum obtained from FONLL and/or PYTHIA calculations, the $p_{T}$ dependence of experimental data of $\Lambda_{c}^{+}/D^{0}$ ratio in high multiplicity events and that in low multiplicity events in $pp$ collisions at $\sqrt{s}=13$ TeV are reasonably understood.

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arXiv2023

Production of Strange and Charm Hadrons in Pb+Pb Collisions at $\sqrt{s_{NN}}=$ 5.02 TeV

Using a quark combination model with the equal-velocity combination approximation, we study the production of hadrons with strangeness and charm flavor quantum numbers in Pb+Pb collisions at $\sqrt{s_{NN}}=$5.02 TeV. We present analytical expressions and numerical results for these hadrons' transverse momentum spectra and yield ratios. Our numerical results agree well with the experimental data available. The features of strange and charm hadron production in the quark--gluon plasma at the early stage of heavy ion collisions are also discussed.

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arXiv2022

Production of single-charm hadrons by quark combination mechanism in $p$-Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV

If QGP-like medium is created in $p$-Pb collisions at extremely high collision energies, charm quarks that move in the medium can hadronize by capturing the co-moving light quark(s) or anti-quark(s) to form the charm hadrons. Using light quark $p_{T}$ spectra extracted from the experimental data of light-flavor hadrons and a charm quark $p_{T}$ spectrum that is consistent with perturbative QCD calculations, the central-rapidity data of $p_{T}$ spectra and the spectrum ratios for $D$ mesons in the low $p_{T}$ range ($p_{T}\lesssim7$ GeV/$c$) in minimum-bias $p$-Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV are well described by quark combination mechanism in equal-velocity combination approximation. The $Λ_{c}^{+}/D^{0}$ ratio in quark combination mechanism exhibits the typical increase-peak-decrease behavior as the function of $p_{T}$, and the shape of the ratio for $p_{T}\gtrsim3$ GeV/$c$ is in agreement with the data of ALICE collaboration in central rapidity region $-0.96<y<0.04$ and the preliminary data of LHCb collaboration in forward rapidity region $1.5<y<4.0$. The global production of single-charm baryons is quantified using the data and the possible enhancement (relative to light flavor baryons) is discussed. The $p_{T}$ spectra of $Ξ_{c}^{0}$, $Ω_{c}^{0}$ in minimum-bias events and those of single-charm hadrons in high-multiplicity event classes are predicted, which serves as the further test of the possible change of the hadronization characteristic for low $p_{T}$ charm quarks in the small system created in $p$-Pb collisions at LHC energies.

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arXiv2022

Averaged transverse momentum correlations of hadrons in relativistic heavy-ion collisions

We compile experimental data for the averaged transverse momentum ($\left\langle p_{T}\right\rangle $) of proton, $Λ$, $Ξ^{-}$, $Ω^{-}$ and $ϕ$ at mid-rapidity in Au+Au collisions at $\sqrt{s_{NN}}=$ 200, 39, 27, 19.6, 11.5, 7.7 GeV and in Pb+Pb collisions at $\sqrt{s_{NN}}=$ 2.76 TeV, and find that experimental data of these hadrons exhibit systematic correlations. We apply a quark combination model with equal-velocity combination approximation to derive analytic formulas of hadronic $\left\langle p_{T}\right\rangle $ in the case of exponential form of quark $p_{T}$ spectra at hadronization. We use them to successfully explain the systematic correlations exhibited in $\left\langle p_{T}\right\rangle $ data of $pΛ$, $ΛΞ^{-}$, $Ξ^{-}Ω^{-}$ and $Ξ^{-}ϕ$ pairs. We also use them to successfully explain the regularity observed in $\left\langle p_{T}\right\rangle $ of these hadrons as the function of $(dN_{ch}/dy)/(N_{part}/2)$ at mid-rapidity in central heavy-ion collisions at both RHIC and LHC energies. Our results suggest that the constituent quark degrees of freedom and the equal-velocity combination of these constituent quarks at hadronization play important role in understanding the production of baryons and $ϕ$ meson at these RHIC and LHC energies.

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arXiv2021

Signals of quark combination at hadronization in $pp$ collisions at $\sqrt{s}=200$ GeV

We find signals of quark combination at hadronization from the experimental data of $p_{T}$ spectra of hadrons at mid-rapidity in $pp$ collisions at $\sqrt{s}=200$ GeV. The first is the constituent quark number scaling property for $p_{T}$ spectra of $Ω^{-}$ and $ϕ$ and that for $p_{T}$ spectra of $p$ and $ρ^{0}$. The second is that $p_{T}$ spectra of $Λ$, $Ξ^{-}$, and $K^{*0}$ can be self-consistently described using the spectrum of strange quarks from $ϕ$ data and that of up/down quarks from $p$ data in the equal-velocity combination mechanism. The third is that experimental data for $p_{T}$ spectrum of $D^{*+}$ are also well described using the spectrum of up/down quarks from $p$ data and that of charm quarks from perturbative QCD calculations. These results indicate a similarity between hadron production in $pp$ collisions at $\sqrt{s}=200$ GeV and that at LHC energies. We predict $p_{T}$ spectra of single-charm hadrons and their spectrum ratios. We suggest systematic measurements in $pp$ collisions at $\sqrt{s}=200$ GeV in future so as to better understand the property of small parton system created in $pp$ collisions at different collision energies.

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arXiv2021

Production of light flavor and single-charmed hadrons in $pp$ collisions at $\sqrt{s}=5.02$ TeV in an equal-velocity quark combination model

We apply an equal-velocity quark combination model to study the production of light-flavor hadrons and single-charmed hadrons at midrapidity in $pp$ collisions at $\sqrt{s}=5.02$ TeV. We find experimental data for $p_{T}$ spectra of $Ω$ and $ϕ$ exhibit a quark number scaling property, which is a clear signal of quark combination mechanism at hadronization. Experimental data for $p_T$ spectra of $p$, $Λ$, $Ξ$, $Ω$, $ϕ$ and $K^{*0}$ are systematically described by the model. The non-monotonic $p_{T}$ dependence of $Ω/ϕ$ ratio is naturally explained and we find it is closely related to the shape of the logarithm of strange quark $p_{T}$ distribution. Using $p_{T}$ spectra of light-flavor quarks obtained from light-flavor hadrons and a $p_T$ spectrum of charm quarks which is consistent with perturbative QCD calculations, the experimental data for differential cross-sections of $D^{0,+}$, $D_{s}^{+}$ and $Λ_{c}^{+}$ as the function of $p_{T}$ are systematically described. We predict the differential cross-sections of $Ξ_{c}^{0,+}$ and $Ω_{c}^{0}$. The ratio $Ξ_{c}^{0,+}/D^{0}$ in our model is about 0.16 and $Ω_{c}^{0}/D^{0}$ is about 0.012 due to the cascade suppression of strangeness. In addition, the predicted $Ξ_{c}^{0,+}/D^{0}$ and $Ω_{c}^{0}/D^{0}$ ratios exhibit the non-monotonic dependence on $p_{T}$ in the low $p_{T}$ range.

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arXiv2021

Strange hadron production in a quark combination model in Au+Au collisions at RHIC energies

We apply a quark combination model to study yield densities and transverse momentum ($p_{T}$) spectra of strange (anti-)hadrons at mid-rapidity in central Au+Au collisions at $\sqrt{s_{NN}}=$ 7.7, 11.5, 19.6, 27, 39 and 200 GeV. We show that experimental data for $p_{T}$ spectra of (anti-)hadrons in these collisions can be systematically described by the equal velocity combination of constituent quarks and antiquarks at hadronization. We obtain $p_{T}$ spectra of quarks and antiquarks at hadronization and study their collision energy dependence. We also reproduce the yield densities of hadrons and anti-hadrons. In particular, we demonstrate that yield ratios of anti-hadrons to hadrons $K^{-}/K^{+}$, $\bar{p}/p$, $\barΛ/Λ$, $\barΞ^{+}/Ξ^{-}$ and $\barΩ^{+}/Ω^{-}$ simply correlate with each other and their experimental data except $\barΩ^{+}/Ω^{-}$ at $\sqrt{s_{NN}}=$ 7.7 GeV are systematically described by the model. These results suggest that the equal velocity combination mechanism for quarks and antiquarks at hadronization plays an important role in Au+Au collisions at low RHIC energies ($\sqrt{s_{NN}}\geq$ 11.5 GeV).

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arXiv2021

Elliptic flow of hadrons in equal-velocity quark combination mechanism in relativistic heavy-ion collisions

We apply a quark combination model with equal-velocity combination (EVC) approximation to study the elliptic flow ($v_{2}$) of hadrons in heavy-ion collisions in a wide collision energy range ($\sqrt{s_{NN}}=$ 27 - 5020 GeV). Utilizing the simple relationship between $v_{2}$ of hadrons and those of quarks under EVC, we find that $v_{2}$ of up/down quarks obtained by experimental data of proton is consistent with that obtained by data of $Λ$ and $Ξ$. $v_{2}$ of strange quarks obtained by data of $Ω$ is consistent with that obtained by data of $Λ$ and $Ξ$, and at RHIC energies it is also consistent with that obtained by data of $ϕ$. This means that $v_{2}$ of these hadrons have a common quark-level source. Using data of $D^0$, we obtain $v_{2}$ of charm quarks with $p_T\lesssim 6$ GeV/c. We find that under EVC charm quark dominates $v_{2}$ of $D$ mesons at low $p_{T}$ but light-flavor quarks significantly contribute to $v_{2}$ of $D$ mesons in the range $3\lesssim p_{T}\lesssim8$ GeV/c. We predict $v_{2}$ of charmed baryons $Λ_{c}^{+}$ and $Ξ_{c}^{0}$ which show a significant enhancement at intermediate $p_{T}$ due to the double contribution of light-flavor quarks. The properties of the obtained quark $v_{2}$ under EVC are studied and a regularity for $v_{2}$ of quarks as the function of $p_{T}/m$ is found.

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arXiv2020

Quark number scaling of $p_{T}$ spectra for $Ω$ and $ϕ$ in relativistic heavy-ion collisions

We show that the experimental data of transverse momentum ($p_{T}$) spectra of $Ω$ baryon and $ϕ$ meson at mid-rapidity in heavy-ion collisions exhibit the constituent quark number scaling in a wide energy range from RHIC to LHC. Such a scaling behavior is a direct consequence of quark combination mechanism via equal velocity combination and provides a very convenient way to extract the $p_{T}$ spectrum of strange quarks at hadronization. We present the results of strange quarks obtained from the available data and study the properties in particular the energy dependence of the averaged transverse momentum $\langle p_{T}\rangle$ and the transverse radial flow velocity $\langleβ\rangle$ with a hydrodynamics-motivated blast-wave model.

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arXiv2019

Constituent quark number scaling from strange hadron spectra in $pp$ collisions at $\sqrt{s}=$ 13 TeV

We show that the data of $p_{T}$ spectra of $Ω^{-}$ and $ϕ$ at midrapidity in inelastic events in $pp$ collisions at $\sqrt{s}=$ 13 TeV exhibit a constituent quark number scaling property, which is a clear signal of quark combination mechanism at hadronization. We use a quark combination model under equal velocity combination approximation to systematically study the production of identified hadrons in $pp$ collisions at $\sqrt{s}$= 13 TeV. The midrapidity data of $p_{T}$ spectra of proton, $Λ$, $Ξ^{-}$, $Ω^{-}$, $ϕ$ and $K^{*}$ in inelastic events are simultaneously well fitted by the model. The data of multiplicity dependency of yields of these hadrons are also well understood. The strong $p_{T}$ dependence for data of $p/ϕ$ ratio is well explained by the model, which further suggests that the production of two hadrons with similar masses is determined by their quark contents at hadronization. $p_{T}$ spectra of strange hadrons at midrapidity in different multiplicity classes in $pp$ collisions at $\sqrt{s}=$ 13 TeV are predicted to further test the model in the future. The midrapidity $p_{T}$ spectra of soft ($p_T<2$ GeV/c) strange quark and up/down quark at hadronization in $pp$ collisions at $\sqrt{s}=$ 13 TeV are extracted.

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arXiv2019

Statistical method in quark combination model

We present a new method of solving the probability distribution for baryons, antibaryons and mesons at the hadronization of constituent quark and antiquark system. The hadronization is governed by the quark combination rule in the quark combination model developed by the Shandong Group. We use the method of the generating function to derive the outcome of the quark combination rule, which is much simpler and easier to be generalized than the original method. Furthermore, we use the formula of the quark combination rule and its generalization to study the property of multiplicity distribution of net-protons. Taking a naive case of quark number fluctuations and correlations at hadronization, we calculate ratios of multiplicity cumulants of final-state net-protons and discuss the potential applicability of quark combination model in studying hadronic multiplicity fluctuations and the underlying phase transition property in relativistic heavy-ion collisions.

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arXiv2018

New feature of low $p_{T}$ charm quark hadronization in $pp$ collisions at $\sqrt{s}=7$ TeV

Treating the light-flavor constituent quarks and antiquarks that can well describe the data of light-flavor hadrons in $pp$ collisions at $\sqrt{s}=7$ TeV as the underlying source of chromatically neutralizing the charm quarks of low transverse momenta ($p_{T}$), we show that the experimental data of $p_{T}$ spectra of single-charm hadrons $D^{0,+}$, $D^{*+}$ $D_{s}^{+}$, $Λ_{c}^{+}$ and $Ξ_{c}^{0}$ at mid-rapidity in the low $p_{T}$ range ($2\lesssim p_{T}\lesssim7$ GeV/$c$) in $pp$ collisions at $\sqrt{s}=7$ TeV can be well understood by the equal-velocity combination of perturbatively-created charm quarks and those light-flavor constituent quarks and antiquarks. This suggests a possible new scenario of low $p_{T}$ charm quark hadronization, in contrast to the traditional fragmentation mechanism, in $pp$ collisions at LHC energies. This is also another support for the exhibition of the effective constituent quark degrees of freedom for the small parton system created in $pp$ collisions at LHC energies.

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arXiv2017

Different production sources of light nuclei in relativistic heavy-ion collisions

We propose a new method, i.e., an exclusive quark combination model + an inclusive hadron recombination model, to study different production sources of light nuclei in relativistic heavy-ion collisions. We take deuterons and $^3$He produced in Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV as examples to present contributions of different production sources by studying their rapidity densities $dN/dy$, yield ratios and transverse momentum ($p_T$) spectra just after the hadronization as well as at the final kinetic freeze-out. We find that: only very small fractions of $d$ and $^3$He are created just after the hadronization; nucleons from $Δ$ resonance decays make a much larger contribution to the regeneration of light nuclei at the hadronic phase stage, and this contribution takes about 79\% and 92\% for $d$ and $^3$He, respectively, observed at the final kinetic freeze-out. We also find that yield ratios $d/p$, $^3$He$/p$ and $^3$He$/d$ are good observables to probe contributions for light nuclei from different production sources, and provide a natural explanation for constant values of $d/p$ and $^3$He$/p$ as a function of the averaged charged multiplicity measured by the ALICE Collaboration.

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arXiv2017

Multiplicity fluctuation and correlation of mesons and baryons in ultra-relativistic heavy-ion collisions at LHC

We study the multiplicity fluctuation and correlation of identified mesons and baryons formed at the hadronization by the quark combination mechanism in the context of ultra-relativistic heavy-ion collisions. Based on the statistical method of free quark combination, we derive the two-hadron multiplicity correlations such as meson-meson and meson-baryon correlations, and take the effects of quark number fluctuation at hadronization into account by a Taylor expansion method. After including the decay contributions, we calculate the dynamical fluctuation observable $ν_{dyn}$ for $\text{K}π$, $pπ$ and $\text{K}p$ pairs and discuss what underlying physics can be obtained by comparing with the data in Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV and the simulations from HIJING and AMPT event generators.

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