Quark Combination Model Research Articles

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

We apply an equal-velocity quark combination model to study the varLambda _{c}^{+}/D^{0} ratio in the range p_{T}lesssim 10 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 varLambda _{c}^{+}/D^{0} ratio is individually studied. The curvature property of light-flavor quark p_{T} spectrum is the main reason of the non-monotonic p_{T} dependence of varLambda _{c}^{+}/D^{0} ratio exhibited in high multiplicity events. Moreover, the multiplicity dependence of varLambda _{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 varLambda _{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.

Production of Strange and Charm Hadrons in Pb+Pb Collisions at sNN = 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 sNN= 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.

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, $\Lambda$, $\Xi^{-}$, $\Omega^{-}$ and $\phi$ 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 $p\Lambda$, $\Lambda\Xi^{-}$, $\Xi^{-}\Omega^{-}$ and $\Xi^{-}\phi$ 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 $\phi$ meson at these RHIC and LHC energies.

Production characteristics of light (anti-)nuclei from (anti-)nucleon coalescence in heavy ion collisions at energies employed at the RHIC beam energy scan

With the kinetic freeze-out nucleons and antinucleons obtained from the quark combination model, we study the production of light nuclei and antinuclei in the (anti-)nucleon coalescence mechanism in relativistic heavy ion collisions. We derive analytic formulas of the momentum distributions of different light nuclei and apply them to compute transverse momentum ($p_T$) spectra of (anti-)deuterons ($d$, $\bar d$) and (anti-)tritons ($t$, $\bar t$) in Au-Au collisions at $\sqrt{s_{NN}}=$7.7, 11.5, 19.6, 27, 39, 54.4 GeV. We find that the experimental data available for these $p_T$ spectra can be well reproduced. We further study the yields and yield ratios of different light (anti-)nuclei and naturally explain their interesting behaviors as a function of the collision energy. We especially point out that the multi-particle yield ratio $tp/d^2$ should be carefully corrected from hyperon weak decays for protons to probe the production characteristics of light nuclei. All of our results show that the coalescence mechanism for (anti-)nucleons plays a dominant role for the production of light nuclei and antinuclei at the RHIC beam energy scan energies.

Production of light-flavor and single-charmed hadrons in pp collisions at TeV in an equal-velocity quark combination model * *Supported by Shandong Province Natural Science Foundation (ZR2019YQ06,ZR2019MA053), and National Natural Science Foundation of China (11975011) and Higher Educational Youth Innovation Science and Technology Program of Shandong Province (2019KJJ010)

We apply an equal-velocity quark combination model to study the production of light-flavor hadrons and single-charmed hadrons at midrapidity in the collisions at TeV. We find that the experimental data for the spectra of and exhibit the quark number scaling property, which clearly indicates the quark combination mechanism at hadronization. Experimental data for the spectra of , , , , , and are systematically described by the model. The non-monotonic dependence of the ratio is naturally explained, and we find that it is closely related to the shape of the logarithm of the strange quark distribution. Using the spectra of light-flavor quarks obtained from light-flavor hadrons and the spectrum of charm quarks, which is consistent with perturbative QCD calculations, the experimental data for differential cross-sections of , , and as functions of are systematically described. We predict the differential cross-sections of and . The ratio in our model is approximately 0.16, and is approximately 0.012, owing to the cascade suppression of strangeness. In addition, the predicted and ratios exhibit the non-monotonic dependence on in the low range.

Strange hadron production in a quark combination model in Au+Au collisions at energies available at the BNL Relativistic Heavy Ion Collider

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 $K^{-}/K^{+}$, $\bar{p}/p$, $\bar{\Lambda}/\Lambda$, $\bar{\Xi}^{+}/\Xi^{-}$ and $\bar{\Omega}^{+}/\Omega^{-}$ simply correlate with each other and their experimental data except $\bar{\Omega}^{+}/\Omega^{-}$ 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).

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 varLambda and varXi . v_{2} of strange quarks obtained by data of varOmega is consistent with that obtained by data of varLambda and varXi , and at RHIC energies it is also consistent with that obtained by data of phi . 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_Tlesssim 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 3lesssim p_{T}lesssim 8 GeV/c. We predict v_{2} of charmed baryons varLambda _{c}^{+} and varXi _{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.

Statistical method in quark combination model * * Supported by National Natural Science Foundation of China (11535012, 11890713, 11575100), the 973 program (2015CB856902), the Key Research Program of the Chinese Academy of Sciences (XDPB09), and Shandong Province Natural Science Foundation (ZR2019YQ06, ZR2019MA053)

We present a new method for solving the probability distribution for baryons, antibaryons, and mesons at the hadronization of the 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 employ the method of the generating function to derive the outcome of the quark combination rule, which is significantly simpler and easier to generalize than the original method. Furthermore, we use the formula of the quark combination rule and its generalization to study the property of the 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 the quark combination model by studying hadronic multiplicity fluctuations and the underlying phase transition property in relativistic heavy-ion collisions.

Constituent quark number scaling from strange hadron spectra in pp collisions at TeV * * Supported by National Natural Science Foundation of China (11575100), and by Shandong Province Natural Science Foundation(ZR2019YQ06, ZR2019MA053), and by A Project of Shandong Province Higher Educational Science and Technology Program (J18KA228)

We show that the spectra of and at midrapidity in the inelastic events in collisions at 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 with equal velocity combination approximation to systematically study the production of identified hadrons in collisions at = 13 TeV. The midrapidity spectra for protons, , , , and in the inelastic events are simultaneously fitted by the model. The multiplicity dependence of the yields of these hadrons are also well understood. The strong dependence of the ratio is well explained by the model, which further suggests that the production of two hadrons with similar masses is determined by their quark content at hadronization. The spectra of strange hadrons at midrapidity in different multiplicity classes in collisions at 13 TeV are predicted for further tests of the model. The midrapidity spectra of soft ( GeV/c) strange quarks and up/down quarks at hadronization in collisions at 13 TeV are extracted.

Different production sources of light nuclei inultra-relativistic heavy-ion collisions * * Supported by National Natural Science Foundation of China (11505104, 11575100, 11675091)

We systematically study different production sources of light nuclei in ultra-relativistic heavy-ion collisions with a new method, an exclusive quark combination model + an inclusive hadron recombination model. We take deuterons and 3He produced in Pb-Pb collisions at TeV as examples to show the contribution of different production sources by studying their rapidity densities , yield ratios and transverse momentum ( ) spectra just after hadronization and at the final kinetic freeze-out. We find that about a half of and a fourth of 3He created just after hadronization can survive after the hadronic evolution process. Nucleons from resonance decays make a much larger contribution to the regeneration of light nuclei at the hadronic phase stage, and this contribution is about 77% and 90% for and 3He, respectively, calculated at the final kinetic freeze-out. In addition, we give an explanation for the constant behaviors of yield ratios and 3He as a function of the averaged charged multiplicity in Pb-Pb collisions and also provide a possible explanation for the observation that in Pb-Pb collisions is larger by a factor of about two than in pp collisions at LHC energies.

Yield ratios of identified hadrons in p+p, p+Pb , and Pb+Pb collisions at energies available at the CERN Large Hadron Collider

Yield ratios of identified hadrons observed in high multiplicity p+p and p+Pb collisions at LHC show remarkable similarity with those in Pb+Pb collisions, indicating some important and universal underlying dynamics in hadron production for different quark gluon final states. We use the quark combination model to explain the data of yield ratios in these three collision systems. The observed $p/\pi$ and $\Lambda/K_s^0$ can be reproduced simultaneously by quark combination, and these two ratios reflect the rate of baryon production at hadronization which is the same in light sector and strange sector and is roughly constant in p+p, p+Pb and Pb+Pb collision systems over three orders of magnitude in charged particle multiplicity.The data of $K_s^0/\pi$, $\Lambda/\pi$, $\Xi/\pi$ and $\Omega/\pi$ show a hierarchy behavior relating to the strangeness content, and are naturally explained by quark combination both in the saturate stage at high multiplicity and in the increase stage at moderate multiplicity. Our results suggest that the dynamical characteristic of quark combination is necessary in describing the production of hadrons in small systems created in p+p and p+Pb collisions.

Multiplicity fluctuation and correlation of identified baryons in a quark combination model

The dynamical fluctuation and correlation of multiplicity distributions of identified baryons and antibaryons produced by the hadronization of the bulk quark system are systematically studied in quark combination model. Starting from the most basic dynamics of quark combination which are necessary for multiplicity study, we analyze moments (variance, skewness and kurtosis) of inclusive multiplicity distribution of identified baryons, two-baryon multiplicity correlations, and baryon-antibaryon multiplicity correlations after the hadronization of quark system with given quark number and antiquark number. We obtain a series of interesting findings, e.g., binomial behavior of multiplicity moments, coincide flavor dependent two-baryon correlation and universal baryon-antibaryon correlation, which can be regarded as general features of quark combination. We further take into account correlations and fluctuations of quark numbers before hadronization to study their influence on multiple production of baryons and antibaryons. We find that quark number fluctuation and flavor conservation lead to a series of important results such as the negative $p\bar{\Omega}^{+}$ multiplicity correlation and universal two-baryon correlations. We also study the influence of resonance decay in order to compare our results with future experimental data in ultra-relativistic heavy ion collisions at LHC.

Energy dependence of resonance production in relativistic heavy ion collisions**Supported by National Natural Science Foundation of China (11575100, 11305076, 11505104)

The production of the hadronic resonances K*0(892), ϕ(1020), Σ*(1385), and Ξ*(1530) in central AA collisions at , 200, and 2760 GeV is systematically studied. The direct production of these resonances at system hadronization is described by the quark combination model and the effects of hadron multiple-scattering stage are dealt with by a ultra-relativistic quantum molecular dynamics model (UrQMD). We study the contribution of these two production sources to final observation and compare the final spectra with the available experimental data. The pT spectra of K*0(892) calculated directly by quark combination model are explicitly higher than the data at low pT ≲ 1.5 GeV, and taking into account the modification of rescattering effects, the resulting final spectra well agree with the data at all three collision energies. The rescattering effect on ϕ(1020) production is weak and including it can slightly improve our description at low pT on the basis of overall agreement with the data. We also predict the pT spectra of Σ*(1385) and Ξ*(1530), to be tested by the future experimental data.

Hidden-charm pentaquark states in heavy ion collisions at energies available at the CERN Large Hadron Collider

In the framework of the quark combination, we derive the yield formulas and study the yield ratios of the hidden-charm pentaquark states in ultra-relativistic heavy ion collisions. We propose some interesting yield ratios which clearly exhibit the production relationships between different hidden-charm pentaquark states. We show how to employ a specific quark combination model to evaluate the yields of exotic $P_c^+(4380)$, $P_c^+(4450)$ and their partners on the basis of reproducing the yields of normal identified hadrons, and execute the calculations in central Pb+Pb collisions at $\sqrt{s_{NN}}= 2.76$ TeV as an example.

Studying color connection effects ofe+e−→cc¯cc¯→Ξcc+Xprocess within quark combination model

The color connection of the parton system is an important bridge to connect the perturbative process and the hadronization one. The special color connection of four-heavy-quark system in e + e annihilation, which is the necessary one for the doubly heavy baryon and tetraquark productions is revisited. The hadronization effects, investigated with the help of the Quark Combination Model are compared with the corresponding results employing the Lund String Model in our previous work. The global properties related to a certain color connection are not sensitive to various hadronization models. In high energy collisions, hadronization is one of the most important processes for understanding the nonperturbative quantum chromodynamics and the confinement mechanism. e + e − annihilation has the advantage that the hadronization results can be compared with the experimental data directly to extract informations of hadronization because of no hadrons in the initial states. To embed the parton system into a hadronization model, it is necessary to specify the concrete color connection. However, the color connection for multi-parton system is not unique. Some clues can be obtained by analyzing the decomposition of the color space of the final partons [1– 5]. One of the interesting and important examples is the four-heavy-quark system (QQ ′ ¯ Q ¯

K*0andΣ*production in Au+Au collisions atsNN=200GeV and 62.4 GeV

Applying a quark combination model for the hadronization of Quark Gluon Plasma (QGP) and A Relativistic Transport (ART) model for the subsequent hadronic rescattering process, we investigate the production of $K^{*0}$ and $\Sigma^*$ resonances in central Au+Au collisions at $\sqrt{s_{NN}}=$ 200 GeV and 62.4 GeV. The initial $K^{*0}$ produced via hadronization is higher than the experimental data in the low $p_T$ region and is close to the data at 2-3 GeV/c. We take into account the hadronic rescattering effects which lead to a strong suppression of $K^{*0}$ with low $p_T$, and find that the $p_T$ spectrum of $K^{*0}$ can be well described. According to the suppressed magnitude of $K^{*0}$ yield, the time span of hadronic rescattering stage is estimated to be about 13 fm/c at 200 GeV and 5 fm/c at 62.4 GeV. The $p_T$ spectrum of $\Sigma^*$ directly obtained by quark combination hadronization in central Au+Au collisions at 200 GeV is in well agreement with the experimental data, which shows a weak hadronic rescattering effects. The elliptic flow v2 of $\Sigma^*$ in minimum bias Au+Au collisions at 200 GeV and $p_T$ spectrum of $\Sigma^*$ at lower 62.4 GeV are predicted.

Hadronic rapidity spectra in heavy ion collisions at SPS and AGS energies in a quark combination model

The quark combination mechanism of hadron production is applied to nucleus-nucleus collisions at the CERN Super Proton Synchrotron (SPS) and the BNL Alternating Gradient Synchrotron (AGS). The rapidity spectra of identified hadrons and their spectrum widths are studied. The data of π−, K±, φ, Λ, , Ξ− and at 80 and 40 A GeV, and in particular at 30 and 20 A GeV where the onset of deconfinement is suggested to happen, are consistently described by the quark combination model. However, at AGS 11.6 A GeV below the onset, the π±, K± and Λ spectra cannot be simultaneously explained, indicating the disappearance of the intrinsic correlation of their production in the constituent quark level. The collision-energy dependence of the rapidity spectrum widths of the constituent quarks, and the strangeness of the hot and dense quark matter produced in heavy ion collisions, are obtained and discussed.

An investigation of hadronization mechanism at a Z 0 factory

We briefly review the hadronization pictures adopted in the LUND String Fragmentation Model (LSFM), Webber Cluster Fragmentation Model (WCFM) and Quark Combination Model (QCM), respectively. Predictions of hadron multiplicity, baryon to meson ratios and baryon-antibaryon flavor correlations, especially those related to heavy hadrons at a Z 0 factory obtained by LSFM and QCM, are reported.

Entropy puzzle and the quark combination model

We use two available methods, the Duhem-Gibbs relation and the entropy formula in terms of particle phase space distributions, to calculate the entropy in a quark combination model. The entropy of the system extracted from the Duhem-Gibbs relation is found to increase in hadronization if the average temperature of the hadronic phase is lower than that of the quark phase. The increase of the entropy can also be confirmed from the entropy formula if the volume of the hadronic phase is larger than 2.5-3.0 times that of the quark phase. So whether the entropy increases or decreases during combination depends on the temperature before and after combination and on how much expansion the system undergoes during combination. The current study provides an example to shed light on the entropy issue in the quark combination model.

Exotic hadron production in a quark combination model

The philosophy on production of exotic hadrons (multiquark states) in the framework of the quark combination model is investigated, taking f{sub 0}(980) as an example. The production rate and p{sub T} spectra of f{sub 0}(980) considered as (ss) or (sqsq), respectively, are calculated and compared in Au+Au collisions at {radical}(s{sub NN})=200 GeV. The unitarity of various combination models, when open for exotic hadron production, is addressed.