Constituent Quark Number Scaling Research Articles

Elliptic and triangular flow of (multi-)strange hadrons and ɸ mesons in BES-II energies at STAR

In these proceedings, we present the measurements of elliptic (v2) and triangular (v3) flow of (multi-)strange hadrons and ϕ mesons in 19.6 and 14.6 GeV Au+Au collisions from the STAR. The number of constituent quark (NCQ) scaling of v2 and v3 holds well at √SNN=19.6 GeV, which indicates the collective flow is built up in the partonic stage. At these energies, the anti-particles show better NCQ scaling than the particles for both v2 and v3, which may be caused by the different contributions from the produced and transported quarks.

Signals of quark combination at hadronization in pp collisions at s=200 GeV

We find signals of quark combination at hadronization from the experimental data of ${p}_{T}$ spectra of hadrons at midrapidity in $pp$ collisions at $\sqrt{s}=200\text{ }\text{ }\mathrm{GeV}$. The first is the constituent quark number scaling property for ${p}_{T}$ spectra of ${\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}}$ and $\ensuremath{\phi}$ and that for ${p}_{T}$ spectra of $p$ and ${\ensuremath{\rho}}^{0}$. The second is that ${p}_{T}$ spectra of $\mathrm{\ensuremath{\Lambda}}$, ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$, and ${K}^{*0}$ can be self-consistently described using the spectrum of strange quarks from $\ensuremath{\phi}$ 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 by the spectrum of up/down quarks from $p$ data and a spectrum of charm quarks which is consistent with theoretical calculations of the fixed-order next-to-leading-logarithmic approach. These results indicate a similarity between hadron production in $pp$ collisions at $\sqrt{s}=200\text{ }\text{ }\mathrm{GeV}$ 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 $\sqrt{s}=200\text{ }\text{ }\mathrm{GeV}$ in the future so as to better understand the property of the small parton system created in $pp$ collisions at different collision energies.

Disappearance of partonic collectivity in [formula omitted] GeV Au+Au collisions at RHIC

We report on the measurements of directed flow v1 and elliptic flow v2 for hadrons (π±, K±, KS0, p, ϕ, Λ and Ξ−) from Au+Au collisions at sNN=3GeV and v2 for (π±, K±, p and p‾) at 27 and 54.4GeV with the STAR experiment. While at the two higher energy midcentral collisions the number-of-constituent-quark (NCQ) scaling holds, at 3GeV the v2 at midrapidity is negative for all hadrons and the NCQ scaling is absent. In addition, the v1 slopes at midrapidity for almost all observed hadrons are found to be positive, implying dominant repulsive baryonic interactions. The features of negative v2 and positive v1 slope at 3GeV can be reproduced with a baryonic mean-field in transport model calculations. These results imply that the medium in such collisions is likely characterized by baryonic interactions.

Number-of-constituent-quark scaling of elliptic flow: a quantitative study

The number-of-constituent-quark (NCQ) scaling behavior of the elliptic flow of identified particles produced in A+A collisions is studied quantitatively using an empirical function that fits the experimental $v_2$ data available from the RHIC and LHC. The most common approach for NCQ scaling involves (1) doing a scaling of the experimental $v_2$ data of an identified particle with its NCQ, (2) doing the same to its transverse momentum or energy, then (3) combining all the scaled data and identifying the NCQ behavior by intuitively looking (since the measured experimental data are discrete). We define two variables $(d_1, d_2)$ to describe NCQ scaling quantitatively and simultaneously, and identify the approximate region where the NCQ scaling holds. This approach could be applied to study NCQ or other scaling phenomena in future experiments.

Light nuclei collectivity from [formula omitted] GeV Au+Au collisions at RHIC

In high-energy heavy-ion collisions, partonic collectivity is evidenced by the constituent quark number scaling of elliptic flow anisotropy for identified hadrons. A breaking of this scaling and dominance of baryonic interactions is found for identified hadron collective flow measurements in sNN = 3 GeV Au+Au collisions. In this paper, we report measurements of the first- and second-order azimuthal anisotropic parameters, v1 and v2, of light nuclei (d, t, 3He, 4He) produced in sNN = 3 GeV Au+Au collisions at the STAR experiment. An atomic mass number scaling is found in the measured v1 slopes of light nuclei at mid-rapidity. For the measured v2 magnitude, a strong rapidity dependence is observed. Unlike v2 at higher collision energies, the v2 values at mid-rapidity for all light nuclei are negative and no scaling is observed with the atomic mass number. Calculations by the Jet AA Microscopic Transport Model (JAM), with baryonic mean-field plus nucleon coalescence, are in good agreement with our observations, implying baryonic interactions dominate the collective dynamics in 3 GeV Au+Au collisions at RHIC.

NCQ scaling of f0(980) elliptic flow in 200 GeV Au+Au collisions by STAR and its constituent quark content

Searching for exotic state particles and studying their properties have furthered our understanding of quantum chromodynamics (QCD). The f0(980) resonance is an exotic state with relatively high production rate in relativistic heavy-ion collisions, decaying primarily into ππ. Currently the structure and quark content of the f0(980) are unknown with several predictions from theory being a qq¯ state, a qqq¯q¯ state, a KK¯ molecule state, or a gluonium state. We report the first f0(980) elliptic flow (v2) measurement from 200 GeV Au+Au collisions at STAR. The transverse momentum dependence of v2 is examined and compared to those of other hadrons (baryons and mesons). The empirical number of constituent quark (NCQ) scaling is used to investigate the constituent quark content of f0(980), which may potentially address an important question in QCD.

Azimuthal anisotropy measurement of multi-strange hadrons in Au+Au collision at √SNN = 27 and 54.4 GeV at STAR

In these proceedings, we present the second order (ν2) and the third order (ν3) azimuthal anisotropy measurements of strange and multi-strange hadrons such as KS0, Λ, Λ¯, ϕ, Ξ−, Ξ¯+, Ω−, Ω¯+ in Au+Au collisions at √SNN = 27 and 54.4 GeV at STAR. The centrality dependence of ν2 and ν3 as well as the number of constituent quark scaling (NCQ scaling) for all the particles mentioned above are discussed. The ratio of ν2 of ϕ mesons to that of p¯ is presented at √SNN = 54.4 GeV which gives a hint of mass ordering violation at low pT.

Azimuthal anisotropy measurements of strange and multistrange hadrons in U+U collisions at sNN=193 GeV at the BNL Relativistic Heavy Ion Collider

We present systematic measurements of azimuthal anisotropy for strange and multistrange hadrons (Ks0, Λ, Ξ, and Ω) and ϕ mesons at midrapidity (|y|< 1.0) in collisions of U+U nuclei at sNN=193 GeV, recorded by the STAR detector at the Relativistic Heavy Ion Collider. Transverse momentum (pT) dependence of flow coefficients (v2, v3, and v4) is presented for minimum bias collisions and three different centrality intervals. Number of constituent quark scaling of the measured flow coefficients in U+U collisions is discussed. We also present the ratio of vn scaled by the participant eccentricity (ɛn2) to explore system size dependence and collectivity in U+U collisions. The magnitude of v2/ɛ2 is found to be smaller in U+U collisions than that in central Au+Au collisions contradicting naive eccentricity scaling. Furthermore, the ratios between various flow harmonics (v3/v23/2, v4/v24/2) are studied and compared with hydrodynamic and transport model calculations.9 MoreReceived 18 March 2021Accepted 24 May 2021DOI:https://doi.org/10.1103/PhysRevC.103.064907©2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCollective flowRelativistic heavy-ion collisionsNuclear Physics

Number of constituent quark scaling of elliptic flows in high multiplicity p-Pb collisions at [formula omitted

We briefly summarize our recent study on the number of constituent quark (NCQ) scaling of hadron elliptic flows in high multiplicity p-Pb collisions at sNN=5.02TeV. With the inclusion of hadron production via the quark coalescence model at intermediate pT, the viscous hydrodynamics at low pT, and jet fragmentation at high pT, our Hydro – Coal – Frag model provides a nice description of the pT-spectra and differential elliptic flow ν2(pT) of pions, kaons and protons over the pT range from 0 to 6 GeV. Our results demonstrate that including the quark coalescence is essential for reproducing the observed approximate NCQ scaling of hadron ν2 at intermediate pT in experiments, indicating strongly the existence of partonic degrees of freedom and the formation of quark-gluon plasma in high multiplicityp-Pb collisions at the LHC.

Probing the Partonic Degrees of Freedom in High-Multiplicity p-Pb collisions at sqrt[s_{NN}]=5.02 TeV.

We investigate the role of partonic degrees of freedom in high-multiplicity p-Pb collisions at sqrt[s_{NN}]=5.02 TeV carried out at the Large Hadron Collider (LHC) by studying the production and collective flow of identified hadrons at intermediate p_{T} via the coalescence of soft partons from the viscous hydrodynamics (VISH2+1) and hard partons from the energy loss model, linear Boltzmann transport (LBT). We find that combining these intermediate p_{T} hadrons with the low p_{T} hadrons from the hydrodynamically expanding fluid and high p_{T} hadrons from the fragmentation of quenched jets, the resulting hydro-dynamics-coalescence-fragmentation model provides a nice description of measured p_{T} spectra and differential elliptic flow v_{2}(p_{T}) of pions, kaons, and protons over the p_{T} range from 0 to 6GeV. We further demonstrate the necessity of including the quark coalescence contribution to reproduce the experimentally observed approximate number of constituent quark scaling of hadron v_{2} at intermediate p_{T}. Our results thus indicate the importance of partonic degrees of freedom and also hint at the possible formation of quark-gluon plasma in high-multiplicity p-Pb collisions at the LHC.

Quark number scaling of pT spectra for Ω and ϕ in relativistic heavy-ion collisions

We show that the experimental data of transverse momentum ($p_{T}$) spectra of $\Omega$ baryon and $\phi$ 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 $\langle\beta\rangle$ with a hydrodynamics-motivated blast-wave model.

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.

Energy dependence study of directed flow inAu+Aucollisions using an improved coalescence in a multiphase transport model

The rapidity-odd component of directed flow ($v_{1}$) of identified hardons ($\pi^{\pm}$, $K^{\pm}$, $K^{0}_{S}$, $p$, $\bar{p}$, $\phi$, $\Xi$, $\bar{\Xi}$, $\Lambda$, $\bar{\Lambda}$) and partons ($u$, $\bar{u}$, $d$, $\bar{d}$, $s$, $\bar{s}$) in Au+Au collisions at various beam energies ($\sqrt{s_{\rm NN}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4, 200 GeV) using a multi-phase transport model is analyzed. A data driven approach (inspired from the experimental analysis) is performed here to distinguish the transported and produced quarks which are found to have different directed flow values at various collision beam energies. The coalescence sum rule (Number of Constituent Quark scaling) violation is observed at lower energies where hadronic matters dominate. The strange quark ($s$) and $\phi$ meson slope (d$v_{1}$/d$y$) show a double sign change around 14.5 GeV, unlike other partons and hadrons. It suggests that strange quark is more sensitive to the softening of Equation of State (EoS).

Azimuthal anisotropy of strange hadrons in U+U collisions at √SNN = 193 GeV at RHIC

We present the measurement of the azimuthal anisotropy of strange hadrons (K0s, ϕ and Λ) at mid-rapidity (|y| &lt; 1.0) in U+U collisions at [see formula in PDF] = 193 GeV using the STAR detector at RHIC. We present the centrality and transverse momentum dependence of flow coefficients υn for n = 2, 3, 4. A strong centrality dependence of υ2 is observed for the particles K0s, ϕ and Λ in U+U collisions at [see formula in PDF] = 193 GeV similar to Au+Au collisions at [see formula in PDF] = 200 GeV. We studied the number of constituent quark scaling (NCQ) of the flow coefficients. The NCQ scaling of the flow coefficients holds within uncertainties for the particles studied in the U+U collisions. We also present the comparison of the results to the AMPT transport model.

Azimuthal anisotropy in particle distribution in a multiphase transport model

Anisotropic flow of hadronic matter is considered as a sensitive tool to detect the early stage dynamics of high-energy heavy-ion collisions. Taking the event by event fluctuations of the collision geometry into account, the elliptic flow parameter and the triangular flow parameter derived from the azimuthal distribution of produced hadrons, are investigated within the framework of a multiphase transport (AMPT) model, at a collision energy that in near future will typically be available at the Facility for Antiproton and Ion Research. The dependence of elliptic and triangular flow parameters on initial fluctuations, on parton scattering cross-sections, their mass ordering on different hadron species and on the constituent quark number scaling are examined. The AMPT simulation can not exactly match the elliptic flow results on Pb + Pb collision at 40A GeV of the NA49 experiment. The simulation results presented in this work are expected to provide us with an insight to study flow properties at high baryonic density but moderate temperature, and also with an opportunity to compare similar results available from RHIC and LHC experiments.

Investigating the NCQ scaling of elliptic flow at LHC with a multiphase transport model

The number of constituent quark (NCQ) scaling behavior of elliptic flow has been systematically studied at the LHC energy within the framework of a multiphase transport model (AMPT) in this work. We find that the parameters used to generate the initial states and the collision centrality are important for the existence of NCQ scaling even when hadronic rescattering contribution is off in Pb-Pb collisions of $\sqrt{s_{NN}}=2.76$ TeV. By turning on the hadron rescattering process, the hadronic evolution impacts are also found to be significant. Extending the analysis to Pb-Pb collsions of $\sqrt{s_{NN}}=5.02$ TeV, one would observe similar qualitative features.

Scaling of elliptic flow in heavy-ion collisions with the number of constituent quarks in a transport model

We studied the number of constituent quark scaling (NCQ) behaviour of elliptic flow ($v_{2}$) under the framework of A Multi-Phase Transport model (AMPT) at both top-RHIC and LHC energies. The NCQ-scaling in $v_{2}$ holds at top-RHIC energy with AMPT string melting version, while it breaks in Pb+Pb collisions at LHC energy using the same framework. The breaking of NCQ-scaling at LHC energy has been studied by varying the magnitude of parton-parton scattering cross-section and lifetime of hadronic cascade as implemented in AMPT. We find that the breaking of NCQ scaling in Pb+Pb collisions at $\sqrt{s_{NN}}$ =2.76 TeV is independent of the magnitude of parton-parton cross-section and the later stage hadronic interactions. Further we observed that scaling holds in a small collision system like Si+Si at $\sqrt{s_{NN}}$ = 2.76 TeV. We discussed that the breaking of NCQ scaling is possibly due to high phase-space density of constituents quarks in Pb+Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV.

Centrality and Transverse Momentum Dependence of Elliptic Flow of Multistrange Hadrons and ϕ Meson in Au+Au Collisions at √[sNN]=200 GeV.

We present high precision measurements of elliptic flow near midrapidity (|y|<1.0) for multistrange hadrons and ϕ meson as a function of centrality and transverse momentum in Au+Au collisions at center of mass energy √[sNN]=200 GeV. We observe that the transverse momentum dependence of ϕ and Ω v2 is similar to that of π and p, respectively, which may indicate that the heavier strange quark flows as strongly as the lighter up and down quarks. This observation constitutes a clear piece of evidence for the development of partonic collectivity in heavy-ion collisions at the top RHIC energy. Number of constituent quark scaling is found to hold within statistical uncertainty for both 0%-30% and 30%-80% collision centrality. There is an indication of the breakdown of previously observed mass ordering between ϕ and proton v2 at low transverse momentum in the 0%-30% centrality range, possibly indicating late hadronic interactions affecting the proton v2.

Investigating the scaling of higher-order flows in relativistic heavy-ion collisions

The modified number of constituent quark (NCQ) scaling $v_{n}/n_{q}^{n/2} \sim KE_{T}/n_{q}$ for mesons and baryons and the scaling relation $v_{n} \sim v_{2}^{n/2}$ for higher-order anisotropic flows, which were observed experimentally, have been investigated at top RHIC energy. It has been found that the modified NCQ scaling can not be obtained from the naive coalescence even by taking into account event-by-event fluctuations but may be due to hadronic afterburner or thermal freeze-out. In addition, we observed that the behavior of the $v_{n}/v_{2}^{n/2}$ ratio is sensitive to the partonic interaction, and it is different for mesons and baryons from the naive coalescence but is expected to be almost the same experimentally.

Probing novel long-range correlation phenomena in pPb collisions with identified particles at CMS

Observation of a long-range near-side two-particle correlation (known as the ”Ridge”) in high-multiplicity pp and pPb collisions opened up new opportunities of exploring novel QCD dynamics in small collision systems. To further investigate the origin of this phenomenon, studies of two-particle correlations with identified K0s and trigger particles in 5.02 TeV pPb collisions are presented, and compared to PbPb collisions over a similar multiplicity range. The K0s and are cleanly reconstructed via their secondary decay vertices over a wide pseudorapidity and transverse momentum range. The second-order anisotropy harmonics (v2) of K0s and are extracted from long-range correlations as a function of particle multiplicity and pT. The wide pT coverage and rich sample of high multiplicity pPb events allow: (1) a precise examination of the mass ordering effect of vn at low pT as predicted by hydrodynamics for a collectively expanding medium; (2) exploration of possible constituent quark number scaling of v2 between mesons and baryons as was observed in high-energy nucleus- nucleus collisions.