Number Of Constituent Quarks Research Articles

Collective Properties of the Nuclear Matter from the STAR Experiment at RHIC

The study of a collective flow offers valuable insights into the dynamics and properties of the Quark-Gluon Plasma (QGP) medium produced in heavy-ion collisions. The directed flow (v1) slope (dv1/dy) of protons at mid-rapidity is expected to be sensitive to the first-order phase transition. The scaling of the elliptic flow (v2) with the number of constituent quarks (NCQ) can be regarded as a signature of the QGP formation. The triangular flow (v3) typically originates from fluctuations and can offer constraints on the initial state geometry and fluctuations. The STAR experiment at RHIC has gathered data across a wide range of energies and systems. The second phase of the Beam Energy Scan program, including a Fixed-Target mode is done to collect high-statistics data on Au + Au collisions in the high baryon density region of the Quantum Chromodynamics (QCD) phase diagram. In these proceedings, we discuss selected results on the collective properties of the nuclear matter from the STAR experiment at RHIC.

Collision energy dependence of elliptic flow of identified hadrons in heavy-ion collisions using the PHSD model

We report the first predictions of elliptic flow (v2) of identified hadrons at mid-rapidity (|y|< 1.0) in Au+Au collisions at Elab=6.7,8,11,and 25 A GeV using the Parton Hadron String Dynamics (PHSD) model. The transverse momentum (pT) dependence of identified hadron v2 in different centrality intervals (0-10%, 10-40%, and 40-80%) is shown. A clear centrality dependence of v2(pT) is observed for particles at Elab=6.7,8,11,and 25 A GeV. Within the PHSD model, the number of constituent quark (NCQ) scaling of v2 approximately follows in Au+Au collisions at all beam energies. A collision energy (sNN) dependence of π, K, and pv2 is studied in comparison with available published experimental data in the beam energy range of 6-25 A GeV. These predictions will help in interpreting the data from the forthcoming Compressed Baryonic Matter (CBM) experiment at the Facility for Antiproton and Ion Research (FAIR) and Multi-Purpose Detector (MPD) at the Nuclotron-based Ion Collider facility (NICA).

Hadronic spectrum in the chiral large Nc extension of quantum chromodynamics

We study quantum chromodynamics in the chiral large Nc limit which contains a left-handed Weyl fermion in the fundamental representation, a left-handed Weyl fermion in the two index antisymmetric representation and (Nc−3) left-handed Weyl fermions in the antifundamental representation of the SU(Nc) gauge group. We construct gauge singlet composite operators and study their masses and correlation functions at large Nc. It is shown that all hadron masses scale as ∼Nc0nq where nq is the number of constituent quarks in the hadron. In addition by simple gluon exchange considerations it is seen that scattering amplitudes between hadrons have the same Nc scaling as the mass of the lightest hadron involved. This is the case provided the hadrons in the scattering amplitude share a sufficiently large number of constituent quarks. The chiral large Nc extension also allows for other nontrivial processes. For instance we consider two different baryonium states that are unique to this extension and that decay via emissions of two- and three-quark hadrons. Also other nontrivial scattering processes are considered. Finally, we study composites made of a mix of left- and right-handed fields. We categorize multiple groups of hadrons within the full spectrum according to their flavor structure. Within these groups all n-point functions scale the same. Published by the American Physical Society 2024

Elliptic anisotropy of open-charm hadrons from parton scatterings in p -Pb collisions at energies available at the CERN Large Hadron Collider

The elliptic azimuthal anisotropy coefficient (v2) of open-charm hadrons at midrapidity (|η&lt;1|) was studied in p-Pb collisions at sNN=8.16 TeV using a multiphase transport () model including an additional charm quark–antiquark pair production trigger. The model provides a simultaneous description of the measured pT spectrum and v2 of the D0 meson, as well as the v2 of light flavor meson Ks0. We found that the D0 and Ks0 v2 are both significantly affected by different parton scatterings among charm and light quarks. In addition, the predictions for the v2 of other charm hadrons including D+, Ds+, and Λc+ in p-Pb collisions are given for the first time. The v2 of open-charm hadrons reasonably follows the number-of-constituent-quark (NCQ) scaling up to 2.5 GeV, strongly indicating the importance of partonic degrees of freedom for the collectivity of heavy flavors in high-multiplicity p-Pb collisions. These findings may hint at the formation of deconfined matter in small collision systems, and provide referential value for future measurements of azimuthal anisotropy at energies available at the CERN Large Hadron Collider. Published by the American Physical Society 2024

Anisotropic flow and flow fluctuations of identified hadrons in Pb–Pb collisions at sqrt{s_{textrm{NN}}} = 5.02 TeV

The first measurements of elliptic flow of π±, K±, textrm{p}+overline{textrm{p}} , {textrm{K}}_{textrm{S}}^0 , Lambda +overline{Lambda} , ϕ, {Xi}^{-}+{overline{Xi}}^{+} , and {varOmega}^{-}+{overline{varOmega}}^{+} using multiparticle cumulants in Pb–Pb collisions at sqrt{s_{textrm{NN}}} = 5.02 TeV are resented. Results obtained with two- (v2{2}) and four-particle cumulants (v2{4}) are shown as a function of transverse momentum, pT, for various collision centrality intervals. Combining the data for both v2{2} and v2{4} also allows us to report the first measurements of the mean elliptic flow, elliptic flow fluctuations, and relative elliptic flow fluctuations for various hadron species. These observables probe the event-by-event eccentricity fluctuations in the initial state and the contributions from the dynamic evolution of the expanding quark–gluon plasma. The characteristic features observed in previous pT-differential anisotropic flow measurements for identified hadrons with two-particle correlations, namely the mass ordering at low pT and the approximate scaling with the number of constituent quarks at intermediate pT, are similarly present in the four-particle correlations and the combinations of v2{2} and v2{4}. In addition, a particle species dependence of flow fluctuations is observed that could indicate a significant contribution from final state hadronic interactions. The comparison between experimental measurements and CoLBT model calculations, which combine the various physics processes of hydrodynamics, quark coalescence, and jet fragmentation, illustrates their importance over a wide pT range.

Deep learning predicted elliptic flow of identified particles in heavy-ion collisions at the RHIC and LHC energies

Recent developments on a deep learning feed-forward network for estimating elliptic flow ($v_2$) coefficients in heavy-ion collisions have shown us the prediction power of this technique. The success of the model is mainly the estimation of $v_2$ from final state particle kinematic information and learning the centrality and the transverse momentum ($p_{\rm T}$) dependence of $v_2$. The deep learning model is trained with Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV minimum bias events simulated with a multiphase transport model (AMPT). We extend this work to estimate $v_2$ for light-flavor identified particles such as $\pi^{\pm}$, $\rm K^{\pm}$, and $\rm p+\bar{p}$ in heavy-ion collisions at RHIC and LHC energies. The number of constituent quark (NCQ) scaling is also shown. The evolution of $p_{\rm T}$-crossing point of $v_2(p_{\rm T})$, depicting a change in meson-baryon elliptic flow at intermediate-$p_{\rm T}$, is studied for various collision systems and energies. The model is further evaluated by training it for different $p_{\rm T}$ regions. These results are compared with the available experimental data wherever possible.

Azimuthal anisotropy measurement of (multi)strange hadrons in Au+Au collisions at sNN=54.4 GeV

Azimuthal anisotropy of produced particles is one of the most important observables used to access the collective properties of the expanding medium created in relativistic heavy-ion collisions. In this paper, we present second ($v_{2}$) and third ($v_{3}$) order azimuthal anisotropies of $K_{S}^{0}$, $\phi$, $\Lambda$, $\Xi$ and $\Omega$ at mid-rapidity ($|y|<$1) in Au+Au collisions at $\sqrt{s_{\text{NN}}}$ = 54.4 GeV measured by the STAR detector. The $v_{2}$ and $v_{3}$ are measured as a function of transverse momentum and centrality. Their energy dependence is also studied. $v_{3}$ is found to be more sensitive to the change in the center-of-mass energy than $v_{2}$. Scaling by constituent quark number is found to hold for $v_{2}$ within 10%. This observation could be evidence for the development of partonic collectivity in 54.4 GeV Au+Au collisions. Differences in $v_{2}$ and $v_{3}$ between baryons and anti-baryons are presented, and ratios of $v_{3}$/$v_{2}^{3/2}$ are studied and motivated by hydrodynamical calculations. The ratio of $v_{2}$ of $\phi$ mesons to that of anti-protons ($v_{2}(\phi)/v_{2}(\bar{p})$) shows centrality dependence at low transverse momentum, presumably resulting from the larger effects from hadronic interactions on anti-proton $v_{2}$.

Elliptic flow of strange and multi-strange hadrons in isobar collisions at √SNN = 200 GeV at RHIC

We report the elliptic flow (υ2) of Ks0, Λ, Ξ¯+, ϕ, Ξ−, and Ξ+ at midrapidity for Ru+Ru and Zr+Zr collisions at √SNN = 200 GeV. The transverse momentum (pT) and centrality dependence of υ2 have been studied. The number of constituent quark (NCQ) scaling for all the (multi-)strange hadrons has also been tested. The dependence in the ratio of average υ2 (〈υ2〉) on centrality shows a deviation from unity indicating a difference in nuclear structure and deformation between the isobars. The results show a systematic size dependence when compared to Cu+Cu, Au+Au, and U+U collisions at similar beam energies.

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.

Charm and beauty isolation from heavy flavor decay electrons in p+p and Pb+Pb collisions at [formula omitted] = 5.02 TeV at LHC

We present an analysis on the heavy flavor hadron decay electrons with charm and beauty contributions decomposed via a data driven method in p+p and Pb+Pb collisions at sNN = 5.02 TeV at LHC. The transverse momentum pT spectra, nuclear modification factor RAA and azimuthal anisotropic flow v2 distributions of electrons from charm and beauty decays are obtained. We find that the electron RAA from charm (RAAc→e) and beauty (RAAb→e) decays are suppressed at pT>2.0 GeV/c in Pb+Pb collisions, which indicates that charm and beauty interact with and lose their energy in the hot-dense medium. A less suppression of RAAb→e than RAAc→e at 2.0<pT<8.0 GeV/c is observed, which is consistent with the mass-dependent partonic energy loss scenario. A non-zero electron v2 from beauty decays (v2b→e) is observed and in good agreement with ALICE measurement. At low pT from 1.0 to 3.0 GeV/c, a discrepancy between RHIC and LHC results is observed with an 85% confidence level, which might be a possible hint of an energy-dependent behavior of beauty quarks reacting with the medium created in heavy-ion collisions. At 3.0<pT<7.0 GeV/c, v2b→e deviates from a number-of-constituent-quark (NCQ) scaling hypothesis, which favors that beauty quark is unlikely thermalized in heavy-ion collisions at LHC energy.

Event topology and constituent-quark scaling of elliptic flow in heavy-ion collisions at the Large Hadron Collider using a multiphase transport model

Transverse spherocity is an event shape observable, which separates the events based on their geometrical shapes. In this work, we use transverse spherocity to study the identified light flavor production in heavy-ion collisions using A Multi-Phase Transport (AMPT) model. We obtain the elliptic flow coefficients for pions, kaons and protons in Pb+Pb collisions at sqrt{s_mathrm{{NN}}} = 5.02 TeV as a function of transverse spherocity and collision centrality. Also, we study the number of constituent-quark (NCQ) scaling of elliptic flow which interprets the dominance of the quark degrees of freedom at the early stages of the collision. We observe a clear dependence of the elliptic flow for identified particles on transverse spherocity. It is found that the NCQ-scaling is strongly violated in events with low transverse spherocity compared to transverse spherocity-integrated events, confirming the fragmentation-based hadronization mechanism for high-momentum partons involved in the dynamics of jetty-like events.

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 of strange and multi-strange hadrons in U+U collisions at sNN = 193GeV at STAR

In this paper, we present systematic measurements of azimuthal anisotropy for strange hadrons ([Formula: see text], [Formula: see text] and [Formula: see text]) and multi-strange hadrons ([Formula: see text] and [Formula: see text]) at mid-rapidity ([Formula: see text]) in U[Formula: see text]U collisions at [Formula: see text] GeV using the STAR detector at the Relativistic Heavy Ion Collider (RHIC). Flow coefficients ([Formula: see text], [Formula: see text] and [Formula: see text]) are presented as a function of transverse momentum ([Formula: see text]) for minimum bias and three different centrality intervals. The [Formula: see text] sub-event plane method is used to obtain the results. These measurements are compared with the published results from Au[Formula: see text]Au collisions at [Formula: see text] GeV. Number of Constituent Quark (NCQ) scaling of the measured flow coefficients in U[Formula: see text]U collisions is discussed. We also present the ratio of [Formula: see text] scaled by the participant eccentricity ([Formula: see text]) to explore system size dependence and collectivity in U[Formula: see text]U collisions. The measured flow coefficients are compared with hydrodynamic and transport model calculations.

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.

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.

Charm and beauty isolation from heavy flavor decay electrons in Au+Au collisions at [formula omitted] = 200 GeV at RHIC

We present a study of charm and beauty isolation based on a data-driven method with recent measurements on heavy flavor hadrons and their decay electrons in Au+Au collisions at sNN = 200 GeV at RHIC. The individual electron pT spectra, RAA and v2 distributions from charmed and beauty hadron decays are obtained. We find that the electron RAA from beauty hadron decays (RAAb→e) is suppressed in minimum bias Au+Au collisions but less suppressed compared with that from charmed hadron decays at pT > 3.5 GeV/c, which indicates that beauty quark interacts with the hot-dense medium with depositing its energy and is consistent with the mass-dependent energy loss scenario. For the first time, the non-zero electron v2 from beauty hadron decays (v2b→e) at pT > 3.0 GeV/c is observed and shows smaller elliptic flow compared with that from charmed hadron decays at pT < 4.0 GeV/c. At 2.5 GeV/c <pT < 4.5 GeV/c, v2b→e is smaller than a number-of-constituent-quark (NCQ) scaling hypothesis. This suggests that beauty quark is unlikely thermalized and too heavy to be moved in a partonic collectivity in heavy-ion collisions at the RHIC energy.