Constituent Quark Number Scaling Research Articles

Anisotropic Flow of Identified Hadrons by the Event Plane Method at FAIR Energies

A comprehensive study of the elliptic flow of hadrons for non central Au+Au collision with the impact parameter of b =5-9 fm in the mid rapidity region of (-1 ≤ ycm ≤1) with the reaction plane angle Ψ in the mid-pseudorapidity of |ɳ| < 0.35 is investigated in the FAIR energy regime of 25 A Gev by the AMPT model with both the default and the string melting scenarios. In both the versions of AMPT model, we have observed that at low PT regions up to PT ≈ 1.0 GeV/c, elliptic flow shows an almost linear increase with the increase in the transverse momentum. Also, there is a clear mass ordering effect that is particles with higher mass shows a smaller at a given PT than the particles with lower mass. In addition, the constituent quark number scaling of elliptic flow has been investigated where we have observed a universal scaling in the string melting version of the AMPT model i.e with the partonic degrees of freedom due to quark coalescence model compared with the default version of the AMPT model. Further, the scaling behavior has been observed for the transverse kinetic energy with both scenarios.

Self-similarity of hard cumulative processes in fixed target experiment for BES-II at STAR

Search for signatures of phase transition in Au + Au collisions is in the heart of the heavy ion program at RHIC. Systematic study of particle production over a wide range of collision energy revealed new phenomena such as the nuclear suppression effect expressed by nuclear modification factor, the constituent quark number scaling for elliptic flow, the “ridge effect” in Δϕ-Δη fluctuations etc. To determine the phase boundaries and location of the critical point of nuclear matter the Beam Energy Scan (BES-I) program at RHIC has been suggested and performed by STAR and PHENIX Collaborations. The obtained results shown that the program (BES-II) should be continued. In this paper a proposal to use hard cumulative processes in BES Phase-II program is outlined. Selection of the cumulative events is assumed to enrich data sample by new type of collisions characterized by higher energy density and more compressed matter. This would allow finding clearer signatures of phase transition, location of a critical point and studying extreme conditions in heavy ion collisions.

Elliptic flow of identified particles in Pb–Pb collisions at the LHC

The elliptic flow coefficient, v2, is presented for π±, K±, KS0, p+p¯, ϕ, Λ+Λ¯, Ξ−+Ξ¯+, Ω−+Ω¯+ in Pb–Pb collisions at sNN=2.76 TeV with the ALICE detector. Results obtained with the scalar product method are reported as a function of transverse momentum, pT, out to pT=6 GeV/c at different collision centralities. For pT<2 GeV/c, v2 exhibits a particle mass dependence. Particles tend to group into mesons and baryons for pT>3 GeV/c. Deviations from the number of constituent quark scaling at the level of ±20% are found for pT>2–3 GeV/c. The results are compared to hydrodynamic calculations coupled to a hadronic cascade model.

Probing the QCD phase diagram with measurements of ϕ-meson production and elliptic flow in heavy-ion collisions at STAR

We present measurements of ϕ-meson production and elliptic flow (v2) at mid-rapidity in Au + Au collisions at = 7.7 – 200 GeV. Energy dependence of nuclear modification factor (RCP) of ϕ meson is presented. The ϕ-meson RCP has a value ≥ 1.0 for ≤ 39 GeV. The Ω/ϕ ratios are also presented and show a different trend at the intermediate transverse momentum (pT) for = 11.5 GeV compared to higher beam energies. The number-of-constituent quark (NCQ) scaling of v2 has been studied at various beam energies. The NCQ scaling holds for particles and anti-particles separately including the ϕ meson for ≥ 19.6 GeV, which can be considered as an evidence of partonic collectivity. We observe that ϕ-meson v2 falls off the trend from the other hadrons at highest measured pT values by 1.8σ and 2.3σ at = 7.7 and 11.5 GeV, respectively.

Can baryon stopping explain the breakdown of constituent quark scaling and proposed signals of chiral magnetic waves at RHIC?

Azimuthal emission spectra of various hadron species in ultra-relativistic heavy ion collisions at ≈ 200 GeV exhibit a curious hierarchy at intermediate pt (≈ 2 – 3 GeV). Rather than being ordered by mass, the spectra seem to be ordered by whether the species is a baryon or meson. It is seen that when the elliptic flow v2 and transverse momentum pT are both scaled by the number of quarks in each hadron, the spectra fall in line with each other. This number of constituent quark (NCQ) scaling suggests a system where the relevant degrees of freedom are colored partons as opposed to hadrons: the quark-gluon plasma (QGP). Thus, a break down of this scaling as beam energy is reduced could be indicative of the QGP threshold. However, at lower energies, there is also an increase in the number of entrance-channel partons transported to mid-rapidity due to baryon stopping, which can violate NCQ scaling even above the QGP threshold. We describe a specific pattern for the break down of the scaling that includes the observed difference in elliptic flow for positive and negative pions. We also contrast baryon stopping with the Chiral Magnetic Effect (CME)–an alternative model for π+/π− flow difference–and discuss results from tests that can distinguish between them.

Elliptic flow of identified hadrons in Au+Au collisions atsNN=7.7–62.4 GeV

Measurements of the elliptic flow, $v_{2}$, of identified hadrons ($\pi^{\pm}$, $K^{\pm}$, $K_{s}^{0}$, $p$, $\bar{p}$, $\phi$, $\Lambda$, $\bar{\Lambda}$, $\Xi^{-}$, $\bar{\Xi}^{+}$, $\Omega^{-}$, $\bar{\Omega}^{+}$) in Au+Au collisions at $\sqrt{s_{NN}}=$ 7.7, 11.5, 19.6, 27, 39 and 62.4 GeV are presented. The measurements were done at mid-rapidity using the Time Projection Chamber and the Time-of-Flight detectors of the STAR experiment during the Beam Energy Scan program at RHIC. A significant difference in the $v_{2}$ values for particles and the corresponding anti-particles was observed at all transverse momenta for the first time. The difference increases with decreasing center-of-mass energy, $\sqrt{s_{NN}}$ (or increasing baryon chemical potential, $\mu_{B}$) and is larger for the baryons as compared to the mesons. This implies that particles and anti-particles are no longer consistent with the universal number-of-constituent quark (NCQ) scaling of $v_{2}$ that was observed at $\sqrt{s_{NN}}=$ 200 GeV. However, for the group of particles NCQ scaling at $(m_{T}-m_{0})/n_{q}>$ 0.4 GeV/$c^{2}$ is not violated within $\pm$10%. The $v_{2}$ values for $\phi$ mesons at 7.7 and 11.5 GeV are approximately two standard deviations from the trend defined by the other hadrons at the highest measured $p_{T}$ values.

PHENIX Measurements of Higher-order Flow Harmonics for Identified Charged Hadrons in Au + Au collisions at sNN=39–200mboxGeV

The azimuthal anisotropy coefficients v 2 , 3 , 4 , characterizing collective flow in Au + Au collisions, are presented for identified particle species as a function of transverse momentum ( p T ) , centrality (cent) and beam collision energy ( s N N = 0.039 – 0.20 TeV ) . The v n values for each particle species, show little, if any, change over the measured beam energy range, and v n / ( n q ) n / 2 vs. K E T / n q scales to a single curve (constituent quark number ( n q ) scaling) for each n , over a broad range of transverse kinetic energies ( K E T ) . A comparison of v 2 ( p T ) for individual particle species obtained in Au + Au collisions at s N N = 0.20 TeV (RHIC) and Pb + Pb collisions at s N N = 2.76 TeV (LHC), indicate stronger collective flow at the LHC. These flow measurements and their scaling patterns, can provide important additional constraints for extraction of the specific viscosity η / s .

Constituent quark scaling violation due to baryon number transport

In ultrarelativistic heavy-ion collisions at $\sqrt{{s}_{NN}}\ensuremath{\approx}200$ GeV, the azimuthal emission anisotropy of hadrons with low and intermediate transverse momentum (${p}_{T}\ensuremath{\lesssim}4$ GeV/c) displays an intriguing scaling. In particular, the baryon (meson) emission patterns are consistent with a scenario in which a bulk medium of flowing quarks coalesces into three-quark (two-quark) ``bags.'' While a full understanding of this number-of-constituent-quark (NCQ) scaling remains elusive, it is suggestive of a thermalized bulk system characterized by colored dynamical degrees of freedom---a quark-gluon plasma (QGP). In this scenario, one expects the scaling to break down as the central energy density is reduced below the QGP formation threshold; for this reason, NCQ-scaling violation searches are of interest in the energy scan program at the Relativistic Heavy Ion Collider. However, as $\sqrt{{s}_{NN}}$ is reduced, it is not only the initial energy density that changes; there is also an increase in the net baryon number at midrapidity, as stopping transports entrance-channel partons to midrapidity. This phenomenon can result in violations of simple NCQ scaling. Still in the context of the quark coalescence model, we describe a specific pattern for the breakdown of the scaling that includes different flow strengths for particles and their antipartners. Related complications in the search for recently suggested exotic phenomena are also discussed.

Nonequilibrium hadronization and constituent quark number scaling

The constituent quark number scaling of elliptic flow is studied in a non-equilibrium hadronization and freeze-out model with rapid dynamical transition from ideal, deconfined and chirally symmetric Quark Gluon Plasma, to final non-interacting hadrons. In this transition a Bag model of constituent quarks is considered, where the quarks gain constituent quark mass while the background Bag-field breaks up and vanishes. The constituent quarks then recombine into simplified hadron states, while chemical, thermal and flow equilibrium break down one after the other. In this scenario the resulting temperatures and flow velocities of baryons and mesons are different. Using a simplified few source model of the elliptic flow, we are able to reproduce the constituent quark number scaling, with assumptions on the details of the non-equilibrium processes.

Quark Number Scaling in Fluid Dynamics and Hadronization via Quarkyonic Matter

NCQ scaling of elliptic flow is studied in a non-equilibrium hadronization and freeze-out model from ideal, deconfined and chirally symmetric Quark Gluon Plasma (QGP), to final non-interacting hadrons. In this transition the quarks gain constituent quark mass while the background Bag-field breaks up. The constituent quarks then recombine into simplified hadron states, while chemical, thermal and flow equilibrium break down. Then the resulting temperatures and flow velocities of baryons and mesons will be different. In a simplified model, we reproduce the constituent quark number scaling.

Systematic study of QCD matter with flow of identified particles at RHIC

The anisotropic flow of identified particles provides a powerful tool to study the properties of the hot and dense matter which is believed to be created at RHIC. It can be used to study different particle production mechanisms in heavy-ion collisions. The recent measurements of anisotropic flow of identified particles at RHIC will be reviewed in this paper, including light flavors (i.e. strange hadrons) and heavy flavors. Topics such as number of constituent quark scaling, parton energy loss, and jet conversions will be discussed in this paper.

Initial eccentricity and constituent quark number scaling of elliptic flow in ideal and viscous dynamics

In the Israel-Stewart theory of dissipative hydrodynamics, the scaling properties of elliptic flow in $\mathrm{Au}+\mathrm{Au}$ collisions are studied. The initial energy density of the fluid was fixed to reproduce STAR data on $\ensuremath{\phi}$-meson multiplicity in $0--5%$ $\mathrm{Au}+\mathrm{Au}$ collisions such that, irrespective of fluid viscosity, entropy at the freeze-out is similar in ideal or in viscous evolution. The initial eccentricity or constituent quark number scaling is only approximate in ideal or minimally viscous ($\ensuremath{\eta}/s=1/4\ensuremath{\pi}$) fluid. Eccentricity scaling becomes nearly exact in more viscous fluid ($\ensuremath{\eta}/s\ensuremath{\geqslant}0.12$). However, in more viscous fluid, constituent quark number scaled elliptic flow for mesons and baryons splits into separate scaling functions. Simulated flows also do not exhibit ``universal scaling''; that is, elliptic flow scaled by the constituent quark number and charged particles ${v}_{2}$ is not a single function of transverse kinetic energy scaled by the quark number. From a study of the violation of universal scaling, we obtain an estimate of quark-gluon plasma viscosity, $\ensuremath{\eta}/s=0.12\ifmmode\pm\else\textpm\fi{}0.03$. The error is statistical only. The systematic error in $\ensuremath{\eta}/s$ could be as large.

Differential elliptic flow of identified hadrons and constituent quark number scaling at the GSI Facility for Antiproton and Ion Research (FAIR)

Differential elliptic flow $v_2(p_{T})$ for identified hadrons has been investigated in the FAIR energy regime, employing a hadronic-string transport model (UrQMD) as well as a partonic transport model (AMPT). It has been observed that both the models show a mass ordering of $v_2$ at low $p_{T}$ and a switch over resulting a baryon-meson crossing at intermediate $p_{T}$. AMPT generates higher $v_2$ values compared to UrQMD. In addition, constituent quark number scaling behavior of elliptic flow has also been addressed. Scaling behavior in terms of the transverse momentum $p_T$ is found to absent for both the partonic as well as the hadronic model. However UrQMD and AMPT with string melting scenario do exhibit a NCQ scaling of $v_2$ at varying degree, with respect to transverse kinetic energy $KE_T$. But default AMPT, where partonic scatterings are not included, does not show any considerable scaling behavior. A variable $\alpha$ is defined to quantify the degree of $KE_T$ scaling. We found that UrQMD gives better scaling than AMPT at FAIR.

Collective Flow in Ultra-relativistic Collisions

The Fluid Dynamical (FD) models are considered to be a good description of heavy ion reactions with higher collision energies. Recent results indicate that the collective flow develops in the Quark Gluon Plasma (QGP) phase, what results in the Constituent Quark Number (NCQ) scaling of the flow. At the same time, between the deconfined ideal QGP and the Hadronic Matter, a so-called “Quarkyonic Matter” is predicted, where the dominant degrees of freedom are quarks. In FD model we assume the formation of the quarkyonic matter in the final Freeze Out (FO) stage, which includes deconfinement and the simultaneous formation of constituent quarks. Then we reach the conclusion that collective flow must have frozen out early when the quarks were the dominant constituents of matter, and the final hadron masses are reached subsequently.

Footprints of the (Nearly) Perfect Liquid

In relativistic heavy-ion collisions, the system has gone through a series of evolution, almost at every stage of its evolution it leaves behind footprints in flow observable. Those footprints contain valuable information of the bulk property of the (nearly) perfect liquid. By examing footprints of the nearly perfect liquid, we address a few important issues, including the ideal hydrodynamic limit, estimation of η / s , testing the Number of Constituent Quark scaling at low energy, in small system, at large transverse momentum, and in forward region. Future prospect of flow study is discussed.

Measurements ofϕmeson production in relativistic heavy-ion collisions at the BNL Relativistic Heavy Ion Collider (RHIC)

We present results for the measurement of ϕ meson production via its charged kaon decay channel ϕ→K+K− in Au+Au collisions at sNN=62.4,130, and 200 GeV, and in p+p and d+Au collisions at sNN=200 GeV from the STAR experiment at the BNL Relativistic Heavy Ion Collider (RHIC). The midrapidity (|y|<0.5) ϕ meson transverse momentum (pT) spectra in central Au+Au collisions are found to be well described by a single exponential distribution. On the other hand, the pT spectra from p+p, d+Au, and peripheral Au+Au collisions show power-law tails at intermediate and high pT and are described better by Levy distributions. The constant ϕ/K− yield ratio vs beam species, collision centrality, and colliding energy is in contradiction with expectations from models having kaon coalescence as the dominant mechanism for ϕ production at RHIC. The Ω/ϕ yield ratio as a function of pT is consistent with a model based on the recombination of thermal s quarks up to pT~4 GeV/c, but disagrees at higher transverse momenta. The measured nuclear modification factor, RdAu, for the ϕ meson increases above unity at intermediate pT, similar to that for pions and protons, while RAA is suppressed due to the energy loss effect in central Au+Au collisions. Number of constituent quark scaling of both Rcp and v2 for the ϕ meson with respect to other hadrons in Au+Au collisions at sNN=200 GeV at intermediate pT is observed. These observations support quark coalescence as being the dominant mechanism of hadronization in the intermediate pT region at RHIC.14 MoreReceived 17 September 2008DOI:https://doi.org/10.1103/PhysRevC.79.064903©2009 American Physical Society

Resonance recombination model and quark distribution functions in the quark-gluon plasma

We investigate the consequences of space-momentum correlations in quark phase-space distributions for coalescence processes at the hadronization transition. Thus far it has been proved difficult to reconcile such correlations with the empirically observed constituent quark number scaling (CQNS) at the Relativistic Heavy Ion Collider (RHIC). To address this problem we combine our earlier developed quark recombination model with quark phase-space distributions computed from relativistic Langevin simulations in an expanding quark-gluon plasma (QGP). Hadronization is based on resonance formation within a Boltzmann equation that recovers thermal equilibrium and obeys energy conservation in the quark-coalescence process, while the fireball background is adjusted to hydrodynamic simulations of semicentral $\mathrm{Au}\text{\ensuremath{-}}\mathrm{Au}$ collisions at RHIC. To facilitate the applicability of the Langevin process, we focus on strange and charm quarks. Their interactions in the QGP are modeled using leading-order perturbative QCD augmented by effective Lagrangians with resonances that smoothly merge into hadronic states formed at ${T}_{c}$. The interaction strength is adjusted to reproduce the empirical saturation value for the quark-elliptic flow, ${v}_{2,q}^{\mathrm{sat}}\ensuremath{\simeq}7\text{\ensuremath{-}}8%$. The resulting \ensuremath{\phi} and $J/\ensuremath{\psi}$ elliptic flow recover CQNS over a large range in transverse momentum (${p}_{T}$) within a few percent. As a function of transverse kinetic energy, both the quark spectra from the Langevin simulations and the meson spectra generated via resonance recombination recover CQNS from zero to at least $3 \mathrm{GeV}$.

Breaking of the number-of-constituent-quark scaling for identified-particle elliptic flow as a signal of phase change in low-energy data taken at the BNL Relativistic Heavy Ion Collider (RHIC)

We argue that measurements of identified-particle elliptic flow in a wide energy range could shed light on the possible phase change in high-energy heavy ion collisions at the BNL Relativistic Heavy Ion Collider (RHIC). When the hadronization process is dominated by quark coalescence, the number-of-constituent-quark (NCQ) scaling for the identified-particle elliptic flow can serve as a probe for studying the strong interacting partonic matter. In the upcoming RHIC low-energy runs, the NCQ scaling behavior may be broken because of the change of the effective degrees of freedom of the hot dense matter, which corresponds to the transition from the dominant partonic phase to the dominant hadronic phase. A multiphase transport model is used to present the dependence of NCQ scaling behavior on the different hadronization mechanisms.

Hadronization via recombination

The recombination model as a model for hadronization from a quark–gluon plasma has been recently revived since it has advantages in explaining several important features of the final state produced in heavy-ion collisions at the RHIC, such as the constituent quark number scaling of the elliptic coefficient versus the transverse energy of identified hadrons, the bending shape of the pT spectrum of hadrons near 5 GeV/c, and the measured large value of baryon-to-meson ratio (of the order of unity) in the same pT range. We have developed a dynamic simulation model of heavy-ion collisions in which a quark–gluon plasma, starting from a certain initial condition, evolves hydrodynamically until it reaches the phase boundary, and then hadronizes by valence quark recombination. Rescattering after hadronization is described by UrQMD. We discuss some details of the model and report first, preliminary results.

Systematic studies of global observables by PHENIX

Systematic studies of global observables in different collision systems are indispensable for mapping the QCD phase diagram. Fluctuations in these quantities can provide fundamental information relevant for the phase transitions. The following global observables relevant to critical behavior are studied: the longitudinal density correlation, K to π and p to π fluctuations, and the constituent quark number scaling for elliptic flows.