Parton Recombination Research Articles

Gluon distribution and mass decomposition of the pion and kaon

We present the gluon distribution functions of the pion and kaon in small-x and large-x regions, and compare them with the results obtained from lattice QCD and continuum Schwinger function methods. Whether in the small-x region or the large-x region, our gluon distribution of the pion is consistent with the results of lattice QCD and continuum Schwinger function methods. We also calculate the first four moments of gluon distributions of the pion and kaon at different Q2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q^{2}$$\\end{document} scales. In addition, we present the mass decomposition of the pion and kaon with the dynamical parton distribution functions calculated by the DGLAP equation with parton–parton recombination corrections. The mass structures of the pion and kaon are completely different from that of the proton.

Simulation of multiple hadron production and transition to quark-gluon plasmas based on nonlinear dynamics

A dynamics of quark-gluon plasmas has been defined by the evolution parameter, which at high energies depends on collision energy of atomic nuclei for appropriate multiplicities of secondary hadrons. The paper is based on the solution of evolution equation for patrons momentum distribution. A transition from regular propagation to irregular chaotic is an indicator of the quark-gluon plasma emerging. Nonlinear renormalization group equation has been solved by the method of Poincaré mappings. The equation is a model of the evolution of the momentum distribution of partons due to competing processes of their creation and fusion. As the energy increases, sequential bifurcation (doubling) of phase trajectories occurs, and scale-invariant fractal structures are to create. At sufficiently high energies of quarks and gluons, a dynamically determined quark-gluon system, corresponding to QGP, arises in space. There are also hadron-like structures. Quantum coherence effects follow by dynamic chaos. As a result, quarks and gluons merge into stable attractor structures with their subsequent decay into hadrons. The nonlinear equation introduced for quark-gluon cascade, which comprises dynamical chaos, has include effects of parton recombination. The chaotic dynamics has been connected specifically to the transverse momenta of partons. Clearly, the formation of dynamically determined stable structures should be unknown before, attractor mechanism of quark hadronization.

A unified study of the production of all identified hadrons over wide ranges of transverse momenta at LHC

The production of all identified hadrons in the heavy-ion collisions at the CERN Large Hadron Collider (LHC) is studied with emphasis on the pT distributions up to 20 GeV/c in central Pb+Pb collisions at . The parton recombination model is used to determine the hadronic pT spectra from the quark distributions. From the heavy hyperon spectra it is known from earlier studies that the u, d, s thermal distributions in pT are exponential with large inverse slopes that cannot be identified with any temperature in conventional fluid models. They are used as inputs in our model together with shower partons determined from our treatment of momentum degradation that uses high-pT pion data as input. Those thermal and shower partons are used to calculate the pT distributions of all observed hadrons (π, K, p, Λ, Ξ, Ω and ϕ) over wide ranges of pT, so the system is highly constrained. We show how well the LHC data can be reproduced with only a few parameters to adjust. Centrality dependence has not been studied. What is learned is that minijets are important, not only in giving rise to abundant shower partons, but also in the conversion of semihard partons in the medium to soft partons that enhance the thermal partons. Since the conversion process can occur throughout the expansion phase of the high-density medium, the results of this work may be taken to imply that advocacy for the assumption of rapid equilibration needs to be reconciled with the phenomenological evidence that we have found for prolonged creation of soft partons.

Global study of nuclear modifications on parton distribution functions

A global analysis of nuclear medium modifications of parton distributions is presented using deeply inelastic scattering data of various nuclear targets. Two obtained data sets are provided for quark and gluon nuclear modification factors, referred as nIMParton16. One is from the global fit only to the experimental data of isospin-scalar nuclei (Set A), and the other is from the fit to all the measured nuclear data (Set B). The scale-dependence is described by DGLAP equations with nonlinear corrections in this work. The Fermi motion and off-shell effect, nucleon swelling, and parton–parton recombination are taken into account together for modeling the complicated x-dependence of nuclear modification. The nuclear gluon shadowing in this paper is dynamically generated by the QCD evolution of parton splitting and recombination processes with zero gluon density at the input scale. Sophisticated nuclear dependence of nuclear medium effects is studied with only two free parameters. With the obtained free parameters from the global analysis, the nuclear modifications of parton distribution functions of unmeasured nuclei can be predicted in our model. Nuclear modification of deuteron is also predicted and shown with recent measurement at JLab.

Looking for quark saturation in proton and nuclei

The quark saturation behavior at low [Formula: see text] is shown in a numeric solution of the DGLAP equation with parton recombination corrections, which resembles the widely discussed JIMWLK saturation of gluons. Our calculation suggests that the partonic saturation can be interpreted as a dynamical balance between the splitting and the fusion processes of partons, without any other condensation mechanisms added. The nuclear shadowing saturation at small [Formula: see text] resulted from the proposed quark saturation is also discussed.

Nucleon spin structure

This paper contains three parts relating to the nucleon spin structure in a simple picture of the nucleon: (i) The polarized gluon distribution in the proton is dynamically predicted starting from a low scale by using a nonlinear quantum chromodynamics (QCD) evolution equation — the Dokshitzer–Gribov–Lipatov–Altarelli–Paris (DGLAP) equation with the parton recombination corrections, where the nucleon is almost consisted only of valence quarks. We find that the contribution of the gluon polarization to the nucleon spin structure is much larger than the predictions of most other theories. This result suggests that a significant orbital angular momentum of the gluons is required to balance the gluon spin momentum. (ii) The spin structure function [Formula: see text] of the proton is studied, where the perturbative evolution of parton distributions and nonperturbative vector meson dominance (VMD) model are used. We predict [Formula: see text] asymptotic behavior at small x from lower Q2to higher Q2. The results are compatible with the data including the early HERA estimations and COMPASS new results. (iii) The generalized Gerasimov–Drell–Hearn (GDH) sum rule is understood based on the polarized parton distributions of the proton with the higher twist contributions. A simple parameterized formula is proposed to clearly present the contributions of different components in the proton to [Formula: see text]. The results suggest a possible extended objects with size 0.2–0.3 fm inside the proton.

Applications of a nonlinear evolution equation II: The EMC effect

The EMC effect is studied by using the DGLAP equation with the ZRS corrections and minimum number of free parameters, where the nuclear shadowing effect is a dynamical evolution result of the equation, the nucleon swelling and Fermi motion in the nuclear environment deform the input parton distributions. Parton distributions of both proton and nucleus are predicted in a unified framework. We show that the parton recombination as a higher twist correction plays an essential role in the evolution of parton distributions either of proton or nucleus. We find that the nuclear anti-shadowing contributes a part of enhancement of the ratio of the structure functions around x ~ 0.1, while the other part origins from the deformation of the nuclear valence quark distributions. In particular, the nuclear gluon distributions are dynamically predicted, which are important information for the recherche of the high energy nuclear physics.

Applications of a nonlinear evolution equation I: The parton distributions in the proton

The nonlinear Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) evolution equations with parton recombination corrections are used to dynamically evaluate the proton's parton distribution functions starting from a low scale μ2, where the nucleon consists of valence quarks. We find that the resulting negative nonlinear corrections can improve the perturbative stability of the QCD evolution equation at low Q2. Our resulting parton distributions, with four free parameters, are compatible with the existing databases. This approach provides a powerful tool to connect the quark models of the hadron and various nonperturbative effects at the scale μ2 with the measured structure functions at the high scale Q2 ≫ μ2.

Heavy quark production in ultra high energy cosmic ray interactions

In this paper we present a comprehensive study of the heavy quark production in ultra high energy cosmic ray interactions in the atmosphere considering that the primary cosmic ray can be either a photon, neutrino or a proton. The analysis is performed using a unified framework – the dipole formalism – and the saturation effects, associated to the physical process of parton recombination, are taken into account. We demonstrate that the contribution of heavy quarks for cosmic ray interactions is in general non-negligible and can be dominant depending of the process considered. Moreover, our results indicate that new dynamical mechanisms should be included in order to obtain reliable predictions for the heavy quark production in pp collisions at ultra high cosmic ray energies.

Directed Flow of Identified Particles inAu+AuCollisions atSNN=200 GeVat RHIC

STAR’s measurements of directed flow (v1) around midrapidity for π±, K±, KS0, p, and p¯ in Au+Au collisions at sNN=200 GeV are presented. A negative v1(y) slope is observed for most of produced particles (π±, K±, KS0, and p¯). In 5%–30% central collisions, a sizable difference is present between the v1(y) slope of protons and antiprotons, with the former being consistent with zero within errors. The v1 excitation function is presented. Comparisons to model calculations (RQMD, UrQMD, AMPT, QGSM with parton recombination, and a hydrodynamics model with a tilted source) are made. For those models which have calculations of v1 for both pions and protons, none of them can describe v1(y) for pions and protons simultaneously. The hydrodynamics model with a tilted source as currently implemented cannot explain the centrality dependence of the difference between the v1(y) slopes of protons and antiprotons.Received 16 December 2011DOI:https://doi.org/10.1103/PhysRevLett.108.202301© 2012 American Physical Society

Formula omitted] production in [formula omitted] collisions at [formula omitted] in the recombination model

We first determine c and c ¯ shower parton distributions in jets induced by light and charm hard partons in the framework of the recombination model from relevant fragmentation functions. The shower parton distributions can be used to calculate other fragmentation functions and study charmed hadron production in other collisions. When the distributions are applied to reproduce the J / ψ production in Au + Au collisions at s N N = 200 GeV , energy loss effect is taken into account for J / ψ production due to its momentum loss in traversing the dense medium. We find that the contribution of thermal–shower parton recombination dominates over other mechanisms of hadronization in the region of 3.3 < p T < 5.8 GeV / c . The calculated J / ψ transverse momentum spectrum is in good agreement with the experimental data.

Negative elliptic flow of J/ψ’s: A qualitative signature for charm collectivity at RHIC

We discuss one of the most prominent features of the very recent preliminary elliptic flow data of J/ψ-mesons from the PHENIX Collaboration (PHENIX Collaboration (C. Silvestre), arXiv:0806.0475 [nucl-ex]). Even within the rather large error bars of the measured data a negative elliptic flow parameter (v2) for J/ψ in the range of p T = 0.5-2.5 GeV/c is visible. We argue that this negative elliptic flow at intermediate pT is a clear and qualitative signature for the collectivity of charm quarks produced in nucleus-nucleus reactions at RHIC. Within a parton recombination approach we show that a negative elliptic flow puts a lower limit on the collective transverse velocity of heavy quarks. The numerical value of the transverse flow velocity $ \beta_{T}^{}$ for charm quarks that is necessary to reproduce the data is $ \beta_{T}^{}$ (charm) ∼ 0.55-0.6c and therefore compatible with the flow of light quarks.

Decreasing elliptic flow at the CERN Large Hadron Collider: Calculations in a parton recombination approach

We apply the parton recombination approach to study the energy dependence of the elliptic flow, ${v}_{2}$, in heavy ion collisions from BNL Alternating Gradient Synchrotron (AGS) to CERN Large Hadron Collider (LHC) energies. The relevant input quantities ($T,{\ensuremath{\mu}}_{B},{\ensuremath{\eta}}_{T}$) at the various center of mass energies are obtained from fits to the available data. The model yields a good description of the integrated ${v}_{2}$ data for charged particles at midrapidity from AGS to BNL Relativistic Heavy Ion Collider (RHIC) energies. In stark contrast to the current expectations, we observe a decrease of the integrated ${v}_{2}$ values above the highest RHIC energy. Thus, we predict a decrease of ${v}_{2}$ at LHC energies compared to the RHIC results. This drop is attributed to negative ${v}_{2}$ values for the underlying parton distributions at low to moderate transverse momenta that develop if the transverse flow velocity is high enough. At energies above the LHC regime, the present approach predicts even negative values for the integrated ${v}_{2}$.

Collisional parton energy loss in a finite size QCD medium reexamined: Off-mass-shell effects

We study the collisional energy loss mechanism for particles produced off mass shell in a finite size QCD medium. The off-mass-shell effects introduced consider particles produced in wave packets instead of plane waves and a length scale associated with an in-medium particle lifetime. We show that these effects reduce the energy loss as compared to the case when the particles are described as freely propagating from the source. The reduction in energy loss is stronger as the scale becomes of the order of or smaller than the medium size. We discuss possible consequences of the result on the description of the energy loss process in the parton recombination scenario.

Pseudorapidity shape of elliptic flow as signature for fast equilibration in relativistic heavy-ion collisions at energies up tosNN=200GeV

The implications of parton recombination processes on the dynamics of ultrarelativistic heavy-ion reactions are investigated. To do so, the quark-gluon string transport model has been extended for partonic recombination and fusion processes. Parton recombination leads to short equilibration times and improves significantly on the theoretical description of measured directed and elliptic flow, i.e., ${v}_{1}$ and ${v}_{2}$, distributions in Au+Au collisions at $\sqrt{{s}_{\mathit{NN}}}=200\phantom{\rule{0.3em}{0ex}}\mathrm{GeV}$, in particular what concerns their pseudorapidity dependence. The shape of ${v}_{2}(\ensuremath{\eta})$ is found to be closely related to fast thermalization.

Forward production with largep/πratio and without jet structure at anypT

Particle production in the forward region of heavy-ion collisions is shown to be due to parton recombination without shower partons. The regeneration of soft partons due to momentum degradation through the nuclear medium is considered. The degree of degradation is determined by fitting the $\bar p/p$ ratio. The data at $\sqrt s=62.4$ GeV and $\eta=3.2$ from BRAHMS on the $p_T$ distribution of average charged particles are well reproduced. Large proton-to-pion ratio is predicted. The particles produced at any $p_T$ should have no associated particles above background to manifest any jet structure.

Hadron Correlations and Parton Recombination

Parton recombination has been found to be an extremely useful model to understand hadron production at the Relativistic Heavy Ion Collider. It is particularly important to explore its connections with hard processes. This article reviews some of the aspects of the quark recombination model and places particular emphasis on hadron correlations.

Is constituent quark scaling a unique sign of parton recombination?

We study the transverse momentum dependence of the anisotropic flow v2 for π, K, nucleon, Λ, Ξ and Ω for Au+Au collisions at $\sqrt{s_{NN}} = 200\,\mathrm{GeV}$ within two independent string-hadron transport approaches (RQMD and UrQMD). Although both models reach only 60% of the absolute magnitude of the measured v2, they both predict the particle-type dependence of v2 as observed by the RHIC experiments: v2 exhibits a hadron-mass hierarchy in the low pT region and a number-of-constituent-quark (NCQ) dependence in the intermediate pT region. The failure of the hadronic models to reproduce the absolute magnitude of the observed v2 indicates that transport calculations of heavy-ion collisions at RHIC must incorporate interactions among quarks and gluons in the early, hot and dense phase. The presence of an NCQ scaling in the string-hadron model results suggests that the particle-type dependences observed in heavy-ion collisions at intermediate pT might be related to the hadronic cross sections in vacuum rather than to the hadronization process itself.

Hadronization of dense partonic matter

The parton recombination model has turned out to be a valuable tool to describe hadronization in high-energy heavy-ion collisions. I review the model and revisit recent progress in our understanding of hadron correlations. I also discuss higher Fock states in the hadrons, possible violations of the elliptic flow scaling and recombination effects in more dilute systems.

Review of Parton Recombination Models

Parton recombination models have been very successful in explaining data taken at RHIC on hadron spectra and emission patterns in Au+Au collisions at transverse momenta above 2 GeV/c, which have exhibited features which could not be understood in the framework of basic perturbative QCD. In this article I will review the current status on recombination models and outline which future challenges need to be addressed by this class of models.