We compute single and double inclusive gluon distributions in classical Yang-Mills simulations of proton-lead collisions and extract the associated transverse momentum dependent Fourier harmonics $v_2(p_T)$ and $v_3(p_T)$. Gluons have a large $v_2$ in the initial state, while odd harmonics such as $v_3$ vanish identically at the initial time $τ=0^{+}$. By the time $τ\lesssim 0.4\,{\rm fm/c}$ final state effects in the classical Yang-Mills evolution generate a non-zero $v_{3}$ and only mildly modify the gluon $v_{2}$. Unlike hydrodynamic flow, these momentum space anisotropies are uncorrelated with the global spatial anisotropy of the collision. A principal ingredient for the generation of $v_2$ and $v_3$ in this framework is the event-by-event breaking of rotational invariance in domains the size of the inverse of the saturation scale $Q_s$. In contrast to our findings in p+Pb collisions Yang-Mills simulations of lead-lead collisions generate much smaller values of $v_{2,3} (p_T)$ and additional collective flow effects are needed to explain experimental data. This is because the locally generated anisotropy due to the breaking of rotational invariance is depleted with the increase in the number of uncorrelated domains.
Strong multiparticle azimuthal correlations have recently been observed in high energy proton-nucleus collisions. While final state collective effects can be responsible for many of the observations, the domain structure in the classical color field of a high energy nucleus also naturally leads to such correlations. We describe recent calculations of the momentum space 2-particle cumulant azimuthal anisotropy coefficients v_n{2}, n=2,3,4 from fundamental representation Wilson line distributions describing the high energy nucleus. We find significant differences between Wilson lines from the MV…
The azimuthal anisotropies of the collective transverse flow of hadrons are investigated in a large range of heavy-ion collision energy within the Parton-Hadron-String Dynamics (PHSD) microscopic transport approach which incorporates explicit partonic degrees of freedom in terms of strongly interacting quasiparticles (quarks and gluons) in line with an equation-of-state from lattice QCD as well as dynamical hadronization and hadronic dynamics in the final reaction phase. The experimentally observed increase of the elliptic flow $v_2$ with bombarding energy is successfully described in terms of…
In the limit of short mean free path, relativistic kinetic theory gives rise to hydrodynamics through a systematically improvable gradient expansion. In the present work, a systematically improvable expansion in the opposite limit of large mean free path is considered, describing the dynamics of particles which are almost, but not quite, non-interacting. This non-hydrodynamic "eremitic" expansion does not break down for large gradients, and may be useful in situations where a hydrodynamic treatment is not applicable. As applications, azimuthal anisotropies at high transverse momentum in Pb+Pb …
Recent experimental data at the Large Hadron Collider (LHC) confirmed that the soft sector azimuthal anisotropies in central XeXe collisions are sensitive to deformations in the wave function of the Xenon nucleus. Additionally, the CMS experiment found that D meson flow is slightly suppressed compared to other particle species when considering quark number scaling in small systems of pPb compared to PbPb. In this talk we used the D and B Mesons Modular (DAB-MOD) code coupled to Trento+v-USPhydro to calculate the $R_{AA}$ and $v_n$'s of D mesons using different energy loss models and Langevin t…
Azimuthal anisotropies of reconstructed jets [$v_{n}^{jet} (n=2, 3)$] have been investigated in Pb+Pb collisions at the center of mass energy $\sqrt{s_{_{\rm NN}}}$ = 2.76 TeV within a framework of a multiphase transport (AMPT) model. The $v_{2}^{jet}$ is in good agreement with the recent ATLAS data. However, the $v_{3}^{jet}$ shows a smaller magnitude than $v_{2}^{jet}$, and approaches zero at a larger transverse momentum. It is attributed to the path-length dependence in which the jet energy loss fraction depends on the azimuthal angles with respect to different orders of event planes. The r…
The azimuthal anisotropies of the collective transverse flow of charged hadrons are investigated in a wide range of heavy-ion collision energies within the microscopic parton-hadron-string dynamics (PHSD) transport approach which incorporates explicit partonic degrees of freedom in terms of strongly interacting quasiparticles (quarks and gluons) in line with an equation of state from lattice QCD as well as the dynamical hadronization and hadronic collision dynamics in the final reaction phase. The experimentally observed increase of the elliptic flow $v_2$ of charged hadrons with collision ene…
Azimuthal momentum isotropization in the Quark-Gluon Plasma thermalization
University of Heidelberg（海德堡大学）；Shanghai Institute for Advanced Studies, University of Science and Technology of China（上海高等研究院，中国科学技术大学）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）；Hefei National Laboratory（合肥国家实验室）；Universidade de Santiago de Compostela（圣地亚哥德孔波斯特拉大学）；Axencia Galega de Innovación (GAIN), Xunta de Galicia（加利西亚自治区创新署（GAIN））
Heavy flavor probes provide important information about the in-medium properties of the quark-gluon plasma produced in heavy-ion collisions. In this work, we investigate the effects of 2D+1 event-by-event fluctuating hydrodynamic backgrounds on the nuclear suppression factor and momentum anisotropies of heavy flavor mesons and non-photonic electrons. Using the state-of-the-art D and B mesons modular simulation code (called "DAB-MOD"), we perform a systematic comparison of different transport equations in the same background, including a few energy loss models --- with and without energy loss f…
We show that flow anisotropies in relativistic heavy-ion collisions can be analyzed using a certain technique of shape analysis of excursion sets recently proposed by us for CMBR fluctuations to investigate anisotropic expansion history of the universe. The technique analyzes shapes (sizes) of patches above (below) certain threshold value for transverse energy/particle number (the excursion sets) as a function of the azimuthal angle and rapidity. Modeling flow by imparting extra anisotropic momentum to the momentum distribution of particles from HIJING, we compare the resulting distributions f…
There is now a substantial body of evidence that a deconfined quark-gluon plasma is created in ultrarelativistic collisions of heavy nuclei. Some key observables which are used to gauge the production of the quark-gluon plasma are the hadronic spectra and multiplicities across many species, azimuthal anisotropies in the production of various hadrons, jet quenching, photon/dilepton production, and heavy quarkonium suppression. A key question in the study of the quark-gluon plasma is what happens to these observables as one changes the system size. In particular, it is very interesting to study …
We summarize some recent ideas relating to anisotropic particle production in high-energy collisions. Anisotropic gluon distributions lead to anisotropies of the single-particle azimuthal distribution and hence to disconnected contributions to multi-particle cumulants. When these dominate, the four-particle elliptic anisotropy $c_2\{4\}$ changes sign. On the other hand, connected diagrams for $m$-particle cumulants are found to quickly saturate with increasing $m$, a ``coherence'' quite unlike conventional ``non-flow'' contributions such as decays. Finally, we perform a first exploratory pheno…
We present results for the azimuthal anisotropy of charged hadron distributions in A+A, p+A, d+A, and He3+A collisions within the IP-Glasma+MUSIC model. Obtained anisotropies are due to the fluid dynamic response of the system to the fluctuating initial geometry of the interaction region. While the elliptic and triangular anisotropies in peripheral Pb+Pb collisions at root-s=2.76 TeV are well described by the model, the same quantities in root-s=5.02 TeV p+Pb collisions underestimate the experimental data. This disagreement can be due to neglected initial state correlations or the lack of a de…
The azimuthal anisotropies of the collective transverse flow of charged hadrons are investigated in a wide range of heavy-ion collision energies within the microscopic Parton-Hadron-String Dynamics (PHSD) transport approach which incorporates explicit partonic degrees-of-freedom in terms of strongly interacting quasiparticles (quarks and gluons) in line with an equation-of-state from lattice QCD as well as the dynamical hadronization and hadronic collision dynamics in the final reaction phase. The experimentally observed increase of the elliptic flow $v_2$ of charged hadrons with collision ene…
The McLerran-Venugopalan model describes a highly boosted hadron/nucleus as a sheet of random color charges which source soft classical Weizsäcker-Williams gluon fields. We show that due to fluctuations, individual configurations are azimuthally anisotropic. We present initial evidence that impact parameter dependent small-x JIMWLK resummation preserves such anisotropies over several units of rapidity. Finally, we compute the first four azimuthal Fourier amplitudes of the S-matrix of a fundamental dipole in such background fields.
It was argued in arXiv:1805.09342 and arXiv:1807.00825 that the systematics of the azimuthal anisotropy coefficients $v_{2,3}$ measured in ultrarelativistic light-heavy ion collisions at RHIC and the LHC can be described in an initial state dilute-dense Color Glass Condensate (CGC) framework. We elaborate here on the discussion in these papers and provide further novel results that strengthen their conclusions. The underlying mathematical framework and numerical techniques employed are very similar to those in the CGC based IP-Glasma model used previously as initial conditions for heavy-ion co…
We argue that energy and momentum deposition from hard partons into quark-gluon plasma induces an important contribution to the final state hadron anisotropies. We also advocate a novel method of Event Shape Sorting which allow to analyse the azimuthal anisotropies of the fireball dynamics in more detail. A use of the method in femtoscopy is demonstrated.
We explore parton collisional effects on the conversion of geometry eccentricities into azimuthal anisotropies in Pb+Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV using a multi-phase transport model. The initial eccentricity $\varepsilon_{n}$ (n = 2,3) and flow harmonics $v_{n}$ (n = 2,3) are investigated as a function of the number of parton collisions ($N_{coll}$) during the source evolution of partonic phase. It is found that partonic collisions leads to generate elliptic flow $v_{2}$ and triangular flow $v_{3}$ in Pb+Pb collisions. On the other hand, partonic collisions also result in an evo…
Anisotropies in the final state of heavy-ion collisions carry information on the creation, expansion and evolution of the quark-gluon plasma. Currently, there is an abundance of studies on azimuthal anisotropies in comparison to longitudinal ones. The purpose of this work is to quantify angular $(θ, ϕ)$ correlations to further the understanding of the full spatial 3-D picture of emitted hadrons. Therefore, public ALICE data from Run 1 (2010) of Pb-Pb collisions at $\sqrt{s_{NN}} = 2.76\mathrm{~TeV}$ is analyzed through the estimation of an angular power spectrum. Issues with $|η| < 0.9$ limita…
The quark gluon plasma as produced in heavy ion collisions is exposed to early anisotropies in momentum space due to its rapid expansion. Such anisotropies can lead to non-abelian plasma instabilities, driven by unstable gluonic modes that can grow exponentially fast. These plasma instabilities can be simulated using a discretized version of gauge-covariant Boltzmann-Vlasov and Yang-Mills equations. In the stationary case, a turbulent cascade forms in the strong-field regime, which is associated with an approximately linear growth of energy in collective fields. Early longitudinal expansion sl…
In this paper we analytically extract the odd azimuthal anisotropy in the Classical Yang-Mills equations for the Glasma for pA collisions. We compute the first non-trivial term in the expansion of the proton sources of color charge. The computation is valid in the limit of a large nucleus when the produced particle momenta are larger than the saturation momentum of the proton.
We investigate the relative importance of initial and final state effects on azimuthal correlations of gluons in low and high multiplicity p+Pb collisions. To achieve this, we couple Yang-Mills dynamics of pre-equilibrium gluon fields (IP-GLASMA) to a perturbative QCD based parton cascade for the final state evolution (BAMPS) on an event-by-event basis. We find that signatures of both the initial state correlations and final state interactions are seen in azimuthal correlation observables, such as $v_2\left\lbrace2PC\right\rbrace(p_T)$, their strength depending on the event multiplicity and tr…
We study how local fluctuations in the initial states of relativistic heavy-ion collisions manifest themselves in the correlations between different orders of harmonic moments of the density profiles, particularly those involving only odd harmonics which purely arise from initial state fluctuations. We find the strengths of those correlations are sensitive to the number of hot and cold spots in the initial states. Hydrodynamic evolution of the fireball translates initial state geometric anisotropies as well as their correlations into final state momentum anisotropies and correlations. We concl…
In this paper, we consider the possibility that a new stage of matter, stemming from hidden/dark sectors beyond the Standard Model, to be formed in $pp$ collisions at the LHC, can significantly modify the correlations among final-state particles. In particular, two-particle azimuthal correlations are studied by means of a Fourier series sensitive to the near-side ridge effect while assuming that hidden/dark particles decay on top of the conventional parton shower. Then, new (fractional) harmonic terms should be included in the Fourier analysis of the azimuthal anisotropies, encoding the hypoth…
We study the influence and interplay of initial state and final state effects in the dynamics of small systems, focusing on azimuthal correlations at different multiplicities. To this end we introduce a new model, matching the classical Yang-Mills dynamics of pre-equilibrium gluon fields (IP-GLASMA) to a perturbative QCD based parton cascade for the final state evolution (BAMPS) on an event-by-event basis. Depending on multiplicity of the event, we see transverse momentum dependent signatures of the initial, but also the final state in azimuthal correlation observables, such as $v_2\left\lbrac…
We calculate the quark self-energy in a quark-gluon plasma that possesses an ellipsoidal momentum-space anisotropy in the local rest frame. By introducing additional transverse momentum anisotropy parameters into the parton distribution functions, we generalize previous results which were obtained for the case of a spheroidal anisotropy. Our results demonstrate that the presence of anisotropies in the transverse directions affects the real and imaginary parts of quark self-energy and, consequently, the self-energy depends on both the polar and azimuthal angles in the local rest frame of the ma…
It is argued that, in heavy ion collisions, thermal dileptons are good probes of the transport properties of the medium created in such events, and also of its early-time dynamics, usually inaccessible to hadronic observables. In this work we show that electromagnetic azimuthal momentum anisotropies do not only display a sensitivity to the shear relaxation time and to the initial shear-stress tensor profile, but also to the temperature dependence of the shear viscosity coefficient.
We explore the influence of a temperature-dependent shear viscosity over entropy density ratio $η/s$ on the azimuthal anisotropies v_2 and v_4 of hadrons at various rapidities. We find that in Au+Au collisions at full RHIC energy, $\sqrt{s_{NN}}=200$ GeV, the flow anisotropies are dominated by hadronic viscosity at all rapidities, whereas in Pb+Pb collisions at the LHC energy, $\sqrt{s_{NN}}=2760$ GeV, the flow coefficients are affected by the viscosity both in the plasma and hadronic phases at midrapidity, but the further away from midrapidity, the more dominant the hadronic viscosity is. We …
We review direct photons in the phenomenology of nuclear collisions at relativistic energies. Direct photons carry information about the space-time evolution of nuclear collisions because the QCD medium is transparent against colorless particles. After a status summary of theoretical and experimental studies, transverse momentum spectra and azimuthal momentum anisotropies of direct photons are studied in the context of the hydrodynamic modeling of relativistic nuclear collisions with emphasis on pre-equilibrium photons. It is implied that pre-equilibrium photons can be as important as thermal …
Following an explicit example, we present the chain of steps required for an event-by-event description of hadron production in high energy hadronic and nuclear collisions. We start from incoming nuclei, described in the Color Glass Condensate effective theory, whose collision creates the gluon fields of the glasma. Individual gluons are then sampled from the gluon fields' Husimi (smeared Wigner) distributions, and clustered using a new spacetime based algorithm. Clusters are fed into the Herwig event generator, which performs the hadronization, conserving energy and momentum. We discuss the p…
Non-linearities in the harmonic spectra of hadron-nucleus and nucleus-nucleus collisions provide evidence for the dynamical response to azimuthal spatial eccentricities. Here, we demonstrate within the framework of transport theory that even the mildest interaction correction to a picture of free-streaming particle distributions, namely the inclusion of one perturbatively weak interaction ("one-hit dynamics"), will generically give rise to all observed linear and non-linear structures. We further argue that transport theory naturally accounts within the range of its validity for realistic sign…
We construct a family of equations of state within a quasiparticle model by relating pressure, energy density, baryon density and susceptibilities adjusted to first-principles lattice QCD calculations. The relation between pressure and energy density from lattice QCD is surprisingly insensitive to details of the simulations. Effects from different lattice actions, quark masses and lattice spacings used in the simulations show up mostly in the quark-hadron phase transition region which we bridge over by a set of interpolations to a hadron resonance gas equation of state. Within our optimized qu…
Subjecting the SU(2) Yang--Mills system to azimuthal symmetries in both the $x-y$ and the $z-t$ planes results in a residual subsystem described by a U(1) Higgs like model with two complex scalar fields on the quarter plane. The resulting instantons are labeled by integers $(m,n_1,n_2)$ with topological charges $q=\frac12 [1-(-1)^m]n_1n_2$. Solutions are constructed numerically for $m=1,2,3$ and a range of $n_1=n_2=n$. It is found that only the $m=1$ instantons are self-dual, the $m>1$ configurations describing composite instanton-antiinstanton lumps.
