Momentum Anisotropy Research Articles

Collective modes of gluons in an anisotropic thermomagnetic medium

We study the collective modes of gluons in an anisotropic thermal medium in the presence of a constant background magnetic field using the hard-thermal-loop perturbation theory. The momentum space anisotropy of the medium has been incorporated through the generalized Romatschke-Strickland form of the distribution function, whereas the magnetic modification arising from the quark loop contribution has been taken into account in the lowest Landau level approximation. We consider two special cases: (i) a spheroidal anisotropy with the anisotropy vector orthogonal to the external magnetic field and (ii) an ellipsoidal anisotropy with two mutually orthogonal vectors describing anisotropies along and orthogonal to the field direction. The general structure of the polarization tensor in both cases is equivalent and consists of six independent basis tensors. We find that the introduction of momentum anisotropy ingrains azimuthal angular dependence in the thermomagnetic collective modes. Our study suggests that the presence of a strong background magnetic field can significantly reduce the growth rate of the unstable modes, which may have important implications in the equilibration of magnetized quark-gluon plasma.

Raman photogalvanic effect: Photocurrent at inelastic light scattering

We show theoretically that electromagnetic waves propagating in the transparency region of a noncentrosymmetric medium can induce a DC electric current. The origin of the effect is the Raman scattering of light by free carriers in the system. Due to the photon scattering, electrons undergo real quantum transitions resulting in the formation of their anisotropic momentum distribution and in shifts of electronic wave packets giving rise to a steady-state photocurrent. We present the microscopic theory of the Raman photogalvanic effect (RPGE) focusing on two specific situations: (i) generic case of a bulk gyrotropic semiconductor and (ii) a quantum well structure where the light is scattered by intersubband excitations. We uncover the relation of the predicted RPGE and the traditional photogalvanic effect at the light absorption.

Early time behavior of spatial and momentum anisotropies in kinetic theory across different Knudsen numbers

We investigate the early time development of the anisotropic transverse flow and spatial eccentricities of a fireball with various particle-based transport approaches using a fixed initial condition. In numerical simulations ranging from the quasi-collisionless case to the hydrodynamic regime, we find that the onset of v_n and of related measures of anisotropic flow can be described with a simple power-law ansatz, with an exponent that depends on the amount of rescatterings in the system. In the few-rescatterings regime we perform semi-analytical calculations, based on a systematic expansion in powers of time and the cross section, which can reproduce the numerical findings.

Predictions and postdictions for relativistic lead and oxygen collisions with the computational simulation code Trajectum

We introduce a global analysis of relativistic heavy ion collisions using Trajectum of a significantly higher precision and including a new option to vary the normalization of the centrality estimator. We use the posterior distribution of our parameters to generate a set of high-statistics samples that allows us to make precise predictions including statistical and systematic uncertainties estimated from the model parameter distribution. The results are systematically compared with experiment whereby we also include many observables not included in the global analysis. This includes in particular (extremely) ultracentral anisotropic flow and mean transverse momentum, whereby we find satisfactory agreement with experiment where data are available. Lastly, we compute spectra and anisotropic flow for oxygen-oxygen collisions performed at the BNL Relativistic Heavy Ion Collider (RHIC) and to be performed at the the CERN Large Hadron Collider (LHC) and comment on how these collisions may inform us on properties of the quark-gluon plasma.

Anisotropic turbulence in relativistic plasmas

Signs of turbulence have been observed at the relativistic heavy ion collision at high collision energies. We study the signatures of turbulence in this system and find that there are significant departures from isotropic turbulence in the initial and the pre-equilibrium stages of the collision. As the anisotropic fluctuations are subleading to the isotropic fluctuations, the Kolmogorov spectrum can usually be obtained even for the initial stages. However, the energy spectrum and the temperature fluctuations indicate deviations from isotropic turbulence. Since a strong momentum anisotropy exists between the transverse and the longitudinal plane, we study the energy density spectrum in these two planes by slicing the sphere into different planes. The geometrical anisotropy is reflected in the anisotropic turbulence generated in the rotating plasma and we find that the scaling exponent is different in the two planes. We also obtain the temperature spectrum in the pre-equilibrium stages. The spectrum deviates from the Gaussian spectra expected for an isotropic turbulence. All these seem to indicate that the large scale momentum anisotropy persists in the smaller length scales for the relativistic heavy ion collisions.

Elliptic flow of charged particles at midrapidity relative to the spectator plane in Pb–Pb and Xe–Xe collisions

Measurements of the elliptic flow coefficient relative to the collision plane defined by the spectator neutrons v2{ΨSP} in collisions of Pb ions at center-of-mass energy per nucleon–nucleon pair sNN=2.76 TeV and Xe ions at sNN=5.44 TeV are reported. The results are presented for charged particles produced at midrapidity as a function of centrality and transverse momentum for the 5–70% and 0.2–6 GeV/c ranges, respectively. The ratio between v2{ΨSP} and the elliptic flow coefficient relative to the participant plane v2{4}, estimated using four-particle correlations, deviates by up to 20% from unity depending on centrality. This observation differs strongly from the magnitude of the corresponding eccentricity ratios predicted by the TRENTo and the elliptic power models of initial state fluctuations that are tuned to describe the participant plane anisotropies. The differences can be interpreted as a decorrelation of the neutron spectator plane and the reaction plane because of fragmentation of the remnants from the colliding nuclei, which points to an incompleteness of current models describing the initial state fluctuations. A significant transverse momentum dependence of the ratio v2{ΨSP}/v2{4} is observed in all but the most central collisions, which may help to understand whether momentum anisotropies at low and intermediate transverse momentum have a common origin in initial state fluctuations. The ratios of v2{ΨSP} and v2{4} to the corresponding initial state eccentricities for Xe–Xe and Pb–Pb collisions at similar initial entropy density show a difference of (7.0±0.9)% with an additional variation of +1.8% when including RHIC data in the TRENTo parameter extraction. These observations provide new experimental constraints for viscous effects in the hydrodynamic modeling of the expanding quark–gluon plasma produced in heavy-ion collisions at the LHC.

Prehydrodynamic evolution and its impact on quark-gluon plasma signatures

State-of-the-art hydrodynamic models of heavy-ion collisions have considerable theoretical model uncertainties in the description of the very early pre-hydrodynamic stage. We add a new computational module, K$_\mathrm{T}$Iso, that describes the pre-hydrodynamic evolution kinetically, based on the relativistic Boltzmann equation with collisions treated in the Isotropization Time Approximation. As a novelty, K$_\mathrm{T}$Iso allows for the inclusion and evolution of initial-state momentum anisotropies. To maintain computational efficiency K$_\mathrm{T}$Iso assumes strict longitudinal boost invariance and allows collisions to isotropize only the transverse momenta. We use it to explore the sensitivity of hadronic observables measured in relativistic heavy-ion collisions to initial-state momentum anisotropies and microscopic scattering during the pre-hydrodynamic stage.

Early time behavior of spatial and momentum anisotropies in a kinetic approach to nuclear collisions

We derive a general formula for the early time dependence of a phase space distribution evolving according to the kinetic Boltzmann equation. Assuming that the early evolution of the system created in high-energy nuclear collisions can be described by kinetic theory, we calculate the scaling behaviors for the onset of various characteristics of the transverse dynamics. In particular, we show that the scaling behavior of the anisotropic flow coefficients v_n at early times does not depend on the details of the collision kernel or the system composition, while at the same time it differs from the prediction of fluid dynamics.

Drag of heavy quarks in an anisotropic QCD medium beyond the static limit

Heavy quark dynamics in an anisotropic QCD medium have been analyzed within the Fokker-Planck approach. Heavy quark drag force and the momentum diffusion tensor have been decomposed by employing a general tensor basis for an anisotropic medium. Depending upon the relative orientation of the direction of the momentum anisotropy of the medium and heavy quark motion, two drag and four diffusion coefficients have been estimated in the anisotropic QCD medium. The relative significance of different components of drag and momentum diffusion coefficients has been explored. The dependence of the angle between the anisotropic vector and heavy quark motion to the drag and diffusion coefficients has also been studied. Furthermore, the energy loss of heavy quarks due to the elastic collisional process in an anisotropic medium has been studied. It is seen that the anisotropic contributions to heavy quark transport coefficients and its collisional energy loss have a strong dependence on the direction and strength of momentum anisotropy in the QCD medium.

Direct photons in hydrodynamic modeling of relativistic nuclear collisions

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 and prompt photons for comprehensive understanding of direct photon production.

Out-of-equilibrium photon production in the late stages of relativistic heavy-ion collisions

In this work, we assess the importance of nonequilibrium dynamics in the production of photons from the late stages of relativistic heavy-ion collisions. The ${p}_{\mathrm{T}}$-differential spectra and ${v}_{2}$ of photons from the late hadronic stage are computed within a nonequilibrium hadron transport approach, and compared to the results of a local equilibrium evolution using ideal relativistic hydrodynamics. It is found that nonequilibrium dynamics enhance the late-stage photon production at low ${p}_{\mathrm{T}}$ and decreases it at higher ${p}_{\mathrm{T}}$ compared to the estimate from hydrodynamics. This same comparison points to a significant increase in the momentum anisotropies of these photons due to nonequilibrium dynamics. Once combined with photons produced above the particlization temperature in the hydrodynamics evolution, the differences between the two approaches appear modest for the ${p}_{\mathrm{T}}$ differential spectra, but are clearly noticeable at low ${p}_{\mathrm{T}}$ for the elliptic flow: nonequilibrium dynamics enhance the photon ${v}_{2}$ below ${p}_{\mathrm{T}} \ensuremath{\approx}1.4$ GeV.

Saturation of the asymmetric current filamentation instability under conditions relevant to relativistic shock precursors

The current filamentation instability, which generically arises in the counterstreaming of plasma flows, is known for its ability to convert the free energy associated with anisotropic momentum distributions into kinetic-scale magnetic fields. The saturation of this instability has been extensively studied in symmetric configurations where the interpenetrating plasmas share the same properties (velocity, density, temperature). In many physical settings, however, the most common configuration is that of asymmetric plasma flows. For instance, the precursor of relativistic collisionless shock waves involves a hot, dilute beam of accelerated particles reflected at the shock front and a cold, dense inflowing background plasma. To determine the appropriate criterion for saturation in this case, we have performed large-scale two-dimensional particle-in-cell simulations of counterstreaming electron-positron pair and electron-ion plasmas. We show that, in interpenetrating pair plasmas, the relevant criterion is that of magnetic trapping as applied to the component (beam or plasma) that carries the larger inertia of the two; namely, the instability growth suddenly slows down once the quiver frequency of those particles equals or exceeds the instability growth rate. We present theoretical approximations for the saturation level. These findings remain valid for electron-ion plasmas provided that electrons and ions are close to equipartition in the plasma flow of larger inertia. Our results can be directly applied to the physics of relativistic, weakly magnetized shock waves, but they can also be generalized to other cases of study.

On transverse momentum broadening in real-time lattice simulations of the glasma and in the weak-field limit

In these proceedings, we report on our numerical lattice simulations of partons traversing the boost-invariant, non-perturbative glasma as created at the early stages of collisions at RHIC and LHC. Since these highly energetic partons are produced from hard scatterings during heavy-ion collisions, they are already affected by the first stage of the medium's time evolution, the glasma, which is the pre-equilibrium precursor state of the quark-gluon plasma. We find that partons quickly accumulate transverse momentum up to the saturation momentum during the glasma stage. Moreover, we observe an interesting anisotropy in transverse momentum broadening of partons with larger broadening in the rapidity than in the azimuthal direction. Its origin can be related to correlations among the longitudinal color-electric and color-magnetic flux tubes in the initial state of the glasma. We compare these observations to the semi-analytic results obtained by a weak-field approximation, where we also find such an anisotropy in a parton's transverse momentum broadening.

The effective complex heavy-quark potential in an anisotropic quark-gluon plasma

We introduce a method for reducing anisotropic heavy-quark potentials to isotropic potentials by using an effective screening mass that depends on the quantum numbers l and m of a given state. We demonstrate that, using the resulting 1D effective potential model, one can solve a 1D Schrödinger equation and reproduce the full 3D results for the energies and binding energies of low-lying heavy-quarkonium bound states to relatively high accuracy. This includes the splitting of different p-wave polarizations. The resulting 1D effective model provides a way to include momentum anisotropy effects in open quantum system simulations of heavy-quarkonium dynamics in the quark-gluon plasma.

Ab initio coupling of jets to collective flow in the opacity expansion approach

We calculate the leading corrections to jet momentum broadening and medium-induced branching that arise from the velocity of the moving medium at first order in opacity. These results advance our knowledge of jet quenching and demonstrate how it couples to collective flow of the quark-gluon plasma in heavy-ion collisions and to the orbital motion of partons in cold nuclear matter in deep inelastic scattering at the electron-ion collider. We also compute the leading corrections to jet momentum broadening due to transverse gradients of temperature and density. We find that these effects lead to both anisotropic transverse momentum diffusion proportional to the medium velocity and anisotropic medium-induced radiation emitted preferentially in the direction of the flow. We isolate the relevant sub-eikonal corrections by working with jets composed of scalar particles with arbitrary color factors interacting with the medium by scalar QCD. Appropriate substitution of the color factors and light-front wave functions allow us to immediately apply the results to a range of processes including $q \rightarrow q g$ branching in real QCD. The resulting general expressions can be directly coupled to hydrodynamic simulations on an event-by-event basis to study the correlations between jet quenching and the dynamics of various forms of nuclear matter.

Electromagnetic response of hot QCD medium in the presence of background time-varying fields

The response of the hot QCD medium in the presence of external time dependent electromagnetic fields has been studied within the relativistic Boltzmann transport theory. The impact of the time dependence of the electromagnetic fields and collisional aspects of the medium to the induced electric and Hall current densities has been explored. The non-equilibrium momentum distribution of degrees of freedom has been obtained in the presence of space-time varying electromagnetic fields. Further, the analysis has been extended to an anisotropic QCD medium while incorporating the in-medium interaction effects. It is observed that the electric charge transport is sensitive to the inhomogeneity of the fields and the momentum anisotropy of the QCD medium.

Trapping and migration of P-state atoms in rare gas solids: effect of angular momentum anisotropy for model O(3P) and C(3P) atoms

Classical simulations of model O(P) atom isolated in Ar, Kr and Xe crystals with the variable magnitude and sign of the angular momentum anisotropy are performed. The guest–host interaction anisotropy remarkably affects the structure of the atomic trapping sites and the barriers to the temperature-induced atomic mobility. For interstitial trapping, inversion of anisotropy induces a kind of critical phenomenon, which transforms the migration path saddle point to a minimum and another saddle. As a result, a new peculiar axially symmetric interstitial site is formed with the migration barrier reduced. Preliminary ab initio-based study of the C(P) atom, whose interactions with Ar, Kr and Xe have the anisotropy opposite to oxygen, fully confirms the model analysis. Our results emphasise profound effect of the angular momentum anisotropy on the structure and dynamics of the open-shell atoms at matrix isolation.

Non-flow effects in correlation between harmonic flow and transverse momentum in nuclear collisions

A large anti-correlation signal between elliptic flow v2 and average transverse momentum [pT] was recently measured in small collision systems, consistent with a final-state hydrodynamic response to the initial geometry. This negative v2–[pT] correlation was predicted to change to positive correlation for events with very small charged particle multiplicity Nch due to initial-state momentum anisotropies of the gluon saturation effects. However, the role of non-flow correlations is expected to be important in these systems, which is not yet studied. We estimate the non-flow effects in pp, pPb and peripheral PbPb collisions using Pythia and Hijing models, and compare them with the experimental data. We show that the non-flow effects are largely suppressed using the rapidity-separated subevent cumulant method (details of the cumulant framework are also provided). The magnitude of the residual non-flow is much less than the experimental observation in the higher Nch region, supporting the final-state response interpretation. In the very low Nch region, however, the sign and magnitude of the residual non-flow depend on the model details. Therefore, it is unclear at this moment whether the sign change of v2–[pT] can serve as evidence for initial state momentum anisotropies predicted by the gluon saturation.

Dependence on beam energy and nuclear equation of state of anisotropic flow and particle production in low-energy heavy-ion collisions

We analyze various flow coefficients of anisotropic momentum distribution of final state particles in mid-central ($b=5\text{--}9\phantom{\rule{0.16em}{0ex}}\mathrm{fm}$) $\mathrm{Au}\phantom{\rule{4pt}{0ex}}+\phantom{\rule{4pt}{0ex}}\mathrm{Au}$ collisions in the beam energy range ${E}_{\mathrm{Lab}}=1A\text{--}158A$ GeV. Different variants of the ultrarelativistic quantum molecular dynamics (UrQMD) model, namely the pure transport (cascade) mode and the hybrid mode, are employed for this investigation. In the hybrid UrQMD model, the ideal hydrodynamical evolution is integrated with the pure transport calculation for description of the evolution of the fireball. We opt for the different available equations of state (EoS) replicating the hadronic as well as partonic degrees of freedom together with possible phase transitions, viz., hadron gas, chiral $+$ deconfinement EoS, and bag model EoS, to investigate their effect on the properties of the final state particles. We also attempt to gain insights about the dynamics of the medium by studying different features of particle production such as particle ratios and net-proton rapidity distribution. The results and conclusions drawn here would be useful to understand the response of various observables to the underlying physics of the model as well as to make comparisons with the upcoming measurements of the future experiments at the Facility for Antiproton and Ion Research (FAIR) and the Nuclotron-based Ion Collider fAcility (NICA).

Tunneling in an anisotropic cubic Dirac semi-metal

Motivated by a recent first principles prediction of an anisotropic cubic Dirac semi-metal in a real material Tl(TeMo)3, we study the behavior of electrons tunneling through a potential barrier in such systems. To clearly investigate effects from different contributions to the Hamiltonian we study the model in various limits. First, in the limit of a very thin film material where the linearly dispersive z-direction is frozen out at zero momentum and the dispersion in the x–y plane is rotationally symmetric. In this limit we find a Klein tunneling reminiscent of what is observed in single layer graphene and linearly dispersive Dirac semi-metals. Second, an increase in thickness of the material leads to the possibility of a non-zero momentum eigenvalue kz that acts as an effective mass term in the Hamiltonian. We find that these lead to a suppression of Klein tunneling. Third, the inclusion of an anisotropy parameter λ≠1 leads to a breaking of rotational invariance. Furthermore, we observed that for different values of incident angle θ and anisotropy parameter λ the Hamiltonian supports different numbers of modes propagating to infinity. We display this effect in form of a diagram that is similar to a phase diagram of a distant detector. Fourth, we consider coexistence of both anisotropy and non-zero kz but do not find any effect that is unique to the interplay between non-zero momentum kz and anisotropy parameter λ. Last, we studied the case of a barrier that was placed in the linearly dispersive direction and found Klein tunneling T−1∝θ6+O(θ8) that is enhanced when compared to the Klein tunneling in linear Dirac semi-metals or graphene where T−1∝θ2+O(θ4).