In a series of previous papers, we have presented a new approach, based on perturbative QCD, for the evolution of a jet in a dense quark-gluon plasma. In the original formulation, the plasma was assumed to be homogeneous and static. In this work, we extend our description and its Monte Carlo implementation to a plasma obeying Bjorken longitudinal expansion. Our key observation is that the factorisation between vacuum-like and medium-induced emissions, derived in the static case, still holds for an expanding medium, albeit with modified rates for medium-induced emissions and transverse momentum broadening, and with a modified phase-space for vacuum-like emissions. We highlight a scaling relation valid for the energy spectrum of medium-induced emissions, through which the case of an expanding medium is mapped onto an effective static medium. We find that scaling violations due to vacuum-like emissions and transverse momentum broadening are numerically small. Our new predictions for the nuclear modification factor for jets $R_{AA}$, the in-medium fragmentation functions, and substructure distributions are very similar to our previous estimates for a static medium, maintaining the overall good qualitative agreement with existing LHC measurements. In the case of $R_{AA}$, we find that the agreement with the data is significantly improved at large transverse momenta $p_T\gtrsim 500$ GeV after including the effects of the nuclear parton distribution functions.
We use kinetic theory in order to study the role of quantum fluctuations in the isotropization of the pressure tensor in a system subject to fast longitudinal expansion, such as the matter produced in the early stages of a heavy ion collision.
Bose-Einstein correlations and momentum distributions are calculated for longitudinally expanding systems, like jets or high energy heavy ion collisions with light projectiles. The expansion generates a thermal length-scale in the longitudinal direction, and the geometrical length-scale is also finite. The Bose-Einstein correlation functions are dominated by the smaller while the invariant momentum distribution by the longer of the two longitudinal length-scales.
We report on the discovery of new analytical solutions of the equations of relativistic ideal hydrodynamics. In this solution, the fluid expands in the longitudinal direction and contains a plateau structure that extends over a finite range in rapidity and can be either symmetric or asymmetric in that variable. We further calculate the corresponding pseudo-rapidity distribution of hadron yields, and find decent agreement with experimental measurements in high-energy Pb+Pb, Au+Au, p+Pb, and d+Au collisions.
A simple kinematical argument suggests that the classical approximation may be inadequate to describe the evolution of a system with an anisotropic particle distribution. In order to verify this quantitatively, we study the Boltzmann equation for a longitudinally expanding system of scalar particles interacting with a $ϕ^4$ coupling, that mimics the kinematics of a heavy ion collision at very high energy. We consider only elastic $2\to 2$ scatterings, and we allow the formation of a Bose-Einstein condensate in overpopulated situations by solving the coupled equations for the particle distribut…
We present new, exact, finite solutions of relativistic hydrodynamics for longitudinally expanding fireballs for arbitrary constant value of the speed of sound. These new solutions generalize earlier, longitudinally finite, exact solutions, from an unrealistic to a reasonable equation of state, characterized by a temperature independent (average) value of the speed of sound. Observables like the rapidity density and the pseudorapidity density are evaluated analytically, resulting in simple and easy to fit formulae that can be matched to the high energy proton-proton and heavy ion collision dat…
We study the dihadron fragmentation functions (DiFF) of longitudinally polarized quarks into pion pairs. The quark-jet framework is used to model the sequential hadronization of a polarized quark into hadrons, where the polarization transfer to the remnant quark in each hadron emission step is calculated using the spin density matrix formalism. Using Monte Carlo (MC) simulations of the hadronization process, we find a nonvanishing helicity dependent DiFF, $G_1^\perp$ , which is also related to the longitudinal jet handedness. A method is developed for extracting the angular moments of this DiF…
In Phys. Rev. Lett. 114 (2015) 6, 061601, we reported on a new universality class for longitudinally expanding systems, encompassing strongly correlated non-Abelian plasmas and $N$-component self-interacting scalar field theories. Using classical-statistical methods, we showed that these systems share the same self-similar scaling properties for a wide range of momenta in a limit where particles are weakly coupled but their occupancy is high. Here we significantly expand on our previous work and delineate two further self-similar regimes. One of these occurs in the deep infrared (IR) regime of…
We use the Hamiltonian formulation of kinetic theory to perform a stability analysis of non-thermal fixed points in a non-Abelian plasma. We construct a perturbative expansion of the Fokker-Planck collision kernel in an adiabatic approximation and show that the (next-to-)leading order solutions reproduce the known non-thermal fixed point scaling exponents. Working at next-to-leading order, we derive the stability equations for scaling exponents and find the relaxation rate to the non-thermal fixed point. This approach provides the basis for an understanding of the prescaling phenomena observed…
In two previous works [arXiv:1009.4363,arXiv:1107.0668], we studied the time evolution of a system of real scalar fields with quartic coupling which shares important features with the Color Glass Condensate description of heavy ion collisions. Our primary objective was to understand how such a system, when initialized with a non-perturbatively large classical field configuration, reaches thermal equilibrium. An essential goal of these works was to highlight the role played by the quantum fluctuations. However, these studies considered only a system confined within a box of fixed volume. In the…
We investigate the possible thermalization process of the highly occupied and weakly coupled Yang-Mills fields expanding along the beam axis through an evaluation of the entropy, particle number, and pressure anisotropy. The time evolution of the system is calculated by solving the equation of motion for the Wigner function in the semiclassical approximation with initial conditions mimicking the glasma. For the evaluation of the entropy, we adopt the Husimi-Wehrl (HW) entropy, which is obtained by using the Husimi function, a positive semidefinite quantum distribution function given by smearin…
We present real-time lattice simulation results for nonequilibrium quark production from an over-occupied gluon plasma in longitudinally expanding geometry. The quark number density per unit transverse area and rapidity shows almost linear growth in time, and its growth rate appears to be consistent with a simple kinetic theory estimate involving only two-to-two scattering processes in small-angle approximation. We also find that quarks produced at early times satisfy a nonequilibrium scaling law.
We calculate the production of large mass dileptons from the jet-dilepton conversion in the expanding quark-gluon plasma at Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) energies. The jet-dilepton conversion exceeds the thermal dilepton production and Drell-Yan process in the large mass region of 3.9 GeV$<M<$5.8 GeV and 6.3 GeV$<M<$8.7 GeV in central Pb+Pb collisions at $\sqrt{s_{NN}}$=2.76 TeV and 5.5 TeV, respectively. We present the numerical solution of ideal fluid hydrodynamics. We find that the transverse flow leads to a rapid cooling of the fire ball. The suppre…
In this paper we study the performance in $e^+e^-$ collisions of classical $e^+e^-$ jet reconstruction algorithms, longitudinally invariant algorithms and the recently-proposed Valencia algorithm. The study includes a comparison of perturbative and non-perturbative jet energy corrections and the response under realistic background conditions. Several algorithms are benchmarked with a detailed detector simulation at $\sqrt{s}= 3$~\tev. We find that the classical $e^+e^-$ algorithms, with or without beam jets, have the best response, but are inadequate in environments with non-negligible backgro…
The diffusion wake accompanying the jet-induced Mach cone provides a unique probe of the properties of quark-gluon plasma in high-energy heavy-ion collisions. It can be characterized by a depletion of soft hadrons in the opposite direction of the propagating jet. We explore the 3D structure of the diffusion wake induced by $γ$-triggered jets in Pb+Pb collisions at the LHC energy within the coupled linear Boltzmann transport and hydro model. We identify a valley structure caused by the diffusion wake on top of a ridge from the initial multiple parton interaction (MPI) in jet-hadron correlation …
We study the (3+1)-dimensional evolution of non-Abelian plasma instabilities in the presence of a longitudinally expanding background of hard particles using the discretized hard loop framework. The free streaming background dynamically generates a momentum-space anisotropic distribution which is unstable to the rapid growth of chromomagnetic and chromoelectric fields. These fields produce longitudinal pressure that works to isotropize the system. Extrapolating our results to energies probed in ultrarelativistic heavy-ion collisions we find, however, that a pressure anisotropy persists for a f…
We perform real-time lattice simulations of nonequilibrium quark production in the longitudinally expanding QCD plasma. Starting from a highly occupied gluonic state with vacuum quark sector, we extract the time evolution of quark and gluon number densities per unit transverse area and rapidity. The total quark number shows after an initial rapid increase an almost linear growth with time. Remarkably, this growth rate appears to be consistent with a simple kinetic theory estimate involving only two-to-two scattering processes in small-angle approximation. This extends previous findings about t…
We study the transport dynamics of momenta deposited from jets in ultrarelativistic heavy-ion collisions. Assuming that the high-energy partons traverse expanding quark-gluon fluids and are subject to lose their energy and momentum, we simulate dijet asymmetric events by solving relativistic hydrodynamic equations numerically without linearization in the fully (3+1)-dimensional coordinate. Mach cones are formed and strongly broadened by radial flow of the background medium. As a result, the yield of low-$p_{T}$ particles increases at large angles from the jet axis and compensates the dijet mom…
The gluon radiation induced by multiple scattering of a hard parton in expanding quark-gluon plasma is investigated. The radiative energy loss of hard parton jet is shown to decrease considerably when angular size of extracted jet goes up, but the fraction of loss survives even for the reasonable wide cone of angles due to the coherent effects taking into account the rescattering of the radiated gluons in the QCD medium. The possible application to the jet quenching phenomenon in heavy ion collisions at LHC energies is discussed.
Comprehensive understanding of medium-induced radiative energy loss is of a paramount importance in describing observed jet quenching in heavy-ion collisions. In this work, we have calculated the medium-modified gluon splitting rates for different profiles of the expanding partonic medium, namely profiles for static, exponential, and Bjorken expanding medium. Here in this study, we have used the Baier-Dokshitzer-Mueller-Peigne-Schiff-Zakharov (BDMPSZ) formalism for multiple soft scatterings with a time-dependent transport coefficient for characterizing the expanding medium. Using the kinetic r…
We study analytically the medium-induced energy loss of a high energy parton passing through a finite size QCD plasma, which is expanding longitudinally according to Bjorken's model. We extend the BDMPS formalism already applied to static media to the case of a quark which hits successive layers of matter of decreasing temperature, and we show that the resulting radiative energy loss can be as large as 6 times the corresponding one in a static plasma at the reference temperature $T = T (L)$, which is reached after the quark propagates a distance $L$.
We reexamine the scenario of homogeneous nucleation of the quark-gluon plasma produced in ultra-relativistic heavy ion collisions. A generalization of the standard nucleation theory to rapidly expanding system is proposed. The nucleation rate is derived via the new scaling parameter $λ_Z$. It is shown that the size distribution of hadronic clusters plays an important role in the dynamics of the phase transition. The longitudinally expanding system is supercooled to about 3-6%, then it is reheated, and the hadronization is completed within 6-10 fm/c, i.e. 5-10 times faster than it was estimated…
We use the holographic principle to study quark jets with trailing strings in an expanding plasma that asymptotes Bjorken hydrodynamics. We make use of the fact that the trailing string is the locus of the light delay in bulk to obtain the explicit form for quark jets in the expanding plasma. From the trailing string solution we calculate the drag coefficient of a heavy quark in the strongly coupled expanding plasma. The energy scaling of the maximum penetration length of an ultrarelativistic light quark jet using light rays in bulk is estimated.
Using the Janik-Peschanski dual to a Bjorken flow, a Langevin equation is derived for a heavy quark in an expanding N = 4 supersymmetric Yang-Mills plasma. Such a plasma is characterized by a proper-time dependence of the temperature and corresponds to a system out of equilibrium. The analysis first focuses on a quark at rest in the plasma comoving frame. The case of a quark moving across a longitudinally expanding plasma is then considered. The two-point functions for the random noise acting on such heavy quark probes are computed.
We present a study of the impact of the expansion of deconfined medium on single-gluon emission spectra and the jet suppression factor ($Q_{AA}$) within the BDMPS-Z formalism. These quantities are calculated for three types of media (static medium, exponentially decaying medium and Bjorken expanding medium). The distribution of medium-induced gluons and the jet $Q_{AA}$ are calculated using the evaluation of in-medium evolution with splitting kernels derived from the gluon emission spectra. Scaling behavior of splitting kernels is derived for low-x and high-x regimes in the asymptote of large …
Going beyond the simplified gluonic cascades, we introduce both gluon and quark degrees of freedom for partonic cascades inside the medium. We then solve the set of coupled evolution equations numerically with splitting kernels calculated for static, exponential, and Bjorken expanding media to arrive at medium-modified parton spectra for quark and gluon initiated jets. Using these, we calculate the inclusive jet $R_{AA}$ where the phenomenologically driven combinations of quark and gluon jet fractions are included. Then, the rapidity dependence of the jet $R_{AA}$ is examined. We also study th…
We present a new definition of the jet quenching parameter $\hat{q}$ in a weakly-coupled quark-gluon plasma undergoing boost-invariant longitudinal expansion. We propose a boost-invariant definition of $\hat{q}$, which is proportional to the broadening of the angular variables $η$ (the pseudo-rapidity) and $ϕ$ (the azimuthal angle). We furthermore consider radiative corrections to $\hat{q}$ and find potentially large corrections enhanced by a double logarithm like the case of a static medium. But unlike for the static medium, these corrections are now local in (proper) time.
We study Mach shocks generated by fast partonic jets propagating through a deconfined strongly-interacting matter. Our main goal is to take into account different types of collective motion during the formation and evolution of this matter. We predict a significant deformation of Mach shocks in central Au+Au collisions at RHIC and LHC energies as compared to the case of jet propagation in a static medium. The observed broadening of the near-side two-particle correlations in pseudorapidity space is explained by the Bjorken-like longitudinal expansion. Three-particle correlation measurements are…
We study the phenomenon of transverse momentum broadening for a high-$p_T$ parton propagating through a weakly-coupled quark-gluon plasma undergoing boost-invariant longitudinal expansion. We propose a boost-invariant description for this phenomenon, in which the broadening refers to the angular variables $η$ (the pseudo-rapidity) and $ϕ$ (the azimuthal angle). The jet quenching parameter $\hat{q}$ which enters this description depends upon the proper time alone. We furthermore consider radiative corrections to $\hat q$. As in the case of a static medium, we find potentially large corrections …
We study the hydrodynamic response to jet quenching in expanding quark-gluon plasma (QGP) and its signal in the resulting particle distribution. The ideal hydrodynamic simulations of the $γ$-jet events in heavy-ion collisions are performed in a full (3 + 1)-dimensional setup. The jet-induced Mach cone and the radial expansion of the background mutually push and distort each other. As a result, the particle emission is suppressed in the direction in which the radial flow is pushed back by the Mach cone when the jet path is an off-central one. This is the direct signal of hydrodynamic response t…
In this work, we introduce both gluon and quark degrees of freedom for describing the partonic cascades inside the medium. We present numerical solutions for the set of coupled evolution equations with splitting kernels calculated for the static, exponential and Bjorken expanding media to arrive at medium-modified parton spectra for quark and gluon initiated jets respectively. We discuss novel scaling features of the partonic spectra between different types of media. Next, we study the inclusive jet $R_{AA}$ by including phenomenologically driven combinations of quark and gluon fractions insid…
Non-Abelian plasma instabilities play a crucial role in the nonequilibrium dynamics of a weakly coupled quark-gluon plasma and they importantly modify the standard perturbative bottom-up thermalization scenario in heavy-ion collisions. Using the auxiliary-field formulation of the hard-loop effective theory, we study numerically the real time evolution of instabilities in an anisotropic collisionless Yang-Mills plasma expanding longitudinally in free streaming. In this first real-time lattice simulation we consider the most unstable modes, long-wavelength coherent color fields that are constant…
We study dynamics of a QGP fluid induced by energetic partons propagating through it. We construct a (3+1)-dimensional QGP-fluid+Jet model. When a jet traverses a uniform fluid, it induces a Mach cone structure of energy density distribution and a vortex ring surrounding a path of the jet. When a pair of jets travels through a radially expanding fluid, low momentum particles are dominantly induced at large angles from the quenched jet. This result is qualitatively consistent with observation of the CMS Collaboration at LHC.
Direct photon production from a longitudinally expanding quark-gluon plasma (QGP) at Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) energies is studied with a real-time kinetic description that is consistently incorporated with hydrodynamics. Within Bjorken's hydrodynamical model, energy nonconserving (anti)quark bremsstrahlung q(\bar{q})\to q(\bar{q})γand quark-antiquark annihilation q\bar{q}\to γare shown to be the dominant nonequilibrium effects during the transient lifetime of the QGP. For central collisions we find a significant excess of direct photons in the rang…
We use a set of simple angular moments to solve the Boltzmann equation in the relaxation time approximation for a boost invariant longitudinally expanding gluonic plasma. The transition from the free streaming regime at early time to the hydrodynamic regime at late time is well captured by the first two-moments, corresponding to the monopole and quadrupole components of the momentum distribution, or equivalently to the energy density and the difference between the longitudinal and the transverse pressures. We relate this property to the existence of fixed points in the infinite hierarchy of eq…
Detailed insight into the interplay between parton energy loss and the way deconfined medium created in heavy-ion collisions expands is of great importance for improving the understanding of the jet quenching phenomenon. In this paper we study the impact of the expansion of deconfined medium on the single-gluon emission spectrum, its resummation and the jet suppression factor ($Q_{AA}$) within the BDMPS-Z formalism. We calculate these quantities for three types of expansion scenarios, namely static, exponentially decaying and Bjorken expanding media. The distribution of medium-induced gluons i…
EPOS3-Jet is an integrated framework for jet modelling in heavy ion collisions, where the initial hard (jet) partons are produced along with soft (medium) partons in the initial state EPOS approach. The jet partons then propagate in the hydrodynamically expanding medium. The energy and momentum lost by the jet partons is added to the hydrodynamic medium via the source terms. The full evolution proceeds in a concurrent mode, without separating hydrodynamic and jet parts. In this report, we examine the medium recoil effects in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV LHC energy in the EP…
We report the evolution effects on jet energy loss with detailed balance. The initial conditions and parton evolution based on perturbative QCD in the chemical non-equilibrated medium and Bjorken expanding medium at RHIC are determined. The parton evolution affect the jet energy loss evidently. This will increase the energy and propagating distance dependence of the parton energy loss and will affect the shape of suppression of moderately high P_{T} hadron spectra.
Recent data on the azimuthal and transverse momentum dependence of high-pT>10 GeV pion nuclear modification factors in nuclear collisions at RHIC/BNL and LHC/CERN are analyzed in terms of a wide class of jet-energy loss models and a variety of transverse expanding collective flow backgrounds. RHIC data at 200 AGeV are found to be surprisingly consistent with rather different dE/dx models when coupled to recent 2+1D minimally viscous QGP flow field predictions. However, extrapolations to LHC, with parameters fixed at RHIC, favor running coupling QCD based energy-loss models over fixed coupling …
The plasma of quarks and gluons created in ultrarelativistic heavy-ion collisions turns out to be paramagnetic. In the presence of a background magnetic field, this paramagnetism thus leads to a pressure anisotropy, similar to anisotropies appearing in a viscous fluid. In the present paper, we use this analogy, and develop a framework similar to anisotropic hydrodynamics, to take the pressure anisotropy caused, in particular, by the nonvanishing magnetization of a plasma of quarks and gluons into account. We consider the first two moments of the classical Boltzmann equation in the presence of …
We show that partons traversing a quark-gluon plasma can lose substantial amounts of energy also by scatterings, and not only through medium-induced radiation as mainly considered previously. Results from Monte Carlo simulations of soft interactions of partons, emerging from a hard scattering, through multiple elastic scatterings on gluons in an expanding relativistic plasma show a sizeable jet quenching which can account for a substantial part of the effect observed in RHIC data.
We consider synchrotron-like radiation in QCD by generalizing Schwinger's treatment of quantum synchrotron radiation in QED to the case of a constant chromomagnetic field. We suggest a novel mechanism for {\em jet quenching} in heavy ion collisions, whereby high-$p_t$ partons get depleted through strong (classical) color fields. The latters are encountered in the color glass condensate or in the form of expanding shells of exploding sphalerons. Unlike bremsstrahlung radiation through multiple soft rescattering, synchrotron radiation converts a jet into a wide shower of soft gluons. We estimate…
