The observation of jet quenching and associated away--side Mach cone--like correlations at RHIC provide powerful ``external'' probes of the sQGP produced in A+A reactions, but it simultaneously raises the question where the jet energy was deposited. The nearly perfect bulk fluidity observed via elliptic flow suggests that Mach cone--like correlations may also be due to rapid local equilibration in the wake of penetrating jets. Multi-particle correlations lend further support to this possibility. However, a combined study of energy deposition and fluid response is needed. We solve numerically 3--dimensional ideal hydrodynamical equations to compute the flow correlation patterns resulting from a variety of possible energy-momentum deposition models. Mach--cone correlations are shown to depend critically on the energy and momentum deposition mechanisms. They only survive for a special limited class of energy--momentum loss models, which assume significantly less longitudinal momentum loss than energy loss per unit length. We conclude that the correct interpretation of away--side jet correlations will require improved understanding and independent experimental constraints on the jet energy--momentum loss to fluid couplings.
This letter is based on a kinetic theory approach to anisotropic hydrodynamics. We derive the sound wave equation in anisotropic hydrodynamics and show that a corresponding wave front is ellipsoidal. The phenomenon of Mach cone emission in anisotropic hydrodynamics is studied. It is shown that Mach cone in anisotropic case becomes asymmetric, i. e. in this limit they're two different angles, left and right with respect to the ultrasonic particle direction, which are determined by the direction of ultrasonic particle propagation and the asymmetry coefficient.
The first 3D calculation of shock wave propagation in a homogeneous QGP has been performed within the new formulation of relativistic dissipative hydrodynamics which preserves the causality. We found that the relaxation time plays an important role and also affects the angle of Mach cone.
We derive the space-time distribution of energy and momentum deposited by a fast parton traversing a weakly coupled quark-gluon plasma by treating the fast part on as the source of an external color field perturbing the medium. We then use our result as a source term for the linearized hydrodynamical equations of the medium. We show that the solution contains a sonic Mach cone and a dissipative wake if the parton moves at a supersonic speed.
Energy and momentum lost by hard jets propagating through hot and dense nuclear matter have to be redistributed in the medium. It has been conjectured that collective sound modes are excited. Those lead to Mach cone nuclear shock waves in the nuclear medium that are shown to account for three and four particle angular correlation structures of hadrons with a (semi-)hard trigger hadron in heavy-ion collisions at RHIC.
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…
Employing a microscopic transport model we investigate the evolution of high energetic jets moving through a viscous medium. For the scenario of an unstoppable jet we observe a clearly strong collective behavior for a low dissipative system $η/s \approx 0.005$, leading to the observation of cone-like structures. Increasing the dissipation of the system to $η/s \approx 0.32$ the Mach Cone structure vanishes. Furthermore, we investigate jet-associated particle correlations. A double-peak structure, as observed in experimental data, is even for low-dissipative systems not supported, because of th…
By studying the Euclidean partition function on a cone, we argue that pure and mixed gravitational anomalies generate a "Casimir momentum" which manifests itself as parity violating coefficients in the hydrodynamic stress tensor and charge current. The coefficients generated by these anomalies enter at a lower order in the hydrodynamic gradient expansion than would be naively expected. In 1+1 dimensions, the gravitational anomaly affects coefficients at zeroth order in the gradient expansion. The mixed anomaly in 3+1 dimensions controls the value of coefficients at first order in the gradient …
To investigate the formation and the propagation of relativistic shock waves in viscous gluon matter we solve the relativistic Riemann problem using a microscopic parton cascade. We demonstrate the transition from ideal to viscous shock waves by varying the shear viscosity to entropy density ratio $η/s$. Furthermore we compare our results with those obtained by solving the relativistic causal dissipative fluid equations of Israel and Stewart (IS), in order to show the validity of the IS hydrodynamics. Employing the parton cascade we also investigate the formation of Mach shocks induced by a hi…
The experimental azimuthal dihadron distributions at RHIC show a double peak structure in the away side ($Δϕ= π\pm 1.2$ rad.) for intermediate $p_t$ particles. A variety of models have appeared trying to describe this modification. We will review most of them, with special emphasis in the Conical Flow scenario in which the observed shape is a consequence of the emission of sound by a supersonic high momentum particle propagating in the Quark Gluon Plasma.
Fast thermalization and a strong build up of elliptic flow of QCD matter were investigated within the pQCD based 3+1 dimensional parton transport model BAMPS including bremsstrahlung $2 \leftrightarrow 3$ processes. Within the same framework quenching of gluonic jets in Au+Au collisions at RHIC can be understood. The development of conical structure by gluonic jets is investigated in a static box for the regimes of small and large dissipation. Furthermore we demonstrate two different approaches to extract the shear viscosity coefficient $η$ from a microscopical picture.
Particle correlation measurements associated with a hard or semi-hard trigger in heavy-ion collisions may reflect Mach cone shockwaves excited in the bulk medium by partonic energy loss. This is of great interest because, when compared with theory, such measurements can provide information on the transport properties of the medium. Specifically, the formation of Mach cone shockwaves is sensitive to the viscosity and speed of sound, as well as the detailed nature of the jet medium interaction. However, modeling the physics of shockwave excitation to obtain a meaningful comparison with the measu…
We compare away-side hadron correlations with respect to tagged heavy quark jets computed within a weakly coupled pQCD and a strongly coupled AdS/CFT model. While both models feature similar far zone Mach and diffusion wakes, the far zone stress features are shown to be too weak to survive thermal broadening at hadron freeze-out. Observable away-side conical correlations are dominated by the jet-induced transverse flow in near zone "Neck" region, which differs significantly for both models. Unlike in AdS/CFT, the induced transverse flow in the Neck zone is too weak in pQCD to produce conical c…
We investigate in a microscopical transport model the evolution of conical structures originating from the supersonic projectile moving through the matter of ultrarelativistic particles. Using different scenarios for the interaction between projectile and matter, and different transport properties of the matter, we study the formation and structure of Mach cones. Furthermore, the two-particle correlations for different viscosities are extracted from the numerical calculations and we compare them to an analytical approximation. In addition, by adjusting he cross section we investigate the influ…
The formation of Mach cones is studied in a full $(3+1)$-dimensional setup of ultrarelativistic heavy-ion collisions, considering a transverse and longitudinal expanding medium at Relativistic Heavy-Ion Collider energies. For smooth initial conditions and central collisions the jet-medium interaction is investigated using high-energy jets and various values of the ratio of shear viscosity over entropy density, $η/s$. For small viscosities, the formation of Mach cones is proven, whereas for larger viscosities the characteristic structures smear out and vanish eventually. The formation of a doub…
The pattern of angular correlations of hadrons with a (semi-)hard trigger hadron in heavy-ion collisions has attracted considerable interest. In particular, unexpected large angle structures on the away side (opposite to the trigger) have been found. Several explanations have been brought forward, among them Mach shockwaves and Cherenkov radiation. Most of these scenarios are characterized by radial symmetry around the parton axis, thus angular correlations also determine the rapidity dependence of the correlation. If the observed correlations are remnants of an away side parton after interact…
The energy loss of a hard parton is regarded as a useful tool to probe properties of a soft medium. However, the information obtained by a measurement of the nuclear suppression R_AA is not very sensitive to medium properties. Thus, more differential observables are needed. Here we focus on the pattern of angular correlation of hadrons associated with a hard trigger. These show rich pattern when going from low p_T to high p_T associate momentum. At low p_T, the pattern of associate hadrons can be understood in terms of Mach shocks excited by the energy lost from the away side parton while the …
Using a microscopic transport model we investigate the evolution of conical structures originating from the supersonic projectile moving through the hot matter of ultrarelativistic particles. Using different scenarios for the interaction between projectile and matter, and different transport properties of the matter, we study the formation and structure of Mach cones. Especially, a dependence of the Mach cone angle on the details and rate of the energy deposition from projectile to the matter is investigated. Furthermore, the two-particle correlations extracted from the numerical calculations …
Fast thermalization and a strong buildup of elliptic flow of QCD matter as found at RHIC are understood as the consequence of perturbative QCD (pQCD) interactions within the 3+1 dimensional parton cascade BAMPS. The main contributions stem from pQCD bremsstrahlung $2 \leftrightarrow 3 $ processes. By comparing to Au+Au data of the flow parameter $v_2$ the shear viscosity to entropy ratio $η/s$ has been extracted dynamically and lies in the range of 0.08 and 0.2. Also jet-quenching has been investigated consistently within a full dynamical picture of the heavy ion collision. The results for glu…
In a framework of a multi-phase transport model with both partonic and hadronic interactions, azimuthal correlations between trigger particles and associated scattering particles in Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV/$c$ have been studied by the mixing-event technique. The Mach-like structure has been observed in correlation function for central collisions. It is shown that the Mach-like structure is basically born in the partonic process and further developed in hadronic rescattering process. However, hadronic rescattering alone cannot reproduce the amplitude of Mach-like cone on…
The energy and momentum lost by a hard parton propagating through hot and dense matter has to be redistributed in the nuclear medium. Apart from heating the medium, there is the possibility that collective modes are excited. We outline a formalism that can be used to track the propagation of such a mode through the evolving medium if its dispersion relation is known. Under the assumption that a sound wave is created, we track the jet energy loss as a function of spacetime and follow the resulting mach cone throughout the fireball evolution.We compare with the angular correlation pattern of har…
MMedium excitation by jet shower propagation inside a quark-gluon plasma is studied within a linear Boltzmann transport and a multiphase transport model. Contrary to the naive expectation, it is the deflection of both the jet shower and the Mach-cone-like excitation in an expanding medium that is found to gives rise to a double-peak azimuthal particle distribution with respect to the initial jet direction. Such deflection is the strongest for hadron-triggered jets which are often produced close to the surface of dense medium due to trigger-bias and travel against or tangential to the radial fl…
We study the energy-momentum deposited by fast moving partons within a medium using linearized viscous hydrodynamics. The particle distribution produced by this energy-momentum is computed using the Cooper-Frye formalism. We show that for the conditions arising in heavy-ion collisions, energy momentum is preferentially deposited along the head shock of the fast moving partons. We also show that the double hump in the away-side of azimuthal correlations can be produced by two (instead of one) away-side partons that deposit their energy-momentum along their directions of motion. These partons ar…
We compute the energy and momentum deposited by a fast moving parton in a quark-gluon plasma using linear viscous hydrodynamics with an energy loss per unit length profile proportional to the path length and with different values of the shear viscosity to entropy density ratio. We show that when varying these parameters, the transverse modes still dominate over the longitudinal ones and thus energy and momentum is preferentially deposited along the head-shock, as in the case of a constant energy loss per unit length profile and the lowest value for the shear viscosity to entropy density ratio.
Within the AMPT Monte Carlo model, hot spots in the initial transverse parton density are shown to lead to harmonic flows which all contribute to dihadron azimuthal correlation. The net back-to-back dihadron correlation after subtraction of harmonic flows still has a double-peak that is independent of the initial geometric triangularity at a fixed impact-parameter and unique to the structure of jet-induced Mach cone and expanding hot spots dragged by radial flow. The longitudinal structure of hot spots also leads to a near-side ridge in dihadron correlation with a large rapidity gap. By succes…
A 1+1 dimensional hydrodynamical model in the light-cone coordinates is used to describe central heavy-ion collisions at ultrarelativistic bombarding energies. Deviations from Bjorken's scaling are taken into account by choosing finite-size profiles for the initial energy density. The sensitivity of fluid dynamical evolution to the equation of state and the parameters of initial state is investigated. Experimental constraints on the total energy of produced particles are used to reduce the number of model parameters. Spectra of secondary particles are calculated assuming that the transition fr…
We study the nuclear modifications of full jets and their structures in relativistic heavy-ion collisions including the effect of hydrodynamic medium response to jet quenching. To study the evolutions of the full jet shower and the traversed medium with energy and momentum exchanges between them, we formulate a coupled jet-fluid model consisting of a set of jet transport equations and relativistic hydrodynamics equations with source terms. In our model, the full jet shower interacts with the medium and gets modified via collisional and radiative processes during the propagation. Meanwhile, the…
In the framework of a multi-phase transport model (AMPT) with both partonic and hadronic interactions, azimuthal correlations between trigger particles and associated scattering particles have been studied by the mixing-event technique. The momentum ranges of these particles are $3< p^{trig}_T< 6$ GeV/$c$ and $0.15< p_{T}^{assoc} < 3$ GeV/$c$ (soft), or $2.5<p^{trig}_T<$ 4 GeV/$c$ and $1< p_{T}^{assoc} < 2.5$ GeV/$c$ (hard) in Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. A Mach-like structure has been observed in correlation functions for central collisions. By comparing scenarios with and…
I use the space-time distribution of energy and momentum deposited by a fast parton traversing a perturbative quark-gluon plasma as a source term for the linearized hydrodynamical equations of the medium. A method of solution for the medium response is presented in detail. Numerical results are given for different values of the shear viscosity to entropy density ratio, $η/s$, and speed of sound, $c_s$. Furthermore, I investigate the relevance of finite source structure by expanding the source term up to first order in gradients of a $δ$ function centered at the fast parton and comparing the re…
We study the interaction of a fast moving particle in the Quark Gluon Plasma with linearized hydrodynamics. We derive the linearized hydrodynamic equations on top of an expanding fireball, and detail the solutions for a static medium. There are two modes far from the jet -- a sound mode and a diffusion mode. The diffusion mode is localized in a narrow wake behind the jet while the sound mode propagates at the Mach angle, $\cos(θ_M) = c_s/c$. A general argument shows that the strength of the diffusion mode relative to the sound mode is directly proportional to the entropy produced by the jet-me…
The strong suppression of high-$p_T$ jets in heavy ion collisions is a result of elastic and inelastic energy loss suffered by the jet multi-prong collection of color charges that are resolved by medium interactions. Hence, quenching effects depend on the fluctuations of the jet substructure that are probed by the cone size dependence of the spectrum. In this letter, we present the first complete, analytic calculation of the inclusive $R$-dependent jet spectrum in PbPb collisions at LHC energies, including resummation of energy loss effects from hard, vacuum-like emissions occurring in the med…
The purpose of this paper is twofold. Firstly, we study the dynamical density fluctuations around the critical point(CP) of Quantum Chromodynamics(QCD) using dissipative relativistic fluid dynamics in which the coupling of the density fluctuations to those of other conserved quantities is taken into account. We show that the sound mode which is directly coupled to the mechanical density fluctuation is attenuated and in turn the thermal mode becomes the genuine soft mode at the QCD CP. We give a speculation on the possible fate of a Mach cone in the vicinity of the QCD CP as a signal of the exi…
The heavy quark energy loss puzzle is explained by collective flow effects in a dynamic medium. The dead cone and LPM effect are found to be changed comparing to the static medium case. Instead of only one dead cone in the static medium, the collective flow induces two dead cones from two different kinds of processes. One is from the projectile emitting gluon process, the same as that in the static medium. The other is from the gluon emission off the exchanged gluon process, decreasing with increasing flow velocity $v_z$ along jet direction, which lead to the increase of heavy quark energy los…
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…
