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Register a new userTransition From Ideal To Viscous Mach Cones In A Kinetic Transport Approach
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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 are compared to an analytical approximation. We find that the propagation of a high energetic particle through the matter does not lead to the appearance of a double peak structure as observed in the ultrarelativistic heavy-ion collision experiments. The reason is the strongly forward-peaked energy and momentum deposition in the head shock region. In addition, by adjusting the cross section we investigate the influence of the viscosity to the structure of Mach cones. A clear and unavoidable smearing of the profile depending on a finite ratio of shear viscosity to entropy density is clearly visible.
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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 influence of the viscosity to the structure of Mach cones.
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 $eta/s approx 0.005$, leading to the observation of cone-like structures. Increasing the dissipation of the system to $eta/s approx 0.32$ 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 the large influence of the head shock.
We derive the relativistic non-resistive, viscous second-order magnetohydrodynamic equations for the dissipative quantities using the relaxation time approximation. The Boltzmann equation is solved for a system of particles and antiparticles using Chapman-Enskog like gradient expansion of the single-particle distribution function truncated at second order. In the first order, the transport coefficients are independent of the magnetic field. In the second-order, new transport coefficients that couple magnetic field and the dissipative quantities appear which are different from those obtained in the 14-moment approximation cite{Denicol:2018rbw} in the presence of a magnetic field. However, in the limit of the weak magnetic field, the form of these equations are identical to the 14-moment approximation albeit with a different values of these coefficients. We also derive the anisotropic transport coefficients in the Navier-Stokes limit.
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, $eta/s$. 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 double-peak structure both in a single- and in a multiple-jet event is discussed.
The time evolution of Mach-like structure (the splitting of the away side peak in di-hadron $Deltaphi$ correlation) is presented in the framework of a dynamical partonic transport model. With the increasing of the lifetime of partonic matter, Mach-like structure can be produced and developed by strong parton cascade process. Not only the splitting parameter but also the number of associated hadrons ($N_{h}^{assoc}$) increases with the lifetime of partonic matter and partonic interaction cross section. Both the explosion of $N_{h}^{assoc}$ following the formation of Mach-like structure and the corresponding results of three-particle correlation support that a partonic Mach-like shock wave can be formed by strong parton cascade mechanism. Therefore, the studies about Mach-like structure may give us some critical information, such as the lifetime of partonic matter and hadronization time.
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