The effects of longitudinal bulk viscous pressure on the heavy quark dynamics have been estimated in a strongly magnetized quark-gluon plasma within the Fokker-Planck approach. The bulk viscous modification to the momentum distribution of bulk degrees of freedom has been obtained in the presence of a magnetic field while incorporating the realistic equation of state of the hot magnetized QCD medium. As the magnetic field breaks the isotropy of the medium, the analysis is done along the directions longitudinal and transverse to the field. The longitudinal bulk viscous contribution is seen to have sizable effects in the heavy quark momentum diffusion in the magnetized medium. The dependence of higher Landau levels and the equation of state on the viscous correction to the heavy quark transport has been explored in the analysis.
We investigate hydrodynamic evolution of the quark gluon plasma for the colour glass condensate type initial conditions. We solve full second-order viscous hydrodynamic equations in the longitudinal direction to find that non-boost invariant expansion leads to visible deformation on the initial rapidity distribution. The results indicate that hydrodynamic evolution with viscosity plays an important role in determining parameters for the initial distributions.
The longitudinal current density induced by the inhomogeneous electric field in the hot magnetized quark-gluon plasma has been investigated and utilized in obtaining the conductivity of the medium. The analysis has been done in the regime where inhomogeneity of the field is small so that the collision effect could be significant. The modeling of the QCD medium is based on a quasiparticle description where the medium effects have been encoded in the effective quarks, antiquarks and gluons. The temperature dependence of the linear longitudinal current density (in terms of the electric field) and…
The expressions of the shear viscosity and the bulk viscosity components in the presence of an arbitrary external magnetic field for a system of hot charged scalar Bosons (spin-0) as well as for a system of hot charged Dirac Fermions (spin-$\frac{1}{2}$) have been derived by employing the one-loop Kubo Formalism. This is done by explicitly evaluating the thermo-magnetic spectral functions of the energy momentum tensors using the real time formalism of finite temperature field theory and the Schwinger proper time formalism. In the present work, a rich quantum field theoretical structure in the …
Longitudinal hydrodynamic expansion of the fluid created in relativistic heavy-collisions is considered taking into account shear viscosity. Both a on-vanishing viscosity and a soft equation of state make particle distributions in rapidity narrower. The presence of viscosity has dramatic consequence on the value of the initial energy density. The reduction of the longitudinal work and dissipative processes due to the shear viscosity, increase the total entropy and the particle multiplicity at central rapidities. The total energy in the collision, dominated by the longitudinal motion, is conser…
The solutions of relativistic viscous hydrodynamics for longitudinal expanding fireballs is investigated with the Navier-Stokes theory and Israel-Stewart theory. The energy and Euler conservation equations for the viscous fluid are derived in Rindler coordinates with the longitudinal expansion effect is small. Under the perturbation assumption, an analytical perturbation solution for the Navier-Stokes approximation and numerical solutions for the Israel-Stewart approximation are presented. The temperature evolution with both shear viscous effect and longitudinal acceleration effect in the long…
The properties of non-interacting $σ$ and $π^{0}$ mesons are studied at finite temperature, chemical potential and in the presence of a constant magnetic field. To do this, the energy dispersion relations of these particles, including nontrivial form factors, are derived using a derivative expansion of the effective action of a two-flavor, hot and magnetized Nambu--Jona-Lasinio (NJL) model up to second order. The temperature dependence of the pole and screening masses as well as the directional refraction indices of magnetized neutral mesons are explored for fixed magnetic fields and chemical …
I compute the first viscous correction to the thermal distribution function. With this correction, I calculate the effect of viscosity on spectra, elliptic flow, and HBT radii. Indicating the breakdown of hydrodynamics, viscous corrections become of order one for $p_{T}\sim 1.5$ GeV. Viscous corrections to HBT radii are particularly large and reduce the outward and longitudinal radii. This reduction is a direct consequence of the reduction in longitudinal pressure.
The charged-particle's final state spectrum is derived from an analytic perturbative solution for the relativistic viscous hydrodynamics. By taking into account the longitudinal acceleration effect in relativistic viscous hydrodynamics, the pseudorapidity spectrum describes well the nucleus-nucleus colliding systems at RHIC and LHC. Based on both the extracted longitudinal acceleration parameters $λ^{*}$ and a phenomenological description of the $λ^{*}$, the charged-particle's pseudorapidity distributions for $\sqrt{s_{NN}}$ = 5.44 TeV Xe+Xe collisions are computed from the final state express…
We demonstrate how to match pre-equilibrium dynamics of a 0+1 dimensional quark gluon plasma to 2nd-order viscous hydrodynamical evolution. The matching allows us to specify the initial values of the energy density and shear tensor at the initial time of hydrodynamical evolution as a function of the lifetime of the pre-equilibrium period. We compare two models for the pre-equilibrium quark-gluon plasma, longitudinal free streaming and collisionally-broadened longitudinal expansion, and present analytic formulas which can be used to fix the necessary components of the energy-momentum tensor. Th…
Quarks produced in the early stage of non-central heavy-ion collisions could develop a global spin polarization along the opposite direction of the reaction plane due to the spin-orbital coupling via parton interaction in a medium that has finite longitudinal flow shear along the direction of the impact parameter. We study how such polarization evolves via multiple scattering in a viscous quark-gluon plasma with an initial laminar flow. The final polarization is found to be sensitive to the viscosity and the initial shear of local longitudinal flow.
We show that by requiring positivity of the longitudinal pressure it is possible to constrain the initial conditions one can use in 2nd-order viscous hydrodynamical simulations of ultrarelativistic heavy-ion collisions. We demonstrate this explicitly for 0+1 dimensional viscous hydrodynamics and discuss how the constraint extends to higher dimensions. Additionally, we present an analytic approximation to the solution of 0+1 dimensional 2nd-order viscous hydrodynamical evolution equations appropriate to describe the evolution of matter in an ultrarelativistic heavy-ion collision.
The effect of a strong magnetic field on the electric polarization of a three-flavor color superconducting medium is investigated. We found that the electric susceptibility of this strongly magnetized medium is highly anisotropic. In the direction transverse to the applied magnetic field the susceptibility reduces to that of the vacuum, while in the longitudinal direction it depends on the magnetic field and decreases with it. The nature of this behavior is associated with the field's dependence of the Cooper pairs' coherence length, which plays the role of the electric dipole length. The fiel…
We present a calculation of the heavy quark momentum diffusion coefficients in a quark-gluon plasma under the presence of a strong external magnetic field, within the Lowest Landau Level (LLL) approximation. In particular, we apply the Hard Thermal Loop (HTL) technique for the resummed effective gluon propagator, generalized for a hot and magnetized medium. Using the derived effective HTL gluon propagator and the LLL quark propagator we analytically derive the full results for the longitudinal and transverse momentum diffusion coefficients as well as the energy losses for charm and bottom quar…
We investigate the screening masses of neutral pions and sigma mesons in hot and magnetized quark matter in the framework of a two-flavor lattice-improved Nambu-Jona-Lasinio (NJL) model with a magnetic field dependent coupling constant, which is determined by utilizing the results from lattice QCD simulations. Since such model can well reproduce inverse magnetic catalysis (IMC), by comparing with the standard NJL model, we systemically analyze the impacts of IMC on the temperature and magnetic field dependences of the longitudinal and transverse screening masses of the chiral partners, i.e. π^…
We derive the form of the viscous corrections to the phase-space distribution function due to the bulk viscous pressure and shear stress tensor using the iterative Chapman-Enskog method. We then calculate the transport coefficients necessary for the second-order hydrodynamic evolution of the bulk viscous pressure and the shear stress tensor. We demonstrate that the transport coefficients obtained using the Chapman-Enskog method are different than those obtained previously using the 14-moment approximation for a finite particle mass. Specializing to the case of boost-invariant and transversally…
We express the transport coefficients appearing in the second-order evolution equations for bulk viscous pressure and shear stress tensor using Bose-Einstein, Boltzmann, and Fermi-Dirac statistics for the equilibrium distribution function and Grad's 14-moment approximation as well as the method of Chapman-Enskog expansion for the non-equilibrium part. Specializing to the case of transversally homogeneous and boost-invariant longitudinal expansion of the viscous medium, we compare the results obtained using the above methods with those obtained from the exact solution of the massive 0+1d relati…
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…
Anisotropic hydrodynamics improves upon standard dissipative fluid dynamics by treating certain large dissipative corrections non-perturbatively. Relativistic heavy-ion collisions feature two such large dissipative effects: (i) Strongly anisotropic expansion generates a large shear stress component which manifests itself in very different longitudinal and transverse pressures, especially at early times. (ii) Critical fluctuations near the quark-hadron phase transition lead to a large bulk viscous pressure on the conversion surface between hydrodynamics and a microscopic hadronic cascade descri…
The thermodynamic properties of a non-interacting ideal Hadron Resonance Gas (HRG) of finite volume have been studied in the presence of an external magnetic field. The inclusion of background magnetic field in the calculation of thermodynamic potential is done by the modification of the dispersion relations of the charged hadrons in terms of Landau quantization. The generalized Matsubara prescription has been employed to take into account the finite size effects in which a periodic (anti-periodic) boundary conditions is considered for the mesons (baryons). We find significant effects of the m…
A new formulation of second-order viscous hydrodynamics, based on an expansion around a locally anisotropic momentum distribution, is presented. It generalizes the previously developed formalism of anisotropic hydrodynamics (aHydro) to include a complete set of dissipative currents for which equations of motion are derived by solving the Boltzmann equation in the 14-moment approximation. By solving the vaHydro equations for a transversally homogeneous, longitudinally boost-invariant system ((0+1)-dimensional expansion) and comparing with the exact solution of the Boltzmann equation in relaxati…
The thermomagnetic behavior of quark-gluon plasma has recently received a lot of attention. In this work, we make use of the extended self-consistent quasiparticle model to study the thermodynamic properties of magnetized (2+1) flavor quark-gluon plasma. The system is considered as a non-interacting system of quasiparticles with masses depending on both temperature and magnetic field. This allows obtaining the equation of state of the system and the other thermodynamic properties such as the speed of sound. We use the extended self-consistent model to obtain the magnetization and show that QGP…
Based on transversality condition of gauge boson self-energy we have systematically constructed the general structure of the gauge boson two-point functions using four linearly independent basis tensors in presence of a nontrivial background, i.e., hot magnetized material medium. The hard thermal loop approximation has been used for the heat bath to compute various form factors associated with the gauge boson's two point functions both in strong and weak field approximation. We have also analyzed the dispersion of a gauge boson (e.g., gluon) using the effective propagator both in strong and we…
Following the Boz$\dot{\textrm{e}}$k-Wyskiel parametrization tilted initial condition, an alternative way to construct a longitudinal tilted fireball based on the Glauber collision geometry is presented. This longitudinal tilted initial condition combined with the Ideal-CLVisc (3 + 1)D hydrodynamic model, a nonvanishing directed flow coefficient $v_{1}$ in a wide rapidity range is observed. After comparing the model's results with experimentally observed data of directed flow coefficient $v_{1}(η)$ from $\sqrt{s_{NN}}$ = 200 GeV Cu + Cu, Au + Au collisions at RHIC energy to $\sqrt{s_{NN}}$ = 2…
We derive a system of moment-based dynamical equations that describe the 1+1d space-time evolution of a cylindrically symmetric massive gas undergoing boost-invariant longitudinal expansion. Extending previous work, we introduce an explicit degree of freedom associated with the bulk pressure of the system. The resulting form generalizes the ellipsoidal one-particle distribution function appropriate for massless particles to massive particles. Using this generalized form, we obtain a system of partial differential equations that can be solved numerically. In order to assess the performance of t…
In this work we describe the dynamics of a highly anisotropic system undergoing boost-invariant longitudinal and azimuthally symmetric radial expansion (Gubser flow) for arbitrary shear viscosity to entropy density ratio. We derive the equations of motion of dissipative anisotropic hydrodynamics by applying to this situation the moments method recently derived by Molnár et al. (MNR) [1,2], based on an expansion around an arbitrary anisotropic one-particle distribution function. One requires an additional evolution equation in order to close the conservation laws. This is achieved by selecting …
Following an extremely interesting idea \cite{R1}, published long ago, the work function at the outer crust region of a strongly magnetized neutron star is obtained using relativistic version of Thomas-Fermi type model. In the present scenario, the work function becomes anisotropic; the longitudinal part is an increasing function of magnetic field strength, whereas the transverse part diverges. An approximate estimate of the electron density in the magnetosphere due to field emission and photo emission current, from the polar cap region are obtained.
We compute the time evolution of elliptic flow in non-central relativistic heavy-ion collisions, using a (2+1)-dimensional code with longitudinal boost-invariance to simulate viscous fluid dynamics in the causal Israel-Stewart formulation. We show that even ``minimal'' shear viscosity eta/s=hbar/(4pi) leads to a large reduction of elliptic flow compared to ideal fluid dynamics, raising questions about the interpretation of recent experimental data from the Relativistic Heavy Ion Collider.
We study the dissipative evolution of (0+1)-dimensionally expanding media with Bjorken symmetry using the Boltzmann equation for massive particles in relaxation-time approximation. Breaking conformal symmetry by a mass induces a non-zero bulk viscous pressure in the medium. It is shown that even a small mass (in units of the local temperature) drastically modifies the well-known attractor for the shear Reynolds number previously observed in massless systems. For generic nonzero particle mass, neither the shear nor the bulk viscous pressure relax quickly to a non-equilibrium attractor; they app…
We study viscous effects on heavy quark radiative energy loss in a dynamically screened medium with boost-invariant longitudinal expansion. We calculate, to first order in opacity, the energy loss by incorporating viscous corrections in the single-particle phase-space distribution function within relativistic dissipative hydrodynamics. We consider the Grad's 14-moment and the Chapman-Enskog-like methods for the nonequilibrium distribution functions. Our numerical results for the charm quark radiative energy loss show that, as compared to static fluid, an expanding ideal (nonviscous) fluid caus…
We present the first calculation of longitudinal decorrelation of anisotropic flow at RHIC Beam Energy Scan (BES) energies using event-by-event viscous hydrodynamic model (vHLLE), with two different initial states (GLISSANDO2 and UrQMD) and hadronic cascade. We investigate the origin of the observed decorrelation by checking separately flow angle and flow magnitude decorrelation and by calculating decorrelation in the initial state eccentricity.
We explore the effects of shear viscosity on the hydrodynamic evolution and final hadron spectra of Cu+Cu collisions at ultrarelativistic collision energies, using the newly developed (2+1)-dimensional viscous hydrodynamic code VISH2+1. Based on the causal Israel-Stewart formalism, this code describes the transverse evolution of longitudinally boost-invariant systems without azimuthal symmetry around the beam direction. Shear viscosity is shown to decelerate the longitudinal and accelerate the transverse hydrodynamic expansion. For fixed initial conditions, this leads to a longer quark-gluon p…
We consider weakly magnetized hot QED plasma comprising electrons and positrons. There are three distinct dispersive (longitudinal and two transverse) modes of a photon in a thermo-magnetic medium. At lowest order in coupling constant, photon is damped in this medium via Compton scattering and pair creation process. We evaluate the damping rate of hard photon by calculating the imaginary part of the each transverse dispersive modes in a thermo-magnetic QED medium. We note that one of the fermions in the loop of one-loop photon self-energy is considered as soft and the other one is hard. Consid…
I calculate the first correction to the thermal distribution function of an expanding gas due to shear viscosity. With this modified distribution function I estimate viscous corrections to spectra, elliptic flow, and HBT radii in hydrodynamic simulations of heavy ion collisions using the blast wave model. For reasonable values of the shear viscosity, viscous corrections become of order one when the transverse momentum of the particle is larger than 1.7 GeV. This places a bound on the $p_{T}$ range accessible to hydrodynamics for this observable. Shear corrections to elliptic flow cause $v_{2}(…
We describe the details of 3+1 dimensional relativistic hydrodynamic code for the simulations of quark-gluon/hadron matter expansion in ultra-relativistic heavy ion collisions. The code solves the equations of relativistic viscous hydrodynamics in the Israel-Stewart framework. With the help of ideal-viscous splitting, we keep the ability to solve the equations of ideal hydrodynamics in the limit of zero viscosities using a Godunov-type algorithm. Milne coordinates are used to treat the predominant expansion in longitudinal (beam) direction effectively. The results are successfully tested again…
In this article, shear viscosity, bulk viscosity, and thermal conductivity of a hot QCD medium have been studied in the presence of a strong magnetic field. To model the hot magnetized QCD matter, an extended quasi-particle description of the hot QCD equation of state in the presence of the magnetic field has been adopted. The effects of higher Landau levels on the temperature dependence of viscous coefficients (bulk and shear viscosities) and thermal conductivity have been obtained by considering the $1\rightarrow 2$ processes in the presence of the strong magnetic field. An effective covaria…
We propose several new observables/correlators, based on correlations between two or more subevents separated in pseudorapidity $η$, to study the longitudinal flow fluctuations. We show that these observables are sensitive to the event-by-event fluctuations, as a function of $η$, of the initial condition as well as the non-linear mode-mixing effects. Experimental measurement of these observables shall provide important new constraints on the boost-variant event-by-event initial conditions required by all 3+1-dimensional viscous hydrodynamics models.
We compare 2->2 covariant transport theory and causal Israel-Stewart hydrodynamics in 2+1D longitudinally boost invariant geometry with RHIC-like initial conditions and a conformal e = 3p equation of state. The pressure evolution in the center of the collision zone and the final differential elliptic flow v2(pT) from the two theories agree remarkably well for a small shear viscosity to entropy density ratio eta/s ~ 1/(4 pi), and also for a large cross section sigma ~ 50 mb. A key to this agreement is keeping ALL terms in the Israel-Stewart equations of motion. Our results indicate promising pr…
The neutron-proton-electron(npe) matter under a strong magnetic field is studied in the context of the covariant Vlasov approach. We use a Walecka-type hadronic model and the dispersion relations for the longitudinal and transverse modes are obtained. The instability regions for longitudinal and transverse modes are also studied. The crust-core transition of a magnetized neutron star is discussed.
