We review the various aspects of anisotropic quark-gluon plasma (AQGP) that have recently been discussed by a number of authors. In particular, we focus on the electromagnetic probes of AQGP, inter quark potential, quarkonium states in AQGP, and the nuclear modifications factor of various bottomonium states using this potential. In this context, we will also discuss the radiative energy loss of partons and nuclear modification factor of light hadrons in the context of AQGP. The features of the wake potential and charge density due to the passage of jet in AQGP will also be demonstrated.

Ever since the possibility of creating the quark-gluon plasma (QGP) in relativistic heavy ion collision was envisaged, numerous indirect signals were proposed to probe the properties of such an exotic state of matter. For example, electromagnetic probes (photon and dilepton) [

In the absence of a theoretical proof favoring the rapid thermalization and the uncertainties in the hydrodynamical fits of experimental data, it is very hard to assume hydrodynamical behavior of the system from the very beginning. The rapid expansion of the matter along the beam direction causes faster cooling in the longitudinal direction than in the transverse direction [

To characterize the presence of initial state of momentum space anisotropy, it has been suggested to look for some observables which are sensitive to the early time after the collision. The effects of preequilibrium momentum anisotropy on various observables have been studied quite extensively over the past few years. The collective oscillations in an AQGP have been studied in [

Effects of anisotropy on photon and dilepton yields have been investigated rigorously in [

The organization of the review is as follows. In Section

Photons and dileptons have long been considered to be the good probes to characterize the initial stages of heavy ion collisions as these interact “weakly” with the constituents of the medium and can come out without much distortion in their energy and momentum. Thus, they carry the information about the space-time point where they are produced. Since anisotropy is an early stage phenomena, photons and dileptons are the efficient probes to characterize this stage. The yield of dileptons (henceforth called medium dileptons/photons) in an AQGP has been calculated using a phenomenological model of space-time evolution in (1 + 1) dimension [

For

The other model (referred to as model II hereafter) of space-time evolution of highly AQGP is the boost invariant dissipative dynamics in (0 + 1) dimension [

The zeroth-order and first-order moments of the Boltzmann equation give the time dependence for

(Color online) Time evolutions of (a) the anisotropy parameter

The assumption of boost invariant in the longitudinal direction can be relaxed and such a space-time model (the so called AHYDRO) has been proposed in [

We first consider the medium photon production from AQGP. The detail derivation of the differential rate is standard and can be found in [

We plot the total photon yield coming from thermal QGP, thermal hadrons and the initial hard contribution in Figure

(Color online) Photon transverse momentum distributions at RHIC energies. The initial conditions are taken as

The dilepton production from AQGP has been estimated in [

Using the anisotropic distribution functions for the quark (antiquark) defined earlier the differential dilepton production rate can be written as [

The invariant mass and

The numerical results are shown in Figure

(Color online) Invariant mass (a) and momentum (b) distribution of midrapidity dileptons in central Pb + Pb collisions at LHC. The figures are taken from [

In this section, we will discuss the heavy quark potential in AQGP that has been calculated in [

Due to the anisotropy direction, the self-energy, apart from momentum

The collective modes in a collisional AQGP have been investigated in [

In order to calculate the quark-quark potential, we resort to the covariant gauge. Using the previous expression for gluon self-energy in anisotropic medium the propagator, in covariant gauge, can be calculated after some cumbersome algebra [

The structure functions (

For arbitrary

Next, we consider quarkonium states in an AQGP where the potential, to linear order in

Quarkonium binding energies have also been calculated using a realistic potential including the complex part in [

Thermal bottomonium suppression (

Next, we discuss the effect of the initial state momentum anisotropy on the survival probability of

Bhanot and Peskin first calculated the quarkonium-hadron interaction cross-section using operator product expansion [

To calculate the survival probability of

We now first discuss the numerical result of the thermal averaged gluon dissociation cross-section in the anisotropic system. The results are displayed in Figure

(Color online) The thermal-averaged gluon

Equation (

(Color online) The survival probability of

(Color online) The survival probability of

In this section, we calculate the radiative energy loss in an infinitely extended anisotropic plasma. We assume that an on-shell quark produced in the remote past is propagating through an infinite QCD medium that consists of randomly distributed static scattering centers which provide a color-screened Yukawa potential originally developed for the isotropic QCD medium given by [

Now the parton scatters with one of the color center with the momentum

Now in anisotropic medium we have [

In the present scenario, we assume that the parton is propagating along the

The fractional energy loss in anisotropy medium for the light quark is shown in Figure

Color online: fractional energy loss for the light quark for

(Color online) Same as 7 for charm quark (a) and bottom quark (b) with

Next, we consider the nuclear modification factor of light hadrons incorporating the light quark energy loss in AQGP discussed in the previous paragraphs. When a parton is propagating in the direction of anisotropy it is found that the fractional energy loss increases. In this section, we will apply this formalism to calculate the nuclear modification factor of the light hadrons. Starting with two-body scattering at the parton level, the differential cross-section for the hadron production is [

For an expanding plasma, the anisotropy parameter

Figure

(Color Online) Nuclear modification factor at RHIC energies. The initial conditions are taken as (a)

It is mentioned earlier that when a jet propagates through hot and dense medium it loses energy mainly by the radiative process. As mentioned earlier, it also creates wake in the charge density as well as in the potential. Now, we calculate the wake in charge density and the wake potential due to the passage of a fast parton in a small

In the presence of the test charge particle, the induced charge density and the wake potential depend on the velocity of the external charged parton and also on the distribution of the background particle [

The passage of external test charge through the plasma also disturbs the plasma and creates induced color charge density [

Substituting (

Numerical evaluation of the previous equation leads to the contour plots of the induced charge density shown in Figure

(Color online) Left Panel: the plot shows equicharge line with parton velocity

Next, we consider the case when the parton moves perpendicular to the anisotropy direction in which case the induced charge density can be written as

(Color online) The left (right) panel shows the equicharge lines for

According to the Poisson equation, the wake potential induced by the fast parton reads as [

Figure

(Color online) (a): scaled wake potential along the motion of the fast parton, that is,

Next, we consider the case when the parton moves perpendicular to the beam direction. The wake potential in (

(Color online) The left (right) panel shows scaled wake potential for

We have reviewed the effect of initial state momentum anisotropy that can arise in an AQGP on various observables. It is shown that electromagnetic probes could be a good signal that can be used to characterize this anisotropic state as this can only be realized in the early stages of heavy ion collisions. It has been demonstrated that the isotropization time of the QGP can be extracted by comparing the photon yield with the experimental data. We further estimate the radiative energy loss of a fast moving parton (both heavy and light flavours) in an AQGP and show that the it is substantially different from that in the isotropic QGP. Moreover, it depends on the direction of propagation of the parton with the anisotropic axis. Related to this is the nuclear modification factor of light hadrons that is produced due to the fragmentation of light partons which lose energy in the medium. Thus,we have also discussed the nuclear modification factor in the context of AQGP and compared it with the RHIC data to extract the isotropization time. The extracted value is compatible with that obtained from photon data.

It might be mentioned here that the presence of unstable modes in AQGP may affect radiative energy loss. However, in [

The heavy quark potential and the quarkonium states in AQGP have also been reviewed with both real and complex valued potential. In all these calculations, it has been found that the dissociation temperature of various quarkonium states increases in comparison with the isotropic case. We have also focused on the nuclear modification factors of various bottomonium states which have been calculated by combining hydrodynamics and solutions of 3D Schrodinger equation using two types of complex valued potentials.

Apart from the energy loss of a jet in a medium, the jet also creates wake in the plasma. We have demonstrated that due to the jet propagation in an AQGP, the wake potential and the charge density are significantly modified in comparison with the isotropic case.

We end by mentioning that the ADS/CFT calculation of the electromagnetic correlator has been performed in strongly coupled

_{s}) and

_{b1}Suppression at

_{T}spectra

_{T}hadron spectra in high-energy nuclear collisions

^{0}mesons at high transverse momentum in Au+Au collisions at