We have studied the dissociation of heavy quarkonium states in a hot QCD medium by investigating the medium modifications to a heavy quark potential. Our model shows that in-medium modification causes the screening of the charge in contrast to the screening of the range of the potential. We have then employed the medium-modified potential to estimate the dissociation pattern of the charmonium and bottomonium states and also explore how the pattern changes as we go from the perturbative to nonperturbative domain in the Debye mass. The results are in good agreement with the other current theoretical works both from the spectral function analysis and the potential model study.

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We have studied the quasi-free dissociation of quarkonia through a complex potential which is obtained by correcting both the perturbative and nonperturbative terms of the QQ potential at T=0 through the dielectric function in real-time formalism. The presence of confining nonperturbative term even above the transition temperature makes the real-part of the potential more stronger and thus makes the quarkonia more bound and also enhances the (magnitude) imaginary-part which, in turn contributes more to the thermal width, compared to the medium-contribution of the perturbative term alone. These cumulative observations result the quarkonia to dissociate at higher temperatures. Finally we extend our calculation to a medium, exhibiting local momentum anisotropy, by calculating the leading anisotropic corrections to the propagators in Keldysh representation. The presence of anisotropy makes the real-part of the potential stronger but the imaginary-part is weakened slightly. However, since the medium corrections to the imaginary-part is a small perturbation to the vacuum part, overall the anisotropy makes the dissociation temperatures higher, compared to isotropic medium.

We have investigated the properties of quarkonium states in an anisotropic hot QCD medium by correcting the full Cornell potential, not the Coulomb term alone as usually done in the literature, with a dielectric function from the hard-loop resummed gluon propagator. We have found that in-medium modification in anisotropic medium causes less screening than in isotropic medium. In the short distance limit, potential does not show any medium dependence whereas in the long-distance limit, it reduces to the Coulomb potential with a dynamically screened color charge. In addition, anisotropy in momentum space introduces a characteristic angular dependence in the potential and as a result, quarkonium states in anisotropic medium are more tightly bound than in isotropic medium. In particular, quark pairs aligned in the direction of anisotropy are more bound than perpendicular to the direction of anisotropy.Comment: 29 page, 6 figure

We have explored how the electrical (σ el ) and thermal (κ) conductivities in a thermal QCD medium get affected in weak-momentum anisotropies arising either due to a strong magnetic field or due to asymptotic expansion in a particular direction. This study, in turn, facilitates to understand the longevity of strong magnetic field through σ el , Lorenz number in Wiedemann-Franz law, and the validity of local equilibrium by the Knudsen number through κ. We calculate the conductivities by solving the relativistic Boltzmann transport equation in relaxation-time approximation, where the interactions are incorporated through the distribution function within the quasiparticle approach at finite T and strong B. However, we also compare with the noninteracting scenario, which gives unusually large values, thus validating the quasiparticle description. We have found that both σ el and κ get enhanced in a magnetic field-driven anisotropy, but σ el monotonically decreases with the temperature, opposite to the faster increase in the expansion-driven anisotropy. Whereas κ increases very slowly with the temperature, contrary to its rapid increase in the expansion-driven anisotropy. Therefore, the conductivities may distinguish the origin of anisotropies. The above findings are broadly attributed to three factors: the stretching and squeezing of the distribution function due to the momentum anisotropies generated by the strong magnetic field and asymptotic expansion, respectively, the dispersion relation and the resulting phase-space factor, the relaxation-time in the absence and presence of strong magnetic field. Thus, σ el extracts the time-dependence of initially produced strong magnetic field, which expectedly decays slower than in vacuum but the expansion-driven anisotropy makes the decay faster. The variation in κ transpires that the Knudsen number (Ω) decreases with the temperature, but the expansion-driven anisotropy reduces its magnitude, and the strong magnetic field-driven anisotropy raises its value but to less than one, thus the system can still be in local equilibrium in a range of temperature and magnetic field. Finally, the ratio, κ=σ el in Wiedemann-Franz law in magnetic field-driven anisotropy increases linearly with temperature but its magnitude is smaller than in expansiondriven anisotropic medium. Thus, the slope, i.e., the Lorenz number can make the distinction between the anisotropies of different origins.

The study of transport coefficients of strongly interacting matter got impetus after the discovery of perfect fluid ever created at ultrarelativistic heavy ion collision experiments. In this article, we have calculated one such coefficient viz. electrical conductivity of the quark gluon plasma (QGP) phase which exhibits a momentum anisotropy. Relativistic Boltzmann's kinetic equation has been solved in the relaxation-time approximation to obtain the electrical conductivity. We have used the quasiparticle description to define the basic properties of QGP. We have compared our model results with the corresponding results obtained in different lattice as well as other model calculations. Furthermore, we extend our model to calculate the electrical conductivity at finite chemical potential.

We have investigated the properties of quarkonia in a thermal QCD medium in the background of strong magnetic field. For that purpose, we employ the Schwinger proper-time quark propagator in the lowest Landau level to calculate the one-loop gluon self-energy, which in the sequel gives the effective gluon propagator. As an artifact of strong magnetic field approximation (eB >> T 2 and eB >> m 2 ), the Debye mass for massless flavors is found to depend only on the magnetic field which is the dominant scale in comparison to the scales prevalent in the thermal medium. However, for physical quark masses, it depends on both magnetic field and temperature in a low temperature and high magnetic field but the temperature dependence is very meager and becomes independent of the temperature beyond a certain temperature and magnetic field. With the above mentioned ingredients, the potential between heavy quark (Q) and anti-quark (Q) is obtained in a hot QCD medium in the presence of a strong magnetic field by correcting both short-and longrange components of the potential in the real-time formalism. It is found that the long-range part of the quarkonium potential is affected much more by magnetic field as compared to the short-range part. This observation facilitates us to estimate the magnetic field beyond which the potential will be too weak to bind QQ together. For example, the J/ψ is dissociated at eB ∼ 10 m 2 π and ϒ is dissociated at eB ∼ 100 m 2 π whereas its excited states, ψ and ϒ are dissociated at smaller magnetic field eB = m 2 π , 13m 2 π , respectively.

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