THERMOELECTRIC AND HEAVY QUARK TRANSPORT COEFFICIENTS OF HOT QCD MATTER IN THE PRESENCE OF MAGNETIC FIELD

Abstract

The aim of this thesis is twofold: a) A comprehensive study of the thermoelectric response in a hot QCD medium [called quark gluon plasma (QGP)] in the absence and presence of a background magnetic field, b) Exploring the dynamics of heavy quarks traversing in QGP in the presence of a weak background magnetic field. Ultra-relativistic heavy ion collisions (ULRHICs) create huge energy densities in the reaction zone causing nucleons to “melt”, thereby leading to the creation of a medium of deconfined quarks and gluons. Fluctuations in the initial energy densities can lead to significant temperature differences between the central and peripheral regions of the expanding fireball. Coupled with a small but finite quark chemical potential, this sets the ground for the QGP to exhibit Seebeck effect. Also, noncentral nucleus-nucleus collisions give rise to magnetic fields (B) which affect the evolution of QGP. A temperature gradient coupled with a finite magnetic field sets the conditions for the system to exhibit the other thermoelectric phenomenon-The Nernst effect. Thermoelectricity in QGP provides for a new source of electric current, hence, a new source of magnetic field and entropy. We have evaluated the strength of the aforementioned response in QGP quantified by the Seebeck and Nernst coefficients, first in the absence of a background magnetic field, and then in the presence of a strong magnetic field (eB T2). This is followed by the evaluation of the coefficients in the presence of a weak magnetic field (eB T2). Each of the above-mentioned scenarios is investigated under the assumption that the QGP is isotropic. Realistically, however, the fireball expands anisotropically due to anisotropic pressure gradients caused by geometrical anisotropies in the overlap zone between the two nuclei. We try to incorporate this by using an anisotropic distribution function (Romatchke-Strickland form) for the quarks and evaluate the Seebeck and Nernst coefficients to investigate the effects of anisotropy. The formalism adopted in the calculation of these coefficients is that of kinetic theory. Specifically, the system is assumed to deviate slightly away from equilibrium due to the temperature gradient, and the deviation is evaluated using the relativistic Boltzmann transport equation (RBTE) within the relaxation time approximation (RTA). Interactions among partons are incorporated via the quasiparticle masses of thermal quarks and gluons. We find that the thermoelectric response is the strongest when the background magnetic field is strong, and weakest in the absence of magnetic field. We also observe that a finite anisotropy reduces the strength of the thermoelectric response. The other part of this thesis deals with HQ dynamics in the QGP. HQs have been recognised as very good probes of the QGP owing to their large masses (MQ T2). As a result, they do not fully thermalize with the medium, and hence, carry a memory of their interactions therein. We have calculated the HQ energy loss dE/dx, longitudinal and transverse momentum diffusion coefficients L/T , and spatial diffusion coefficient Ds, to leading order in the strong coupling , for both Charm and Bottom quarks. We consider Coulomb scattering of the HQ with thermal quarks and gluons, and ignore Compton scatterings to evaluate the scattering rate 􀀀 from which, all the aforementioned coefficients are obtained. We find that the values of normalised momentum diffusion coefficients ( L/T /T3) increase in the presence of a weak magnetic field (compared to the B = 0 case), and the anisotropy therein ( L/T3 􀀀 T /T3) is also heightened in the presence of the magnetic field. Ds is found to decrease in the presence of magnetic field, compared to its value at B = 0.