SOME ASPECTS OF A HOT QCD MEDIUM IN PRESENCE OF MAGNETIC FIELD

Abstract

Quantum chromodynamics (QCD) is a fundamental theory that describes the interaction between the color-charged quarks and gluons. It is a non-abelian gauge theory, which exhibits asymptotic freedom and confinement at high and low energies, respectively. As a consequence, the interaction between the quarks and gluons becomes feeble in the extreme conditions of temperature and/or density and a transition from the hadronic matter to a deconfined phase of asymptotically free quarks and gluons takes place. This deconfined phase of matter is dubbed as quark gluon plasma (QGP). The study of the properties of QGP is important in the context of astrophysics and cosmology also since it is believed that our present day universe was in the QGP phase in its early stages. Such kind of matter is also predicted in the core of some densed stars formed as a result of the supernova explosion. In the laboratory, this extreme state of matter is created in the heavy-ion collision experiments at Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC). In non-central collisions, a magnetic field of the order of m2 π at RHIC and 15m2 π at LHC is also produced due to the relative motion of the spectator particles. The magnetic field decays fast in the vacuum but due to the finite electrical conductivity of the medium its life-time gets elongated, which influences the various properties of QGP such as thermodynamic and transport properties, particle production, dynamics of heavy quarks and their bound states (quarkonia) and in general many other aspects of the QCD phase diagram. Apart from it, magnetic field also induces some novel phenomena like the chiral magnetic effect, magnetic and inverse magnetic catalysis and chiral vortical effect etc. Transport coefficients of the hot QCD matter act as input parameters in the dissipative hydrodynamic equations to describe the evolution of the medium. Shear viscosity (η) quantifies the response of the medium to the transverse momentum gradients while bulk viscosity (ζ) to the pressure gradients. Similarly, electrical (σel) and thermal (κ) conductivities measure the response of the system to the electromagii netic fields and temperature gradients, respectively. σel plays an important role in the elongation of the life-time of the generated magnetic field, while κ controls the attenuation of sound through the Prandtl number and also affects the first order phase transition. In this thesis, we have studied various transport coefficients corresponding to the charge, heat and momentum transport in a strongly interacting hot QCD matter in the presence of background strong magnetic field. In magnetic field, the motion of the quarks is quantized in the transverse direction leading to the discrete energy spectrum in terms of Landau levels. When the strength of the magnetic field is large (|qB| >> T2 >> m2), the energy separation between the consecutive Landau levels becomes large (of the order √︁ |qB|), consequently, the quarks get confined in the lowest Landau level (LLL) only. To calculate the transport coefficients, we have exploited the relativistic kinetic theory framework, where the collisional effects have been incorporated via the Bhatnagar-Gross-Krook collision (BGK) term. BGK collision term shows an improvement over the commonly used relaxation time approximation (RTA) because it conserves the particle number instantaneously. The estimation of the transport coefficients with realistic collision integrals such as BGK, is of paramount importance as the collision integral provides the microscopic input to the relativistic Boltzmann transport equation (RBTE). We first calculate the electrical and heat conductivities in the absence of the magnetic field. With the help of these conductivities, we compute the Lorentz and Knudsen numbers. We notice that both σel and κ get enhanced in the BGK collision term as compared to RTA. The Lorentz number (Knudsen number) gets reduced (enhanced). We then compute the same transport coefficients in the presence of the strong magnetic field and found that the Knudsen number acquires large values for the non-interacting partons, which is against the near equilibrium assumption needed to linearize the Boltzmann equation. This motivates us to compute the above mentioned transport coefficients in the quasiiii particle description. Now the Knudsen number becomes less than one manifesting the equilibrium nature of the medium. Similarly, we explore the sensitivity of the momentum transport to the collision integrals of different types and calculate the shear and bulk viscosities in the absence of the magnetic field. η (ζ) gets enhanced (reduced) in the BGK collision term. This behaviour with respect to the collision term is also reflected in the ratios η/s and ζ/s, which tell about the fluidity and transition point of QCD medium, respectively. We also calculate the Reynolds number (tells about nature of flow), Prandtl number (gives the sound attenuation ), γ (interplay between the momentum and charge diffusion) and ratio ζ/η. The magnitude of Pr, RI, γ and ζ/η gets reduced. Then we assess how a strong magnetic field modulates the impact of the collision integral on transport phenomena. The above mentioned transport coefficients show similar trends with respect to the collision integral as B = 0 case except for ratio ζ/s, which is almost identical in both the collision integrals. Strong magnetic field enhances the magnitude of Pr, γ and ζ/η, while RI gets reduced. We further evaluated the Seebeck and Nernst coefficients, which give the thermoelectric response of the medium. In absence of B, the Seebeck coefficient for the individual quark flavors gets reduced in the BGK collision term in comparison to the RTA while for the combined medium it gets enhanced. In strong B, the Seebeck coefficient is large in the BGK term for the individual flavours as well as medium. In addition to Seebeck coefficient, Nernst coefficient also appears in the weak magnetic field. The BGK collision integral does not affect the Seebeck coefficient much but the Nernst coefficient gets changed drastically. In the current study, the quasi-particle mass of the partons has been obtained from the pole of the resummed propagator calculated using the perturbative QCD at finite temperature with a magnetic field.