STUDY OF SOME PROPERTIES OF DECONFINED MATTER: RESUMMED PERTURBATION THEORY AND BEYOND

Abstract

In the present thesis, we have studied and explored some of the critical features of the deconfined state of matter dubbed Quark-Gluon Plasma (QGP). Big Bang theory argues that this state of matter occurred during the universe’s initial evolution. Thus, knowledge of this phase of matter is of significant importance for comprehending the evolution of the universe. For this purpose, the Ultra-Relativistic Heavy Ion Collisions (URHIC) program is designed to gain access to the bulk feature of the extreme quantum chromodynamics (QCD) matter created in the experiments, namely Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL) and the Large Hadron Collider (LHC) at the European Organization for Nuclear Research (CERN). The different properties of the extreme matter that have been studied in this thesis are next-to-leading order (NLO) dispersion properties for soft-moving quarks, screening masses of mesons, drag and diffusion properties of heavy quarks (HQs), the specific shear viscosity of QGP and energy loss of HQs propagating in QGP background. The theoretical techniques which are utilized in order to study these properties are mainly hard thermal loop (HTL) effective theory, which is required when one is interested in studying the soft scale (∼ gT) physics of the underlined theory QCD at finite temperatures, having g as the strength of the interaction and the other technique which are utilized here is the nonperturbative resummation approach dubbed as Gribov quantization. This nonperturbative resummation deals with the magnetic scale of the theory through the mass parameter having g2T order. We have studied and calculated the quark self-energy at NLO and the corresponding dispersion relations for the soft-moving quarks in the real-time formalism (RTF) using an HTL effective theory. The four-point vertex diagram has been calculated apart from the usual three-point vertex diagram, with the effective quark, gluon propagators, and effective vertices taken into account. Since NLO dispersion relations depend on the estimation of NLO quark self-energy, NLO quark selfii energy is expressed in terms of two-quarks-one-gluon and two-quarks-two-gluons HTL effective vertex functions, which are further expressed in terms of solid angle integrals. The solid angles and the momentum integrals in quark self-energy have been computed numerically and plotted as a ratio of quark momentum and quark energy. Utilizing that, we showed the NLO correction to quark damping rate and quark energy for both quark modes. The obtained results for NLO dispersion relations show the converging earlier results in the zero momentum limit. Since HTL resummation deals with the electric scale of the theory, we have incorporated the magnetic scale through the nonperturbative Gribov resummation approach in order to study the mesonic correlation lengths. We have calculated the mesonic screening masses both for quenched QCD and for (2+1) flavor QCD cases following the analogies with the non-relativistic quantum chromodynamics (NRQCD) effective theory. The obtained results show that the Gribov quantization improves the infrared dynamics of the theory, i.e., obtained results of mesonic screening masses improve the earlier perturbative results in the low-temperature domain and are well suited with the recent lattice measurements. Since HQs are considered a suitable probe for QGP, thus we explored the heavy quark (HQ) dynamics using the Gribov-Zwanziger (GZ) approach. We have estimated the drag and diffusion coefficient of HQs moving in the QGP background. The interaction of HQs with the medium constituents, which are encoded in the matrix elements, is calculated through the GZ propagator for the mediator gluons to take into account the nonperturbative outcomes pertinent to the phenomenologically accessible temperature regime in QGP laboratory experiments. The obtained drag coefficient has been utilized to estimate the momentum and temperature variation of HQ energy loss propagating in the QGP background. Also, using the transverse diffusion coefficient, the temperature variation of the specific shear viscosity of the background medium (QGP) has been obtained. We reported a higher energy loss of propagating HQs compared to perturbative estimates. The shear viscosity to entropy density ratio is observed to comply with the anti-de Sitter/conformal field theory (AdS/CFT) estimation over a more significant temperature regime compared to the earlier perturbative expectation.