Non-perturbative study of spectral function and its application in Quark Gluon Plasma

TL;DR

This thesis investigates the properties of quark-gluon plasma using non-perturbative techniques, focusing on spectral functions, dilepton rates, and magnetic effects, providing new insights into QGP behavior under various conditions.

Contribution

It introduces a comprehensive non-perturbative framework for studying QGP properties, incorporating GZ action, OPE, and magnetic effects, with analytical results and comparisons to lattice QCD.

Findings

Non-perturbative effects significantly influence spectral functions and dilepton rates.

Magnetic fields alter Debye screening and quark number susceptibility in QGP.

New quark modes related to the GZ action impact the dilepton production rate.

Abstract

The thesis contains studies of properties quark-gluon plasma, using some non-perturbative techniques. It contains a brief introduction of quark-gluon plasma (QGP) and discussion on various signatures along with a motivation for this thesis work. It presents the basic mathematical tools and ingredients required for the thesis, i.e. basics of QCD, Imaginary and Real Time Formalism, Hard Thermal Loop perturbation theory (HTLpt), Gribov-Zwanziger (GZ) action, the Correlation Function along with the Spectral Function and Operator Product Expansion (OPE) and QCD in magnetized medium. OPE is used to compute the dilepton rate in intermediate mass range by incorporating the non-perturbative dynamics of QCD through the inclusion of non-vanishing quark and gluon condensates in combination with the Green functions in momentum space. Also the magnetic scale (g^2T) in the HTL perturbation theory, related to the confining properties of the QCD is taken into account using the GZ action through a mass parameter, which reflects a new space-like quark mode in the collective excitation. The impact of this new exciting mode on the DPR has been studied and its important consequences has been discussed. A hot magnetized medium introduces another scale in the system in addition to temperature. Electromagnetic spectral properties and DPR are studied completely analytically in presence of both strong and weak background magnetic fields at finite temperature. The Debye screening in a hot and magnetized medium has been studied which reveals some of the intriguing properties of the medium in presence of both strong and weak magnetic field. Also an important quantity that characterizes the QGP, namely quark number susceptibility has been investigated. Most of the non-perturbative results discussed in this thesis are compared with those of perturbative ones and lattice QCD.