QUARKONIUM SUPPRESSION: A PROBE TO THE QGP AT FINITE TEMPERATURE AND DENSITY

Abstract

Quantum chromodynamics (QCD) is a non-abelian gauge theory of strong interaction among quarks and gluons, which exhibits two remarkable features: the asymptotic freedom, where the interaction between quarks either at high energy or short distance diminishes and the confinement, where the quarks are always confined inside the colorless hadrons. In consonance with these features of QCD, the hadronic matter at very high temperature and/or density, which can be achieved either by compressing the hadrons in a small volume or by heating the QCD vacuum, is expected to dissolve into color-conducting quarks and gluons, known as Quark Gluon Plasma (QGP), which has pervaded the early universe a few microseconds after the big bang and may be present in the core of neutron stars. The relativistic heavy-ion collision (rHIC) experiments, viz. Super Proton Synchrotron (SPS) at CERN, Relativistic Heavy Ion Collider (RHIC) at BNL and the Large Hardon Collider (LHC) at CERN etc., availed an unique way to produce and study the QGP at high temperature and small baryon density whereas the exploration at high baryon density and moderate temperature may be possible in the upcoming compressed baryonic matter experiment (CBM) at GSI with the Facility for the Antiproton and Ion Research (FAIR) and NICA in Dubna. The hot and dense quark matter formed at rHIC lasts for a very short time (a few fm/c), thereby expands and cools beyond the hadronization point, Tc before the i ii freeze-out. Although the existence of the QGP is undoubted, its observation has always been a matter of debate due to the complexity of the scenario and the fact that the direct detection of QGP is not possible. Therefore, a clean and experimentally viable probe which can unambiguously identify the existence of the QGP becomes essential. There are various probes, such as photon and dilepton production, strangeness enhancement, quarkonium suppression, jet quenching, collective flow, fluctuations etc. proposed as the signals to the QGP. The quarkonium suppression was first proposed by Matsui and Satz, where the heavy quark potential is susceptible to the color screening analogous to the Debye screening, hence the in-medium properties of quarkonium are used to study the QGP. Recently the Landau damping is thought to be the main source for quarkonium dissociation, where a light parton of the medium scatters off the resonance by exchanging the space-like gluons and splits the quarkonium into an unbound color octet state. Over the time the quarkonium suppression has been identified as a vital signature for the hot and dense deconfined medium produced in collider and future fixed target experiments, respectively. It is thus worthwhile to study the heavy quarkonium suppression at both finite temperature and density through a complex potential to understand the properties of the QGP in both extreme regions of the QCD phase diagram. The present thesis consists of six chapters and a brief description of each chapter is presented hereafter. In Chapter 1 we have briefly introduced the QCD and the phase transitions associated with quark-hadron phase transition (QHPT), namely chiral symmetry, deconfinement etc. In continuation with, we discuss the theoretical tools, viz. thermodynamics, lattice QCD and hydrodynamics to have a better insight about different aspects of QHPT and a brief summary on various signatures of it. We then give a brief review on the thermal field theory in both real and imaginary time to construct a basis for further studies of thesis works for the study of quarkonium bound states iii in a medium. We then discuss the anisotropy in the momentum space created at the early times of rHIC which is suited to model the evolution of the system before it acquires local thermal equilibrium. Since the understanding of recent theoretical developments is necessary in order to know the progress and paradigm shift in the field so we discuss a bit on those developments, viz. the color glass condensate, AdS/CFT correspondence, classical strongly coupled plasma etc. Finally, we narrate the outline of the thesis. In Chapter 2 we have reviewed the properties of quarkonia in vacuum as well as in medium. We have started with the production and formation of quarkonia and thereafter we canvass the different approaches of how quarkonia can be dealt with either in vacuum or in medium. For example, the bound states can usually be tackled theoretically in two ways: the bound state is either treated nonrelativistically in the Schr¨odinger equation by a heavy quark potential or in a first principle lattice QCD which provides the most straightforward way to determine spectral functions by the lattice correlators. However, one can arrive at the potential by the advent of effective field theory, namely potential nonrelativistic QCD (pNRQCD), which is obtained by integrating out the degrees of freedom associated to the mass and the momentum exchange successively from the underlying theory, QCD.We then move on to the expanding medium in nuclear collisions, where we discuss about various mechanisms, such as cold nuclear matter (CNM) effects, color screening, gluo-dissociation, hot hadron or co-movers dissociation etc., responsible to bring down the quarkonium population during their journey from the formation point to the freeze-out boundary and enhancement through recombination at the hadronization point. Chapter 3 onwards we will discuss about our own work. Earlier the color screening was thought to be the only mechanism of the dissociation but recent studies show an equally important mechanism for dissociation, known as the Landau damping, due to which the width of the resonance state gets broadened and then compel the bound iv state to dissociate earlier even though the medium temperature is not too high to dissociate it. The broadening of width is usually estimated by the imaginary component of the potential. Therefore, in this chapter we have studied the quarkonia in a thermal medium through a complex potential. For that we have first obtained the potential by correcting both perturbative and non-perturbative terms of the Cornell potential through the dielectric function in the real-time formalism, compared to the medium modification of the perturbative term alone as usually done in the literature. We found that the presence of nonvanishing confining nonperturbative term, even above the transition point, Tc causes the real-part of the potential stronger and thus bounds quarkonia more tightly. The confining term also enhances the (magnitude) imaginary-part of the potential and hence contributes more to the thermal width. As a result we have found the ground states survive till the higher temperatures. We then extend our calculations to a medium which exhibits a local momentum anisotropy and calculate the leading anisotropic corrections to the HTL self-energy and propagators of quarks and gluons in Keldysh representation to finally obtain the potential. We observed that the presence of anisotropy makes the real part of the potential more stronger whereas the imaginary part becomes slightly weaker. As a result, the anisotropy push the dissociation point towards the higher side compared to the isotropic medium. Chapter 4: In the previous chapter we have investigated how do the remnants of confining force beyond the deconfinment temperature and the presence of momentum anisotropy affect the properties of quarkonia in isotropic as well as in anisotropic medium. With these understandings, we aim to study the dynamical suppression of bottomonium states in relativistic heavy-ion collision at LHC energy as functions of centrality, rapidity, transverse momentum in this chapter. For this purpose we have first solved the Schr¨odinger equation with the complex potential obtained in chapter 3 to obtain the dissociation temperatures for all bottomonium states in family. Since the bottomonium states are produced at very early times where the system v is yet to achieve equilibrium locally so pre equilibrium (anisotropic) evolution needs to be incorporated. Moreover, the bottomonium states are suppressed at very high temperatures which corresponds to very early times of the expansion so the Bjorken picture suits well. Therefore, secondly we model the expansion of medium by the Bjorken hydrodynamics in the presence of both shear and bulk viscosities followed by an additional pre-equilibrium anisotropic evolution. Finally we couple them together to quantify the yields of bottomonium production in nucleus-nucleus collisions at LHC energies and found a better agreement with the CMS data. Our estimate of the inclusive (1S) production indirectly constrains both the uncertainties in isotropization time as well as the shear-to-entropy density ratio, which are found to be 0.3 fm/c and 0.3, respectively. Chapter 5: In previous chapters we probe the phase diagram of QCD at high temperature and very low baryon density regime by the heavy quarkonia. The other extreme regime of the phase diagram, i.e., low temperature and high baryon density is rarely studied theoretically as well as experimentally, thus in this chapter we aim to probe the high baryon density regime by studying the change of properties of quarkonia. The motivation also arises from the prospect of CBM experiment at FAIR (GSI) which is planned to produce the baryon-rich QCD matter and its detection. For the purpose we have generalized our framework developed in the chapter 3 to both finite temperature and finite chemical potential. This happens through the generalization of the Debye mass which now depends not only on the temperature but also on the baryon chemical potential (μ), i.e., mD(T, μ), which, in turn, makes the potential both temperature and chemical potential dependent. Moreover, the potential at finite chemical potential develops an imaginary component, hence the width of the physical (quarkonium) resonances in medium also become temperature- and chemical potential-dependent (􀀀(T, μ). However, we found that in high baryon density limit, the effect of the width, 􀀀(T, μ) on the quarkonia properties is very meagre. Therefore, we explore the properties of quarkonia in high baryon density regime using the real vi part of the potential only. As a result the binding energy becomes temperature- and chemical potential-dependent and then we estimate the dissociation points in high baryon density and low temperature regime of the phase diagram, namely the J/ψ’s are dissociated at baryon chemical potentials, 1611 MeV and 1560 MeV in the system at very low temperatures, T= 40 and 50 MeV, respectively. Thus, our study of dissociation of quarkonia states may help indirectly to trace out the upper limits (T, μ) on the QCD phase diagram where the nuclear matter may undergo to baryon rich QGP. This proposition may be verified in the future experiment at FAIR energies. Finally, in Chapter 6 we present a summary and conclusions drawn from the entire work and finally, some insights in this area for future research work are discussed.