QUARKONIUM SUPPRESSION IN NUCLEUS-NUCLEUS COLLISIONS

Abstract

Statistical quantum chromodynamics predicts that at sufficiently high densities or temperatures the quarks and gluons confined inside the hadrons undergo a deconfining phase transition to a plasma of quarks and gluons, known as quark-gluon plasma (QGP). Experimental attempts to create the QGP in the laboratory and measure its properties have been carried out for more than 30 years by studying collisions of heavy nuclei at CERN SPS, BNL RHIC and CERN LHC and analyzing the fragments and produced particles emanating from such collisions. Strong confirmations arise from recent observations at RHIC of large anisotropic flow of all hadronic species and of a suppression of high-PT hadrons due to parton energy loss in the dense medium. Signatures of direct photon emission, as well as preliminary results on (excess) dilepton production in such collisions, indicative of a hot early state, have also started emerging. The present thesis comprises six chapters which will be discussed now. In Chapter 1, we have reviewed the current status of our understanding regarding the properties of QGP with a brief introduction of QCD and various theoretical tools e.g. lattice QCD and its predictions, QCD thermodynamics, and hydrodynamics etc. which are being used to understand the different aspects of quark-hadron phase transition. Also we briefly summarize the various signatures of QGP and some latest developments in ii QGP such as color glass condensate, AdS/CFT correspondence, etc., to understand the paradigm shift in the field due to RHIC discovery of QGP as a strongly-coupled liquid, unlike a weakly interacting gas. J///) suppression which is considered as a possible signal of QGP has been mea-sured by the different experiments. But understanding the data turned out to be complicated because the suppression pattern seen is not due to single effects, but more likely due to interplay of many effects. The heavy quark pairs are produced in the very early stage of the collisions and then develops into the physical resonance and traverses the plasma and (later) the hadronic matter before leaving the interacting system to decay into a dimuon to be detected. Even before the resonance is formed it may be absorbed by the nucleons streaming past it. By the time the resonance is formed, the screening of the color forces in the plasma may be sufficient to inhibit a binding of the ca Or an energetic gluon or a comoving hadron could dissociate the resonance(s). In order to disentangle different effects, first we have reviewed the basic properties of quarkonia and following this, we considered the main theoretical features of quarkonium production and subsequent interactions in nucleon-nucleon, nucleon-nucleus and nucleus-nucleus collisions in chronological order in Chapter 2. We then continued to survey the different approaches to quarkonium dissociation in static as well as in expanding hot medium produced in a relativistic nucleus-nucleus collisions, giving rise to the transverse momentum and the centrality dependence of quarkonium suppression. Quarkonia at finite temperature are an important tool for the study of quark-gluon plasma formation in heavy ion collisions. The short and intermediate distance properties of the heavy quark interaction is important for the understanding of in-medium modifications of the heavy quark bound states. None of the potential model studies and spectral functions in lattice give a complete framework to study the properties of quarkonia at finite temperature. On the other hand, the large distance behavior plays a crucial role in understanding the bulk properties of the QCD plasma phase e.g. the screening property of the QGP, the equation of state etc. In all of iii these studies, deviations from perturbative calculations and the ideal gas behavior are found at temperatures much larger than the deconfinement temperature. This calls for non-perturbative calculations. Moreover, the phase transition in full QCD appears as a crossover rather than a 'true' phase transition with related singularities in thermodynamic observables. So, in the sequel, the string tension should not vanish abruptly at the deconfinement temperature. So one should study its effects on the behavior of quarkonia in a hot QCD medium. In Chapter 3, we have derived the medium-modified potential by correcting the full Cornell potential with a dielectric function embodying the effects of deconfined medium and not its Coulomb part alone as usually done in the literature. This causes a dynamical screening of color charge which in turn, leads to a temperature-dependent binding energy which have been further studied systematically in gluonic, 2-flavor and 3-flavor QCD medium. We have then determined the dissociation temperatures by employing the Debye masses in leading-order (perturbative) result (min as well as the lattice parametrized form mf3 by extracting from the (lattice) free energy asymptotics. Our estimates of upper bound on dissociation temperatures are consistent with the finding of recent theoreti-cal works based on lattice-based potential models as well as lattice correlator studies. In contrast, the inclusion of nonperturbative contributions to the Debye mass lowers the dissociation temperatures substantially which looks unfeasible. In brief, the up-per bound of dissociation temperature of J/0 is found to be 1.7 7', and 1.2 7', when the Debye masses employed in the effective potential is the leading order perturbative term and the lattice parametrized form, respectively. Similarly, for 1pf , the respective values are 1.2 7-1, and 0.8 For T, the corresponding values are 2.2 7', and 1.6 7',, and 1.6 71, and 1.1 7', for T', respectively. In this chapter, we have also studied the temperature dependence of the binding energies of xc and Xb states by incorporat-ing the corrections coming from the spin and angular momentum dependent terms to the binding energies of O' and T' states, respectively by adopting a variational treatment of the relativistic two-fermion bound-state system. It is found that xc's are dissociated at 1.17',, 1.317',, and 1.267', for the pure, 2-flavor, and 3-flavor QCD, iv respectively whereas Xb's are dissociated at a comparatively much higher temperature with the Debye mass up to the leading-order. On the other hand, our estimates for x, and Xb with the lattice parametrized Debye mass are consistent with the finding of recent works based on potential models. Thus, this study provides us a handle to decipher the extent up to which nonperturbative effects should be incorporated into the Debye mass. In a relativistic nucleus-nucleus collision, QGP is formed at an initial time Ti and have started expanding according to Bjorken's boost invariant hydrodynamic expan-sion. There are many attempts to study charmonium suppression by incorporating the plasma expansion dynamics, but some important points in their calculations were too naive to take account real situations: i) The equation of state employed in the earlier works was either ideal or bag model equation of state and these equations of state were used to calculate the screening energy density es (corresponding to the dis-sociation temperature of a particular resonance) and the screening time up to which a particular state is suppressed during the hydrodynamic expansion. Since we have already learned from the (large) elliptic flow at RHIC, the non-ideal behavior seen in lattice equation of state, etc. that the matter formed is far from its ideal limit even at T > ii) The effects of dissipative forces were not included in the expansion which cause the plasma to expand slowly resulting in more suppression. Chapter 4 is mainly focussed around these important points and their possible remedies. In this chapter, first we use an appropriate equation of state (EoS) which should reproduce the lattice results verifying the strongly-interacting nature of QGP. Secondly with this equation of state as an input, we study the Bjorken boost-invariant expansion in (1 + 1) dimension by including the effects of dissipative terms (only the shear viscos-ity) up to the first-order in the stress-tensor. Thirdly the most important point is to know the properties of quarkonia in a strongly interacting medium by encoding in a medium-modified potential and to calculate the dissociation temperatures. This was already done in Chapter 3 and so we have borrowed the results from Chapter 3. Fi-nally we studied the survival of charmonium states with all the refinements discussed V above in an expanding, strongly interacting QCD medium, produced in nuclear colli-sions and found a nice agreement with the recent experimental results at RHIC. We also come to know the dependence of various parameters on the suppression pattern. In Chapter 5 we have developed an equation of state for a strongly interacting quark-gluon plasma in the framework of strongly-coupled electric plasma by incorpo-rating the non-perturbative effects through the Debye mass and also by retaining the string tension even in the deconfined plasma phase, unlike the Coulomb interactions alone. Our results on thermodynamic observables viz. pressure, energy density, speed of sound, etc., nicely fit with the lattice equation of state for gluon, massless and as well massive flavored plasma. Motivated by this agreement with lattice results, we have employed our equation of state to estimate the quarkonium suppression in an expanding, dissipative strongly interacting QGP produced in relativistic heavy-ion collisions and our prediction matches exactly with the recent PHENIX data on: thecentrality dependence of J/0 suppression in Au+Au collisions at BNL RHIC. We have also predicted for the T suppression in Pb+Pb collisions at LHC energy which could be tested cleanly in the ALICE experiments at CERN LHC. Chapter 6 contains an overall summary and concl