1. Quarkonium Dissociation Temperature in Hot QCD medium within a quasi-particle model

2. Plan of Presentation  What is Quarkonia  Binding Energy of Quarkonia  Dissociation Temperature of Quarkonia  Conclusions  Results

3. o Quarkonium constituents a quark and its own antiquark ( =, ) o charm (m c ≃ 1.3 GeV) bottom (m b ≃ 4.7 GeV) stable: and M D,B open charm/bottom mesons o They are more tightly bound, with binding energies up to 0.5 to 1.0 Gev. Thus they can survive in a QGP up to temperature above the deconfinement point. Quarkonia

4. o Quarkonia spectroscopy via non-relativistic potential theory confining (“Cornell”) potential for at separation distance r o ‘ɑ’ accounts for the effective coupling between a heavy quark and its antiquark and the σ gives the string coupling ≃ 0.184 GeV 2 o is known as the Coulombic part of the potential and σr is known as the confinement part of the potential o The strength of the Coulombic part decreases with the increase in temperature and at a certain temperature one may ignore it. o It provides a separation between the short-distance Coulombic effects and the long-distance confinement effects that can be useful in understanding the quark/anti-quark force generated by QCD. Quarkonia

5. o r- dependence of the medium modified potential: o For large values of temperature the product will be much greater than o is an increasing function of temperature, the effective charge gets waned as the temperature is increased and finally results in screening of the charge. {Agotiya, Chandra, B.K.Patra,2009} Quarkonia

6. Quasiparticle Description Quasiparticles are emergent phenomena that occur when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in free space. It was proposed to explain the equation of state (EoS) of QGP from lattice gauge theory (LGT) simulation of quantum Chromodynamics (QCD) at finite temperature. This model has been developed to capture all the interaction effects present in hot QCD equations of state in terms of non-interacting quasi-gluons and quasi-quarks having temperature dependent effective fugacities. There are other quasi-particle model but the model that is considered here is “effective fugacity model”. {Chandra, Ravishankar,PRD 2011}

7.  Solve Schrodinger equation using a temperature-dependent heavy quark potential V (r, T)  Calculate quarkonium spectrum directly in finite T lattice QCD Two possibilities Potential Models for Quarkonium Dissociation: Model heavy quark potential (Schwinger model) With screening mass μ (T) = 1/r D (T) With increasing T, screening reduces the range of the potential.

8. The relevant Schrodinger equation now becomes: where is the binding energy of charmonium state i at temperature T.  When it vanishes, the bound state i no longer exists, so that determines the dissociation temperature for that state.

9. Binding Energy of heavy quarkonia  Binding energy of a quarkonium state at zero temperature is defined by the energy difference between the mass of the quarkonium and the open charm/bottom threshold.  Our case, binding energy : Ionization potential Solution of Schrodinger equation : Bohr’s famous formula  Schrodinger Equation for the potential gives the energy eigen values for the ground states and the first excited states for charmonium (J/ψ, ψ’) and bottomonium (ϒ,ϒ’) spectra.

10.  For our analysis we have considered the Debye mass: for pure gauge, for full QCD {Chandra, Ravishankar,PRD 2011} Here the function Poly Log[2,z] having form: Binding Energy of heavy quarkonia

11.  The binding energy becomes a temperature- dependent quantity and it decreases with the temperature.  The study of temperature dependence of binding energy will help us to determine the dissociation temperatures of the quarkonium states in thermal medium. Binding Energy of heavy quarkonia

12. Binding Energy vs. Temperature for different flavors Fig.1:The temperature dependence of J/ψ binding energy in units of critical temperature T c.

13. Fig.2 The temperature dependence of  binding energy in units of critical temperature Tc. Binding Energy vs. Temperature for different flavors

14. Dissociation Temperature for Quarkonia  Spectral function technique in potential models defines the dissociation temperature as the temperature above which the quarkonium spectral function shows no resonance-like structures, meaning that particular state is dissolved.  If the binding energy of a state at some temperature becomes smaller than the mean thermal energy then the state is said to be dissociated into its constituents.  Since the (relativistic) thermal energy of the partons is 3T. Hence the lower bound on the dissociation temperature T D is obtained from the relation { Agotiya, Chandra, B.K.Patra,2009 }

15. TABLE 1: Lower (Upper) bound on the dissociation temperature ( ) for the quarkonia states (in units of ) for fugacity = 0. 3 StatePure QCD = 2 = 3 J/ ψ 2.3 (2.7)2.4 (3.2)2.3 (3.0) Ψ’Ψ’ 1.6 (2.1)1.7 (2.3)1.7 (2.2) ϒ 2.9 (3.8)3.0 (4.1)3.8 (3.8) ϒ’ϒ’ 2.1 (2.8)2.3 (3.0)2.2 (2.8) TABLE 2: Lower(Upper) bound on the dissociation temperature ( ) for the quarkonia states (in units of ) for fugacity = 0.7 StatePure QCD = 2 = 3 J/ ψ 1.4 (1.8)1.5 (2.0) Ψ’Ψ’ 1.0 (1.3)1.3 (1.4)1.1 (1.4) ϒ 1.8 (2.4)2.0 (2.6)2.0 (2.5) ϒ’ϒ’ 1.3 (1.7)1.4 (1.9)1.4 (1.8)

16. Conclusion and Results  We have studied the dissociation phenomena of quarkonia in hot QCD medium by using the in-medium modifications to heavy quark potential (Cornell potential).  We have then studied the temperature dependence of the binding energy of the ground (1S) state of charmonium and bottomonium in the pure and realistic QCD medium.  We have then determined the dissociation temperatures of quarkonia in hot QCD medium.

18. Quarkonium Dissociation in QCD Thermodynamics  Heavy quark Binding in Media In vacuum The free energy of the pair have the string form: F(r) ~σr F(r) increases with separation distance and break the string and form two light-heavy mesons ( ) and ( ). String breaking energy for charm quarks is found to be: For the bottom quarks the value will be:

19.  In medium (0<T) The medium begins to contain light mesons, and the large distance potential F decreases, These light hadrons achieve an earlier string breaking through a kind of flip-flop recoupling of quark constituents, resulting a effective screening of the interquark force Increasing T increases hadron density, consequently lowers dissociation energy.  In medium, above Light quarks and gluons become deconfined colour charges, and this quark-gluon plasma leads to a color screening Color screening radius determines range of force Dissociation distance and energy decrease further with ‘T’.

20. The running coupling constant for two loop is determine by