# Presentation: 252039

## Can Quarkonia Survive Deconfinement? 

- Ágnes Mócsy

## Content of This Talk

- what motivated this work
- our approach to determine quarkonium properties
- quarkonia in a gluon plasma
- quarkonia in a quark-gluon plasma
- upper limits on dissociation temperatures

- Á. Mócsy, P. Petreczky 0705.2559[hep-ph]
-                                     0706.2183[hep-ph]

- what motivated this work

## Introduction

- Quarkonium properties at high T interesting
-  proposed signal of deconfinement Matsui,Satz, PLB 86
-  matter thermometer Karsch,Mehr,Satz, ZPhysC 88
-  possibility of bound states in deconfined medium Shuryak,Zahed PRD 04

- Need to calculate quarkonium spectral function because
-  quarkonium well defined at T=0, but can broaden at finite T
-  spectral function contains all information about a given channel:
-  unified treatment of bound states, threshold, continuum
-  can be related to experiments

**Notes:**
T=0 qq well defined - width smaller compared to binding energy . at T will become broader and when
 it is large enough than we should switch from talking instead about individual states rather about spectral function.  

## “J/ survival” in LQCD 

- Conclusions drawn from analysis of lattice data:
-  J/ and c survive up to 2 Tc  “quarkonium survival”
-  c melts by 1.1 Tc
-  b melts by 1.1 Tc “b puzzle”
- based on spectral functions from MEM and (un)modifications of G/Grec

- Asakawa, Hatsuda, PRL 04

- Datta, Karsch, Petreczky, Wetzorke PRD 04

- Jakovác,Petreczky,Petrov,Velytsky, PRD 07

- Aarts, Allton, Oktay, Peardon, Skullerud hep-lat/0705.2198

- Spectral Functions

- Correlators

*see talk by Péter Petreczky*

## “J/ survival” in Potential Models

- Shuryak,Zahed PRD 04
- Wong, PRC 05
- Alberico et al PRD 05
- Cabrera, Rapp 06
- Alberico et al PRD 07
- Wong,Crater PRD 07

- series of potential model studies

- with potentials connected to lattice free and internal energy

- Conclusions
-  states survive
-  dissociation temperatures quoted
-  agreement with lattice is claimed

- Wong,Crater, PRD 07

**Notes:**
many attempts made to connect

## Our Initial Attempt

- correlators calculated in this approach do not agree with lattice

- use a simplified model:  discrete bound states + perturbative continuum

- What is the source of these inconsistencies?
- validity of potential models?
- finding the right potential?
- relevance of screening for quarkonia dissociation?

- Mócsy,Petreczky EJPC 05
-                             PRD 06

- model

- lattice

- our recent approach to determine quarkonium properties

## Spectral Function 

-  bound states/resonances        &

-  continuum above threshold

- nonrelativistic Green’s function

-  ~ MJ/ , s0  nonrelativistic

- S-wave

- P-wave

- medium effects - important near threshold

- PDG 06

-    re-sum ladder diagrams

- first in vector channel Strassler,Peskin PRD 91
-                 also Casalderrey-Solana,Shuryak 04

- S-wave also Cabrera,Rapp 07

**Notes:**
close to the threshold q and antiq move slowly - there is enough time for multiple gluon exchanges 
since an extra Coulomb gluon exchange is not suppressed by alpha we need to resum ladder diagrams
resummation done separately in PS and S channels . but in both cases it reduces to solving scr eq for NR green fct

## Spectral Function

-   s0   perturbative

-  bound states/resonances        &

-  continuum above threshold

- nonrelativistic Green’s function

-  ~ MJ/ , s0  nonrelativistic

- PDG 06

- PDG 06

**Notes:**
high energies NR treatment breaks down , but away from threshold perturbative treatment 

## Spectral Function

- Unified treatment: bound- and scattering states, threshold effects
-                                       together with relativistic perturbative continuum

-  bound states/resonances        &

-  continuum above threshold

-   s0   perturbative

-  ~ MJ/ , s0  nonrelativistic

- smooth matching
- details do not influence the result

- nonrelativistic Green’s function + pQCD

- PDG 06

**Notes:**
the nr spf has been smoothly matched onto the perturb relativistic form  
the details of the matching do not influence the results . 
perfect for studying quarkonium properties in medium

## Potential at T=0 

-  T0  hierarchy of energy scales

- T=0 potential can be derived

- Brambilla et al, CERN Yellow Report 05

- Cornell potential

-  describes quarkonium spectra
-  confirmed on lattice

## Constructing the Potential at T>Tc

- Constructing the Potential at T>Tc

- Potential assumed to share general features with the* *free energy

- also motivated by Megías,Arriola,Salcedo PRD07

- strong screening effects_x0003__x0016_

- Free energy - contains negative entropy contribution
-                     - provides a lower limit for the potential

*see talk by Péter Petreczky*

- T>0 potential is unknown: use a phenomenological potential constrained by lattice data

- subtract entropy

**Notes:**
and a potential that is physically motivated. 
what we know is F1 
of static Q-Qbar pair in deconfined phase

- quarkonia in a gluon plasma

## S-wave Charmonium in Gluon Plasma

- resonance-like structures disappear already by 1.2Tc
- strong threshold enhancement
- contradicts previous claims

- higher excited states gone
- continuum shifted
- 1S becomes a threshold enhancement

- Mócsy, Petre_x0010_czky hep-ph/0705.2559

- c

**Notes:**
this finding

## S-wave Charmonium in Gluon Plasma

-  resonance-like structures disappear already by 1.2Tc
-  strong threshold enhancement above free case       indication of correlation
-  height of bump in lattice and model are similar

- Mócsy, Petre_x0010_czky hep-ph/0705.2559

**Notes:**
this finidng contradicts 

## S-wave Charmonium in Gluon Plasma

- Mócsy, Petre_x0010_czky hep-ph/0705.2559

- spectral function unchanged across deconfinement

- LQCD measures correlators

**N.B.: 1st time**
**2% agreement between model and lattice correlators for all states at T=0 and T>T****c**
**Unchanged LQCD correlators do not imply quarkonia survival: Lattice data consistent with charmonium dissolution just above T****c**

- or... integrated area under spectral function unchanged

**Notes:**
this finidng contradicts 
the area under the peak 

## Agreement for P-wave as well

- so look at the derivative

- following Umeda 07

- constant contribution in the correlator at finite T

- quark number susceptibility

- 1.5 Tc

- Threshold enhancement of spf compensates for dissolution of states
- Agreement with lattice data for scalar charmonium and bottomonium
*** ****b** “puzzle” resolved*

- c

- b

## P-wave

- >>

- deconfined

- confined

- in free theory

- behavior explained using ideal gas expression for susceptibilities:
-  indicates deconfined heavy quarks carry the quark-number at 1.5 Tc

- charm
- 1.5 Tc

- bottom
- 1.5 Tc

- quarkonia in a quark-gluon plasma

## S-wave Quarkonium in QGP

-  J/ at 1.1Tc is just a threshold enhancement
-  (1S) survives up to ~2Tc with unchanged peak position,
-                                               but reduced binding energy
-  Strong enhancement in threshold region - Q and antiQ remain correlated

- J/

- 

- upper limits on dissociation temperatures

## Most Binding Potential

- need strongest confining effects = largest possible rmed

- Find upper limit for binding

- rmed = distance where
- exponential screening
- sets in

- NOTE: uncertainty in potential - have a choice for rmed or V∞
-             our choices physically motivated
-             all yield agreement with correlator data

## Binding Energy Upper Limits

- Upsilon remains strongly bound up to 1.6Tc
- Other states are weakly bound above 1.2Tc

- When binding energy drops below T
-  state is weakly bound
-  thermal fluctuations can destroy the resonance

## Thermal Dissociation Widths 

- for strong binding Ebin>T

- Thermal Dissociation Widths

- Rate of escape into the continuum due to thermal activation
-               = thermal width   related to the binding energy

-  Kharzeev, McLerran, Satz PLB 95

## Can Quarkonia Survive? 

- Upper bounds on dissociation temperatures
- condition: thermal width > 2x binding energy

## Conclusions

- Quarkonium spectral functions can be calculated within a potential model
- with screening - reliable description of quarkonium dissociation at high T
- Lattice correlators have been explained correctly for the 1st time
- Unchanged correlators do not imply quarkonia survival: **lattice data are consistent with charmonium dissolution just above T****c**
- Contrary to previous statements, we find that all states except  and b are dissolved by at most 1.3 Tc
- Threshold enhancement found: spectral function enhanced over free propagation =>> correlations between Q-antiQ may remain strong
- Outlook
- Implications for heavy-ion phenomenology need to be considered

## ****The END****