# Presentation: 728015

##  Quarkonium states at finite temperature 

** ****Quarkonium states at finite temperature **

- Takashi Umeda (BNL)

***           ******Hard Probes 2006***
*June 9-16, 2006,  Asilomar Conference Grounds*
*                            **Pacific Grove, California*

- Hard Probes 2006

## The aim of this talk 

-   In the QGP phase, heavy quarkonium states exist or not ?
-   If it exists, what temperature does it dissolve at ?
-   First principle calculation is possible by Lattice QCD,
-       but it is applicable for only rather ideal system, for example,
-   thermal equilibrium,
-   homogeneous in finite volume with periodic b.c.,
-   etc...

- Some of them are different from that of actual experiments.

- Hard Probes 2006

**Notes:**
Against our expectations, recent results...

## Contents

-   Introduction
-   I.  Spectral function (SPF) of charmonium at T>0
- 	- How to calculate SPFs on lattice
- 	- Maximum Entropy Method
- 	- Numerical results
-   II.  Wave function
- 	- t-dependence of Wave function at T>0
- 	- Numerical results
-   Summary

- Hard Probes 2006

**Notes:**
Most of this talk is not so recent studies

## part-I : Spectral function

*from “An Introduction to Quantum Field Theory” *
*             **Michael E. Peskin,  Perseus books (1995)*

- Hard Probes 2006

**Notes:**
Most of this talk is not so recent studies

## How to calculate the SPFs on lattice

- Thermal hadron correlation function ( T: temperature )

- Spectral function

- “Inverse problem”

- usually, brute force χ2 analysis fails
- (ill-posed problem)

-  Furthermore, in T>0 lattice QCD,

- where

- T=0

- T>0

- Hard Probes 2006

**Notes:**
Most of this talk is not so recent studies

## Maximum Entropy Method

- L : Likelihood function ( χ2 term)

- m(w) : default model func.

*M.Asakawa et al. *
*Prog.Part.Nucl.Phys.46(2001) 459*

- MEM (based on Bayes’ theorem)
-    searches for the most probable shape of SPFs
-    by maximization of

-   Result depends on the default model function
-   At high temperature
-        it is difficult to check the reliability even if MEM works.
-          melting of bound state?  simple failure of MEM?

- α: parameter  integrated out with a prior prob.

- Hard Probes 2006

**Notes:**
Most of this talk is not so recent studies

## Papers for charmonium SPFs at T>0

-  Umeda, Matsufuru and Nomura (quenched QCD)
- 	T.Umeda et al, Eur.Phys.J.C37S1 (2004) 9.(hep-lat/0211003)
-  Bielefeld group (quenched QCD)
-              S.Datta et al., Phys.Rev.D69(2004)094507.
-  Asakawa and Hatsuda (quenched QCD)
- 	M.Asakawa and T.Hatsuda, Phys. Rev. Lett. 92 (2004) 012001
-  Trin-lat group (2-flavors QCD )
- 	R.Morrin et al., hep-lat/0509115  (Lattice’05)
-  others

- All studies supports existence of J/ψ at not so high-Temp.

- Hard Probes 2006

**Notes:**
Most of this talk is not so recent studies

## Results by T.Umeda et al.

- T<Tc  :  no mass shift,  almost same SPF as T=0
- T>Tc  :  peak structure survives up to 1.2Tc (?)

- ηc :  up to 1.4Tc,   J/ψ : up to 1.2Tc  (at least)

- J/ψ below Tc

- J/ψ above Tc

- lattice unit 1/a=8GeV

- Hard Probes 2006

**Notes:**
Most of this talk is not so recent studies

## Bielefeld group results

-  J/ψ, ηc states survive up to 2.25Tc
-  χc state may dissolve just above Tc

- J/ψ above Tc

- χc above Tc

- (in pp collisions, about 40% of J/ψ production
-   comes from decay of the excited states χc and ψ’)

- Hard Probes 2006

**Notes:**
Most of this talk is not so recent studies

## Hatsuda & Asakawa result

- SPF has peak at
-      the same place as T=0
-      up to 1.6Tc
-      for J/ψ& ηc channels

- J/ψ below & above Tc

- Hard Probes 2006

**Notes:**
Most of this talk is not so recent studies

## Summary for spectral functions

-  From these charmonium SPFs results,
-   J/ψ, ηc states survive even in QGP phase
-   Dissociation temp. may be 1.4~2 Tc  (large uncertainty)
-   χc state may disappear just above Tc

-  Many problems remain...
-   Most studies does not include dynamical quark effects
-   Reliability of the results at high temperature is not so good
- At present we have only qualitative results !!

- Hard Probes 2006

**Notes:**
Most of this talk is not so recent studies

## part-II :  Wave function

*Charmonium wave functions at zero temperature*
*             **from QCD-TARO Collab., JHEP 0308 (2003) 022.*

- Hard Probes 2006

**Notes:**
Most of this talk is not so recent studies

## Wave function

-          spatial correlation of c-bar{c} in QGP

- : Wave function
-   (BS amp. in Coulomb gauge)

- : normalized ωΓ(r,t) at spatial origin

- When the wave function spreads out like free quarks,
-            φ(r,t) has gentle slope at large t.

- Hard Probes 2006

## Wave function

-          spatial correlation of c-bar{c} in QGP

- c-bar{c} has strong
- spatial correlation
- even at T=1.5Tc

*T.Umeda et al. *
*Int.J.Mod.Phy.A16(2001)2215*

- : Wave function
-   (BS amp. in Coulomb gauge)

- : normalized ωΓ(r,t) at spatial origin

- Hard Probes 2006

## Summary of this talk

- Next step

-  From recent MEM results,
-        J/ψ, ηc states survive even in QGP phase
-        dissociation temp. may be 1.4~2 Tc  (large uncertainty)
-        χc state may disappear just above Tc
-  Wave function shows
-         strong spatial correlation even at T=1.5Tc

-  Improvement of MEM analysis
-                  & dynamical quark effects
-  New ideas ...

- Hard Probes 2006