# Presentation: 716750

## Charmonium dissociation temperaturesin lattice QCD with a finite volume technique

- Charmonium dissociation temperaturesin lattice QCD with a finite volume technique

- Takashi Umeda
- for the WHOT-QCD Collaboration

*Quark Matter 2008, Jaipur  India , 4-10 Feb. 2008*

- T.Umeda (Tsukuba)

- QM2008

## Introduction

*PRL70, 383, (1993).*

- 10%

- 30%

- 60%

*Introduction*

- Charmonium dissociation temperatures, Tdis, play
- important role in discussion on J/ψ suppression scenarios

- Recently, Sequential J/ψ suppression scenario is often discussed

- We investigate Tdis for J/ψ, ψ(2S), χc etc...
-         using Finite Temperature Lattice QCD simulations

- AA collisions

- J/ψ

- ψ’

- χc

- T.Umeda (Tsukuba)

- QM2008

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

## Current status on Tdis

-  Lattice QCD studies ( by MEM analysis ) suggest
-      - J/ψ state may survive up to T=1.5Tc or higher
-      - χc states may dissolve just above Tc
-           *e.g. A.Jakovac et al. (2007)*
-      - no results on excited states, ψ’
-  The 2nd statement may be misleading (!)
-       small change even in P-wave state
-       up to 1.4Tc w/o the constant mode
-  On the other hand, the potential model studies
-      suggest charmonium dissociation may also
-      provide small change in the correlators
-            *e.g. A.Mocsy et al. (2007)*
- Therefore we would like to investigate Tdis
-             using new approaches with Lattice QCD

- Fig: Temp. dependence
- of Meff(t) for J/ψ, χc1
- w/o constant mode.
*   **T.Umeda (2007)*

- χc1

- J/ψ

- T.Umeda (Tsukuba)

- QM2008

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

## Spectral functions in finite volume

- In a finite volume of (La)3,  momenta are discretized
-                                                              for the periodic BC

- Lattice QCD simulations are performed in a finite volume

- In a finite volume, discrete spectra does not always indicate bound states !

- T.Umeda (Tsukuba)

- QM2008

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

## bound state or scattering state ?

*bound state or scattering state ?*

-  Volume dependence

-  Boundary Condition (B.C.) dep.

-  Wave function

- We know three ways to identify the state in a finite volume

- We will demonstrate these Tests using Finite Temp. Lattice QCD

- T.Umeda (Tsukuba)

- QM2008

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

## Lattice setup

-  Quenched approximation ( no dynamical quark effect )
-  Anisotropic lattices
-      lattice spacing :  as = 0.0970(5) fm
-      anisotropy :       as/at = 4
-  Quark mass
-      charm quark (tuned with J/ψ mass)
-  Variational analysis with 6 x 6 correlation matrix

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- t

- x,y,z

- T.Umeda (Tsukuba)

- QM2008

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

## (1) B.C. dependence

*The idea has been originally applied for the charmonium study*
*    **in  H. Iida et al., PRD74, 074502 (2006).*

- r

- scattering

- 0

- The wave functions are localized,
- their energies are insensitive to B.C.

- The momenta depends on BC,
- the scattering state energies
-           are sensitive to B.C.

- T.Umeda (Tsukuba)

- QM2008

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

## Test with free quarks

- The free quarks make the trivial scattering states
-          testing our method ( 6 x 6 variational analysis )

- We prepare 3 types of B.C. for charm quarks
-    (1) Periodic B.C.
-    (2) Anti-Periodic B.C.
-    (3) Hybrid B.C.

- (free quarks with L/a=20, ma=0.17)

- PBC

- APBC

- HBC

- Ps
-  &
- Ve

- Sc
-  &
- Av

- HBC

- APBC

- PBC

- T.Umeda (Tsukuba)

- QM2008

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

## Quenched QCD results

-  No significant differences in the different B.C.
-  Lowest energies increase as T increases ( thermal quark mass ? )

- Lowest states
- in each channel
-     Ps : ηc
-     Ve : J/ψ
-     Sc : χc0
-     Av : χc1

- T.Umeda (Tsukuba)

- QM2008

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

## (2) Wave function

- Temperature dependence of
-      “Wave function” ( Bethe-Salpeter amplitude )

- Test with free quarks ( Ls/a=20, ma=0.17 )

- ( ! )  In this talk only
- S-wave state results
- will be presented.

-  Free quarks make Plane waves with
-          an allowed momentum in a box
-  The wave function is constructed with
-     eigen functions of 6 x 6 correlators
-  Our method well reproduces
- 	   the Plane wave solutions ( ! )

- T.Umeda (Tsukuba)

- QM2008

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

## (2) Wave function

*(2) Wave function*

-  No indication of scattering state up to 2.3Tc ( ! )
-  Ve results show the same behavior as the Ps results

- T.Umeda (Tsukuba)

- QM2008

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

## (3) Volume dependence of WF

- Volume dependence at T=2.3Tc

-  Clear signals for 1S and 2S bound states even at T=2.3Tc ( ! )
-  V = ( 2 fm )3 is fairly large for 1S and 2S charmonium

- ηc(1S)

- ηc(2S)

- J/ψ(1S)

- ψ(2S)

- T.Umeda (Tsukuba)

- QM2008

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

## Summary

- We investigated Tdis of charmonia from Lattice QCD
-      using the finite volume technique
- 	- boundary condition dependence of charmonium spectra
- 	- Temp. dependence of charmonium wave functions
- 	- Volume dependence of wave functions at T=2.3Tc
-     We can find no evidence for scattering state
- 	of charm quarks up to T = 2.3 Tc

*Future plan*

-  Discussion on the experimental results of J/ψ suppression
-  P-wave states wave functions
-  Full QCD calculations  ( Nf=2+1 Wilson is in progress )

- T.Umeda (Tsukuba)

- QM2008

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

## Volume dependence at T=2.3Tc

- Expected volume dep.
- in free quark case

- lowest on PBC

- next-lowest on PBC

- lowest on APBC
-               (HBC)

- next-lowest
-      on APBC (HBC)

-  Unlike the trivial scattering state (free quarks) behavior
-  No good quality results in P-wave states

- T.Umeda (Tsukuba)

- QM2008

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