# Presentation: 080697

## A constant contribution in meson correlators               at finite temperature

- A constant contribution in meson correlators               at finite temperature

- Takashi Umeda (BNL)

*Riken Lunch Seminar, BNL, Jan. 25, 2007*

- This talk is based on the hep-lat/0701005.

- T.Umeda (BNL)

- Riken Lunch Seminar

## Contents

-   Introduction
- 	- J/ψ suppression and charmonium states
- 	- constant contribution in meson correlators
-   Free quark calculations
- 	- meson-like correlators
- 	- analyses to avoid the constant contribution
-   Quenched QCD calculations at finite temperature
- 	- lattice setup
- 	- Numerical results
-   Discussion & summary

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Introduction

- Charmonium properties at T>0 play the key role
-    for understanding the QGP formation in Heavy Ion Collis. exp.

- Potential model analysis
- 	Mass shift near Tc    *T. Hashimoto et al., PRL57, 2123 (1986).*
- 	J/ψ suppression      *T. Matsui & H. Satz, PLB178, 416 (1986).*
- Spectral function in lattice QCD
- 	*T. Umeda et al., EPJC39S1, 9, (2005).*
*	**S. Datta et al., PRD69, 094507, (2004).*
*	**T. Hatsuda & M. Asakawa, PRL92, 012001, (2004).*
*	**A. Jakovac et al., hep-lat/0611017.*
*	**G. Aarts et al., hep-lat/0610065.*

- In the studies of SPFs on the lattice,
-   all studies indicate survival of J/ψ state above Tc (1.5Tc?)

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Introduction

- Recently “indirect J/ψ suppression” is discussed.
-      total yield of J/ψ =
-           direct production of J/ψ ( 60% )
-             + decay from higher states, ψ’ & χc (40%)
-            *L. Antoniazzi et al. (E705 Collab.), PRL70, 383, (1993).*
-     If the higher states dissociate at lower temp.
-           a part of the J/ψ suppression may be observed
-                in exp. at a lower temp. than that of J/ψ

- Dissociation temperatures of these states
-          (not only J/ψ but also ψ’& χc)
-          are important for QGP phenomenology.

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Constant contribution  

-   Pentaquark (KN state):
-    two pion state:
-           Dirichlet b.c.
*c.f. **T.T.Takahashi et al.,*
*    **PRD71, 114509 (2005).*

- exp(-mqt) x exp(-mqt)
- = exp(-2mqt)

- exp(-mqt) x exp(-mq(Lt-t))
- = exp(-mqLt)

- mq is quark mass
-    or single quark energy

- Lt is 1/T

-  in imaginary time formalism
-     gauge field : periodic b.c.
-     quark field : anti-periodic b.c.
-  in confined phase: mq is infinite
-    the effect appears
-             only in deconfined phase

- Now we consider the meson correlator with p=0 & mq1=mq2

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Free quark calculations

- for Ps, V, S and Av channels

-  163 x 32 isotropic lattice
-  Wilson quark action
-       with mqa = 0.2

- Obvious constant contribution
-     in P-wave states

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Effective mass (local mass)

- Definition of effective mass

-  for S-wave states:
-      lowest state energy is 2Eq(p=0)
-       where Eq(p=0) = ln(mq+1)
-  for P-wave states:
-      lowest state energy is 2Eq(p=pmin)
-       where pmin=2π/Ls
- free Wilson quark dispersion relation

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Free quark calculations

- Continuum form of the correlators
-                       *calculated by S. Sasaki*

-    : single quark energy with relative mom. p

- where

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Spectral representation

- Spectral function of the correlator

- with

*F. Karsch et al., *
*      **PRD68, 014504 (2003).*
*G. Aarts et al.,*
*      **NPB726, 93 (2005).*

- chiral symmetry in massless limit

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Physical interpretation

- constant contribution remains
- in the continuum form & infinite volume

- The constant term is related to some transport coefficients.

- From Kubo-formula, for example, a derivative of the SPF
- in the V channel is related to the electrical conductivity σ.

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Volume dependence

- Size of the constant contribution depends on the volume Ns3

- The dependence is negligible at Ns/Nt ≳ 2

-  Results on 963 x 32
-         ( Ns/Nt=3  similar to T>0 quench QCD calculation )

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Removing constant contrib. (1)

- An analysis to avoid the constant contribution

- Midpoint subtracted correlator

- SPFs are unchanged

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Removing constant contrib. (2)

- Here we consider the Z3 transformation

- Z3 symmetric

- Z3 asymmetric

- The asymmetry of diag-(b)
-    is coming from a factor of Re[exp(-i2πn/3)]

- Z3 asym. terms are removed because

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Averaged correlators

- However, this is not an exact method to avoid the constant contribution.

- The 3 times wrapping diagram
-         is also Z3 symmetric.
-  the contribution is not canceled.
- but, O(exp(-mqNt)) » O(exp(-3mqNt))

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Quenched QCD at T>0

- Lattice setup

- anisotropic lattices : 203 x Nt
-    1/as = 2.03(1) GeV,   as/at = 4
-    Clover quark action with tadpole imp. on anisotropic lattice
-                          *H. Matsufuru et al., PRD64, 114503 (2001).*
-    rs=1 to reduce cutoff effects in higher energy states
-                          *F. Karsch et al., PRD68, 014504 (2003).*

- We demonstrate the effects of the constant contribution
-      for charmonium correlators in quenched QCD at T>0

- equilib. is 20K sweeps
- each config. is separated
-     by 500 sweeps

- (※ in at units, 803 x Nt  Ns/Nt=3-4 at T>Tc )

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Volume dependence

- Size of the constant contribution depends on the volume Ns3

- The dependence is negligible at Ns/Nt ≳ 2

-  Results on 963 x 32
-         ( Ns/Nt=3  similar to T>0 quench QCD calculation )

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Zero Temp. results

- (our lattice results)
- MPS  = 3033(19) MeV
- MV   = 3107(19) MeV
- (exp. results from PDG06)
- Mηc  = 2980 MeV
- MJ/ψ = 3097 MeV
- Mχc0 = 3415 MeV
- Mχc1 = 3511 MeV

-  One can expect there is no plateau T>0 with the point op.
-                           when the SPF does not change at T>0
-           Nt ⋍ 28 at Tc
-           t = 1 – 14 is available near Tc
-  Spatially extended (smeared) op. is discussed later

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Quenched QCD at T>0

-  small change in S-wave states
-    survival of J/ψ & ηc at T>Tc
-  drastic change in P-wave states
-  dissociation of χc just above Tc (?)

*S. Datta et al., *
*PRD69, 094507 (2004).  etc...*

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Midpoint subtraction analysis

- usual effective masses at T>0

- the drastic change in P-wave states disappears in meffsub(t)
-       the change is due to the constant contribution

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Polyakov loop sector dependence

- Results for Av channel

-  after Z3 transformation
-      const.  Re(exp(-i2πn/3))*const.
-  even below Tc, small const. effect
-        enhances the stat. fluctuation.
-   drastic change in P-states disappears.

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Results with extended op.

- The extended op. yields large overlap with lowest states

- Spatially extended operators:
- with a smearing func. φ(x)
-                 in Coulomb gauge

- point source func.

- smeared source func.

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Results with extended op.

-  extended op. enhances
-        overlap with const. mode
-  small constant effect
-        is visible in V channel
-  no large change above Tc
-        in meffsub(t) and meffave(t)

- usual effective mass

- subtracted effective mass

- averaged effective mass

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Discussion

- The drastic change of P-wave states is due to the const. contribution.
-       There are small changes in SPFs ( except for ω=0 ).
- Why several MEM studies show the dissociation of χc states ?
-       above Tc, χc state is not the lowest state
-   Analysis of non-lowest state is difficult even if MEM is applied.

- point operators

- extended operators

- subtracted          averaged

- subtracted          averaged

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Difficulties on non-lowest states

- M(J/ψ(1S)) = 3097MeV

- M(ψ(2S))  = 3686MeV

- It is difficult to reproduce the non-lowest states peak at T>0
- Furthermore P-wave states have larger noise than S-wave states

*T. Hatsuda & M. Asakawa, *
*PRL92, 012001 (2004).*

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Discussion

*A.Jakovac et al., hep-lat/0611017.*

- Most systematic & reliable calc.
- using MEM for charmonium SPFs
- They have concluded that
-  the results of SPFs for P-states
-      are not so reliable.
-         e.g. large default model dep.
-  the drastic change just above Tc
-       is reliable results.

- In MEM results, we sometimes
- find a kind of divergence at ω=0
-   it may & should be caused by
-         the constant contribution

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Discussion

*H. Iida et al., PRD74, 074502 (2006).*

- Several groups have presented
-  almost no change in Ps channel
-  small but visible change
- 	in V channel

- These results can be explained
- by the constant contribution.
-    - no constant in Ps channel
-    - small constant in V channel
-           (proportional to pi2)
-     in free quark case

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Summary

-  We discuss a constant contribution to meson correlators at T>0
-  The constant mode is important to study temporal correlators
-         in deconfined phase

- As a result of the study, we find that drastic changes in charmonium
- correlators for χc states just above the Tc  are due to the constant
- contribution. The other differences in the χc states are small.
- It may indicate the survival of χc states above Tc, at least T=1.4Tc.

- The result may affect the scenario of J/ψ suppression.
- It is important to take the constant effects into account
-       for studies of the dissociation temp. of χc &ψ’.

- T.Umeda (BNL)

- Riken Lunch Seminar

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

## Discussion

- Polyakov loop sector dependence

*S. Chandrasekharan et al.,*
* **PRL82, 2463, (1999).*

- (*) These is no Z3 symmetry
-      in full QCD.

- T.Umeda (BNL)

- Riken Lunch Seminar

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