# Lattice study of charmonia in Hot QCD

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Lattice study of charmonia in Hot QCDT. Umeda (YITP, Kyoto univ.)H. Ohno, K. Kanaya (Univ. of Tsukuba)

(WHOT-QCD Collaboration)Mini-Workshop on ''Photons and Leptons in Hot/Dense QCD"Nagoya University, Aichi, Japan , March 3rd 2009

T.Umeda (Kyoto Univ.)

Contents of this talk Introduction -- Quark Gluon Plasma & J/ suppression -- Lattice studies on J/ suppression Our approach to study charmonium dissociation Charmonium spectra & wave functions at T>0 Summary & future planfrom the Phenix group web-site

T.Umeda (Kyoto Univ.)

J/ suppression as a signal of QGPLattice QCD calculations: Spectral function by MEM: T.Umeda et al.(02), S.Datta et al.(04), Asakawa&Hatsuda(04), A.Jakovac et al.(07), G.Aatz et al.(06) Wave func.: T.Umeda et al.(00) B. C. dep.: H.Iida et al. (06) all calculations conclude that J/ survives till 1.5Tc or higher

T.Umeda (Kyoto Univ.)

Sequential J/ suppression scenarioE705 Collab.(93) 10%30%60%It is important to study dissociation temperatures for not only J/ but also (2S), csAA collisionsJ/cJ/ (1S) : JPC = 1 M=3097MeV (Vector) (2S) : JPC = 1 M=3686MeV (Vector)c0 (1P) : JPC = 0++ M=3415MeV (Scalar) c1 (1P) : JPC = 1++ M=3511MeV (AxialVector) PDG(06)

T.Umeda (Kyoto Univ.)

Charmonium correlators at T>0 small change in S-wave states survival of J/ & c at T>Tc drastic change in P-wave states dissociation of c just above Tc (?)S. Datta et al., Phys. Rev. D69 (2004) 094507. etc...

T.Umeda (Kyoto Univ.)

c dissociation just above Tc ?A.Jakovac et al., Phys. Rev. D 75 (2007) 014506.c dissociation just above Tc is consistent with the sequential suppression scenario.

In the paper, they concluded that the drastic change of P-states corr. just above Tc is reliable. Spectral functions for P-states are not so reliable. e.g. large default model dep.

T.Umeda (Kyoto Univ.)

Constant mode in meson correlatorsexp(-mqt) x exp(-mqt)= exp(-2mqt)exp(-mqt) x exp(-mq(Lt-t))= exp(-mqLt)mq is quark mass or single quark energyLt = temporal extentWe can separate the constant mode from correlatorsT.Umeda, Phys. Rev. D 75 (2007) 094502.usual effective masssubtracted effective mass

T.Umeda (Kyoto Univ.)

Constant mode effects in charmoniausual effective masses at T>0the drastic change in P-wave states disappears in meffsub(t) the change is due to the constant modesubtracted effective mass0.1at=800MeV

T.Umeda (Kyoto Univ.)

Spectral functions in a finite volume In a finite volume (e.g. Lattice simulations), discrete spectra does not always indicate bound states !Momenta are discretized in finite (V=L3) volumepi/a = 2ni/L (ni=0,1,2,) for Periodic boundary condition

T.Umeda (Kyoto Univ.)

c dissociation just above Tc ?MEM analysis can fail if data quality is not sufficient.P-wave states have larger noise than that of S-wave statesA.Jakovac et al., Phys. Rev. D 75 (2007) 014506.This result is strange ??

T.Umeda (Kyoto Univ.)

Another approach to study charmonium at T>0 It is difficult to extract higher states from lattice correlators (at T>0) even if we use MEM !!

We want to get information about a few lowest states (at T>0)

Constant mode can be separated by the Midpoint subtraction

T.Umeda (Kyoto Univ.)

Bound state or scattering state ?In a finite volume, discrete spectra does not always indicate bound states. Wave functionrrboundscatteringH.Iida et al.(06), N.Ishii et al.(05)

T.Umeda (Kyoto Univ.)

Lattice setup

Quenched approximation ( no dynamical quark effect ) Anisotropic lattices lattice spacing : as = 0.0970(5) fm anisotropy : as/at = 4 rs=1 to suppress doubler effects Variational analysis with 4 x 4 correlation matrixtx,y,z

T.Umeda (Kyoto Univ.)

Boundary condition dependenceThe idea has been originally applied for the charmonium study in H. Iida et al., Phys. Rev. D74 (2006) 074502.rscattering0The 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 (Kyoto Univ.)

Variational analysis in free quark caseTest with free quarks ( Ls/a=20, ma=0.17 ) Mass diff. between the lowest masses in each BCPBC : b=( 1, 1, 1)APBC : b=(-1,-1,-1)MBC : b=(-1, 1, 1)an expected diff.in V=(2fm)3(free quark case) ~ 200MeV

T.Umeda (Kyoto Univ.)

Temperature dependence of charmonium spectra No significant differences in the different B.C. Analysis is difficult at higher temperature ( 2Tc)PBC : b=( 1, 1, 1)APBC : b=(-1,-1,-1)MBC : b=(-1, 1, 1)an expected gapin V=(2fm)3(free quark case) ~ 200MeV

T.Umeda (Kyoto Univ.)

Wave functions at finite temperatureTemp. dependence of ( Bethe-Salpeter ) Wave function using the eigen functions of the variational method we can extract the wave functions of each states

T.Umeda (Kyoto Univ.)

Wave functions in free quark caseTest with free quarks ( Ls/a=20, ma=0.17 ) in case of S-wave channels Free quarks make trivial waves with an allowed momentum in a box

The wave function is constructed with eigen functions of 4 x 4 correlators

Our method well reproduces the analytic solutions ( ! )

T.Umeda (Kyoto Univ.)

Charmonium wave functions at finite temperatures Small temperature dependence in each channels Clear signals of bound states even at T=2.3Tc ( ! ) Large volume is necessary for P-wave states.

T.Umeda (Kyoto Univ.)

T.Umeda (Kyoto Univ.)

Volume dependence at T=2.3TcJ/(1S)(2S) Clear signals of bound states even at T=2.3Tc ( ! ) Large volume is necessary for P-wave states.c1(1P)c1(2P)

T.Umeda (Kyoto Univ.)

Summary and future planWe investigated Tdis of charmonia from Lattice QCD using another approach to study charmonium at T>0 without Bayesian analysis - boundary condition dependence - Wave function (Volume dependence) The result may affect the scenario of J/ suppression.Future plan Interpretations of the experimental results on J/ suppression Higher Temp. calculations ( T/Tc=3~5 ) Full QCD calculations ( Nf=2+1 Wilson is now in progress )

T.Umeda (Kyoto Univ.)

Most of this talk is not so recent studies

Most of this talk is not so recent studies

Most of this talk is not so recent studies

Most of this talk is not so recent studies

Most of this talk is not so recent studies

Most of this talk is not so recent studies

Most of this talk is not so recent studies

Most of this talk is not so recent studies

Most of this talk is not so recent studies

Most of this talk is not so recent studies

Most of this talk is not so recent studies

Most of this talk is not so recent studies

Most of this talk is not so recent studies

Most of this talk is not so recent studies

Most of this talk is not so recent studies

Most of this talk is not so recent studies

Most of this talk is not so recent studies

Most of this talk is not so recent studies

Most of this talk is not so recent studies

Most of this talk is not so recent studies