T. Umeda, H. Ohno (Univ. of Tsukuba) for the WHOT-QCD Collaboration

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Presentation transcript:

The charmonium wave functions at finite temperature from lattice QCD calculations T. Umeda, H. Ohno (Univ. of Tsukuba) for the WHOT-QCD Collaboration RBRC Workshop, BNL, NY, USA , 23 April 2008 RBRC Workshop T.Umeda (Tsukuba) /16

Contents of this talk Introduction from the Phenix group web-site Introduction -- Quark Gluon Plasma & J/ψ suppression -- Lattice studies on J/ψ suppression Our approach to study charmonium dissociation Charmonium wave functions at T>0 Summary & future plan RBRC Workshop T.Umeda (Tsukuba) /16

J/ψ suppression as a signal of QGP Confined phase: linear raising potential  bound state of c - c De-confined phase: Debye screening  scattering state of c - c T.Hashimoto et al.(’86), Matsui&Satz(’86) Most of this talk is not so recent studies Lattice 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/ψ survives till 1.5Tc or higher RBRC Workshop T.Umeda (Tsukuba) /16

Sequential J/ψ suppression scenario ψ’ 10% 60% J/ψ χc AA collisions 30% E705 Collab.(’93) Most of this talk is not so recent studies J/ψ (1S) : JPC = 1– – M=3097MeV (Vector) ψ (2S) : JPC = 1– – M=3686MeV (Vector) χc0 (1P) : JPC = 0++ M=3415MeV (Scalar) χc1 (1P) : JPC = 1++ M=3511MeV (AxialVector) PDG(’06) It is important to study dissociation temperatures for not only J/ψ but also ψ(2S), χc’s RBRC Workshop T.Umeda (Tsukuba) /16

Current status on charmonium Tdis Lattice QCD studies ( by MEM analysis ) indicate - J/ψ may survive up to T=1.5Tc or higher - χc 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 without Bayesian analyses χc1 Most of this talk is not so recent studies J/ψ Fig: Temp. dependence of Meff(t) for J/ψ, χc1 w/o constant mode. T.Umeda (2007) RBRC Workshop T.Umeda (Tsukuba) /16

Another approach to study charmonium at T>0 infinite volume case finite volume case Most of this talk is not so recent studies In a finite volume, discrete spectra does not always indicate bound states ! In order to study a few lowest states, the variational analysis is one of the most reliable approaches ! N x N correlation matrix : C(t) RBRC Workshop T.Umeda (Tsukuba) /16

Bound state or scattering state ? We know three ways to identify the state in a finite volume Volume dependence E V bound scattering E : energy V : volume Φ(r): wave function r : c - c distance Most of this talk is not so recent studies Wave function r φ (r) bound scattering Boundary Condition (B.C.) dep. M BC BC’ bound scattering H.Iida et al.(’06), N.Ishii et al.(’05) RBRC Workshop T.Umeda (Tsukuba) /16

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 matrix t x,y,z Most of this talk is not so recent studies RBRC Workshop T.Umeda (Tsukuba) /16

Boundary condition dependence φ (r) bound M BC BC’ bound The wave functions are localized, their energies are insensitive to B.C. Most of this talk is not so recent studies The momenta depends on BC, the scattering state energies are sensitive to B.C. r φ (r) scattering M BC BC’ scattering The idea has been originally applied for the charmonium study in H. Iida et al., PRD74, 074502 (2006). RBRC Workshop T.Umeda (Tsukuba) /16

Temperature dependence of charmonium spectra J/Ψ  PBC : b=( 1, 1, 1) APBC : b=(-1,-1,-1)  HBC : b=(-1, 1, 1) Most of this talk is not so recent studies an expected gap in V=(2fm)3 (free quark case) ~ 200MeV χc0 χc1 No significant differences in the different B.C. Analysis is difficult at higher temperature ( 2Tc~) RBRC Workshop T.Umeda (Tsukuba) /16

Wave functions at finite temperature Temp. dependence of ( Bethe-Salpeter ) “Wave function” Most of this talk is not so recent studies using the eigen functions of the variational method  we can extract the wave functions of each states RBRC Workshop T.Umeda (Tsukuba) /16

Wave functions in free quark case Test 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 6 x 6 correlators Our method well reproduces the analytic solutions ( ! ) Most of this talk is not so recent studies RBRC Workshop T.Umeda (Tsukuba) /16

Charmonium wave functions at finite temperatures Most of this talk is not so recent studies Small temperature dependence in each channels Clear signals of bound states even at T=2.3Tc ( ! ) RBRC Workshop T.Umeda (Tsukuba) /16

Most of this talk is not so recent studies RBRC Workshop T.Umeda (Tsukuba) /16

Volume dependence at T=2.3Tc χc1(1P) Most of this talk is not so recent studies J/ψ(1S) χc1(2P) ψ(2S) Clear signals of bound states even at T=2.3Tc ( ! ) Large volume is necessary for P-wave states. RBRC Workshop T.Umeda (Tsukuba) /16

Summary and future plan We 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) Most of this talk is not so recent studies No evidence for unbound c-c quarks up to T = 2.3 Tc -  The result may affect the scenario of J/ψ suppression. Future plan higher temperature calculations (T=3Tc or higher) Full QCD calculations ( Nf=2+1 Wilson is now in progress ) RBRC Workshop T.Umeda (Tsukuba) /16