Search for the CharmoniaDissociation in Lattice...

Search for the Charmonia Dissociation in Lattice QCD

H. Ohno, T. Umeda and K. Kanayafor WHOT‐QCD Collaboration

SQM 2008Tsinghua University, Beijing, Oct 8, 2008

Introduction (1) : J/Ψ suppression

• Dissociation of charmonia in deconfined phase is an interesting subject to understand QGP because

– J/Ψ suppression is one of the most important signals in heavy ion collisions.

– Recently, sequential J/Ψ suppression scenario is proposed.

– Not only J/Ψ itself but also other heavier charmonia play important roles for J/Ψ suppression.


1/19

J/Ψ

Ψ’

χc

60%

30%

10%

Heavy ioncollision


L. Antoniazzi et al. [E705 Collaboration], Phys. Rev. Lett. 70, 383 (1993)

• Current lattice studies of the charmonia spectral functions with MEM (based on Bayesian analysis) suggest

– S wave states (ηc, J/Ψ) seem to survive up to 1.5 Tc or higher.

– P wave states (χc) seem to dissolve just above Tc.

– Excited charmonia (Ψ’) have NOT been investigated well yet.

• There are still some problems– Ambiguities of MEM in terms of choice of default models for spectral

functions are known.

– It is suggested that constant mode contribution cause a difficulty to analyze meson correlators, especially for P wave.

We want to cross‐check recent lattice results with other methods.

Introduction (2) : Lattice QCD studies


2 /19H. Ohno, T. Umeda and K. Kanayafor WHOT‐QCD Collaboration

e.g. A. Jackovac et al., Phys. Rev. D75, 014506 (2007)

T. Umeda, Phys. Rev. D75, 094502 (2007)

• We investigate the chamonia dissociation in lattice QCD with following considerations.

– Spectral function consists of discrete spectra only due to spatial lattice size.

– When all charmonia fully dissolved above Tc, we naively expect:• Charmonia peaks should vanish and peaks of some scattering states may appears above Tc.

• Wave function for scattering states extend to large distances.

– To examine the expectations, we• study both effective masses and wave functions

• adopt mult‐state variatonal analysis to extract excited charmonia

• subtract the constant mode contribution from the moesn correlators and wave functions

Our approach


3/19H. Ohno, T. Umeda and K. Kanayafor WHOT‐QCD Collaboration

T<TC T>TC

spectral function

wave function

We test with quenched approximation

ωω

rr

• On the finite volume lattice, scattering states have typical spatialboundary condition and spatial lattice size dependence in terms of discrete momenta.

Charmonia or scattering states?


4 /19

H. Iida et al.,Phys. Rev. D74, 074502 (2006)

Charmonia Scattering states


Wave function

Spectral fu

nction

PBCAPBC

ω ω

r r

There is no mass shift under changing BC There is some mass shift

under changing BC

Localized shape not depending on spatial lattice size and insensitive for BC

Extended shape depending on spatial lattice size and sensitive for BC

Meson correlators & wave functions

• Meson correlator

• Wave function



JPC=0-+

JPC=1--

JPC=0++: meson operator

: meson correlator with zero momentum

: Bethe‐Salpeter amplitude

Nt : temporal lattice size

: to extract charmonia mass

JPC=0-+

JPC=1--

JPC=0++

Constant mode contribution for effective masses

• It is suggested that there is sizable contribution of constant mode above Tc, especially for the P wave.

– Effective mass below Tc and above Tc


6 /19

T. Umeda, Phys. Rev. D75, 094502 (2007)


T<Tc T>Tc

Separating out constant mode effects

• Midpoint subtracted correlator analysis

– Effective mass at 1.1Tc

7/19Search for the Charmonia Dissociation in

Lattice QCDH. Ohno, T. Umeda and K. Kanayafor WHOT‐QCD Collaboration

Constant mode contribution can be separated out.

midpointsubtraction

from normal correlator from midpoint subtarcted correlator

• Smeared meson operator

• Effective mass

– Midpoint subtraction

– General eigenvalue equation

• Wave function

– Midpoint subtraction

Multi‐state variational analysis


8 /19

: smearing functioni=1,2,…,Nstate


A1 A2 A3 A4 A5 A6

0.02 0.05 0.10 0.15 0.20 0.25

The parameters Ai

• Effective masses

Test in free quark case (1) : Effective masses


9 /19

MBC：Mixed B.C. (x, y, z)=(AP, P, P)

solid line : analytical solution

Nstate=6 203×128 anisotropic lattice

Mass shift due to BC

S wave P wave

PBC APBC MBCPBC APBC MBC


• Variational analysis works well to extract both ground and excited states.

• Mass shift due to spatial boundary conditions can be found in free quark case, which is the trivial scattering state case.

Test in free quark case (2) : Wave functions

• Wave functions for Ps Channel



Ψ0

Ψ1Ψ2Ψ3

Ps

dashed line : analytical solution

• Variational analysis works well to extract both ground and excited states.

• Wave functions extend to large distances in free quark case, which is the trivial scattering state case.

Nstate=6 203×128 anisotropic lattice

Lattice setup

• Action– O(a) improved Wilson fermion action ( rs=1 )

– Standard plaquette gauge action

– Quenched approximation

• Lattice– anisotropic lattice → anisotropy ξ=as/at=4

– Ns=16, 20(, 32)

– Nt=(8 (3.2Tc),) 12 (2.3Tc), 16 (1.8Tc), 20 (1.4Tc), 26 (1.1Tc), 32 (0.88Tc)

– as=0.0970(5) fm (2.030(13) GeV)

• Gauge configuration

• Gauge fixing : Coulomb gaugeSearch for the Charmonia Dissociation in

Lattice QCD11 /19

Ns=16 Ns=20 Ns=32

Local op. 800 800 200

Derivative op. 300 300 200

Nt

Ns

asat


Temperatures are changed in terms of changing temporal lattice size.

• Temperature and spatial BC dependence (Ve channel)

Numerical results : effective mass (1)


12 /19

There seems to be no scattering state contribution up to 2.3Tc.


J/Ψ(1S)

Ψ’(2S)

PBCAPBC

Nstate=4(Results with Nstate=6 consistent)203×Nt lattice

: mass shiftin the free case

There is no clear BC dependence up to 2.3 Tc.

• Temperature and spatial BC dependence (Ps and Sc channel)


13/19

Numerical results : effective mass (2)


MBC：Mixed B.C. (x, y, z)=(AP, P, P)

Ps Sc

ηc(1S)

ηc(2S)

χc0(1P)

χc0(2P)

PBCAPBCMBC

• Temperature dependence of wave function (Ve channel)

0.88Tc 1.1Tc 1.4Tc

1.8Tc 2.3Tc

0.88Tc 1.1Tc 1.4Tc

1.8Tc 2.3Tc

Numerical results : wave function (1)



J/Ψ(1S) Ψ’(2S)

Nstate=4(Results with Nstate=6 consistent)203×Nt lattice

The ground state The first excited state

The wave functions of the ground and the first excited state keep their shapes up to 2.3 Tc.


• Temperature dependence of wave function (Ps and Sc channel)



ηc(1S) ηc(2S)

χc0(1P)


Ps

Sc

0.88Tc 1.1Tc 1.4Tc

1.8Tc 2.3Tc

0.88Tc 1.1Tc 1.4Tc

1.8Tc 2.3Tc

0.88Tc 1.1Tc 1.4Tc

1.8Tc 2.3Tc

0.88Tc 1.1Tc 1.4Tc

1.8Tc 2.3Tc

χc0(2P)

• Volume dependence at 2.3 Tc(Ve channel)





• No sensitive volume dependences• Spatially localized even at T=2.3Tc for both ground state and 1st excited state

Ns=32Ns=20Ns=16

J/Ψ(1S) Ψ’(2S)

Nstate=4(Results with Nstate=6 consistent)


• Volume dependence at 2.3 Tc(Ps and Sc channel)



Ns=32Ns=20Ns=16


ηc(1S) ηc(2S)

χc0(1P)

Ps

Scχc0(2P)

Conclusion

• Charmonia dissociation are studied with variational analysis in quenched anisotropic lattice QCD.

– Constant mode contribution for meson correlators is taken into account.

– Spatial boundary condition dependence of effective masses are examined.

– Temperature and spatial size dependence of wave function’s shape are investigated.

– There is large constant mode effect for P wave above Tc.

P wave charmonia have small change up to 2.3Tc when constant mode effect is considered.

– No clear signal of scattering states appears up to 2.3Tc.

– We find no clear evidences of dissociation for the all charmonium states (ηc, J/ψ, χc0 and their first excited states) up to 2.3Tc so far.



Future plan

• Simulation at higher temperature to investigate whether charmonia really dissolve.

• Full QCD simulation



END

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