Heavy Quarkonium in Quark-Gluon Plasma

Cheuk-Yin Wong (黄卓然 ) Oak Ridge National Laboratory & University of Tennessee

IHEP

October 15,2004

• Introduction • Heavy quarkonium in spectral function analysis• Heavy quarkonium in potential model• Heavy quarkonium bound states in QGP• Cross section for g + J/ψ C + C• Cross section for C + C g + J/ψ• Conclusions C.Y.Wong, hep-ph/0408020

J/ψ suppression as a signature of QGP

• J/ψ suppression as a signature of QGP Matsui & Satz, PLB178, 416 (`86)• J/ψ is bound at T slightly greater than Tc Hansson, Lee, & Zahed, PRD37, 2672

(`88)• J/ψ suppresion by collisions with nucleons Gerschel and Huefner, PLB207, 253 (`88)• J/ψ suppresion by collisions with produced particles Vogt, Gavin, Capella, Wong, Barnes,

Swanson,Ko,Lin, Lee,Haglin, Blaschke,……• J/ψ enhancement by recombination Thews & Rafelski, NPA689, 575 (`02)

J/ψ suppression as a signature of QGP

• Lattice gauge results for Fav

Digal, Petreczky, Karsch, PRD64 094015 (`01)• Lattice gauge spectral function analysis Asakawa,Hatsuda, PRL92, 012001 (`03), Datta,Karsch,Petreczky, J. Phys. G,S431 (`04)• Lattice gauge calculations of color-singlet Q-Qbar potential Kaczmarek, Karsch, Petreczky, & Zantow, hep-

lat/030912 Petreczky & Petrov, hep-lat/0405009• Heavy quarkonium bound state calculations

Wong, PRC65,034902(`02) & J. Phys.G28, 2349 (`02)• J/ψ suppression and recombination

Grandchamp, Rapp, and Brown, J. Phys. G30, S1355 (`04)

• QGP at T slightly above Tc supports weakly bound meson states Zahed & Shrylak, hep-ph/0307267,

hep-ph/0403127

Spectral function analysis

Lattice gauge spectral analyses in the quenched approximation show that the width of J/ψ remains narrow up to T ≤ 1.6 TC

M. Asakawa, T. Hatsuda, and Y. Nakahara, Nucl. Phys. A715, 863 (03)

P. Petreczky, S. Datta, F. Karsch, and I. Wetzorke, hep-ph/0309012.

Questions:

1. Are there other independent ways to assess the stability of J/ψ in the quark-gluon plasma?

2 What does the potential model say about the stability of J/ψ?

3. What is the binding energy of J/ ψ?4. How easy is it to dissociate J/ ψ by gluon

collisions?5. How easy is it to recombine C and C to

form J/ ψ in QGP?

T

T)(r,1FTT)(r,1FT)(r,1V

T)/T(r,1Fe(0)TrL(r)L

Kaczmarek, Karsch, Petreczky, Zantow calculated the color-singlet C-C potential in the quenched approximation [hep-lat/0309121]

V1

V1(r,T) was calculated in the Coulomb gauge

We parameterize the color-singlet Q-Q potential as a screened color-Coulomb potential

re

3(T)4α

- C(T) t)(r,V-μ(T)r

eff1

re

3(T)4α

- C(T) t)(r,V-μ(T)r

eff1

Probable reasons for strong coupling αeff(T) just above Tc

• Density of gluons increases substantially above Tc

• Gluons have a spin (in color space)• Spin response is paramagnetic ---- a spin (in color space)

tends to align with the imposed color magnetic field, in such a way to enhance the imposed field

• This enhancement leads to anti-screening• There is a competition between anti-screening and dis-

alignment due to thermal motion• Magnetic anti-screening wins at T slightly greater than Tc• Magnetic anti-screening wins at large T Therefore, there is a strong coupling αs(T) just above Tc.

and αs(T) decreases as T increases.

Solve for Q-Q bound states

T)ε(T)ψ(r,T)ψ(r,T)],(r1VT)(r,1[Vred2μ

2

Solve for Q-Q bound states

T)ε(T)ψ(r,T)ψ(r,T)],(r1VT)(r,1[Vred2μ

2

Dissociation temperatures in quenched QCD

Heavy Quarkonium Potential Model Spectral Analysis

J/ψ ~ 2.0 TC ~ 1.6 TC

χ, ψ ' ~ 1.2 TC ~ 1.1 TC

Υ ~ 4.5 TC

χb,Υ' ~ 2.0 TC

Why different dissociation temperatures?

• Potential model gives the spontaneous dissociation temperature

• Heavy quarkonium can dissociate even before reaching spontaneous dissociation temperature by collision with gluons

• Spectral analysis includes the interaction of gluons with heavy quarkonium

Quarkonium dissociation process in the potential model

octetcolorforC

singletcolorforC

r

eTCTCTrV

c

drrruruI

Ek

B

EBE

IkkE

f

f

rTeff

f

eff

c

effgQ

s

gluon

gQgluondis

6

1

,3

4

)()(),(

6

1|1|

2|8|

)()(

2

2

)(3

4)(

)(

2

1

0

2

2

2122

J/ψ dissociation cross section g + J/ψ → c + c

Average dissociation cross section and dissociation width Γdis

disgdis

disgJ

Tp

gg

Tpdisg

dis

n

ndt

dne

dppgn

e

dppp

ggn

/

/

2

02

/

2

02

12

1)(

2

Cross section for production of J/ψ by collision of C and C

)/(||

||

)/(

_

2/

2

_

_

ccJgp

p

Jgcc

Jg

cc

Rate of J/ψ production

Conclusion

• Just above TC, J/ψ and Υ are strongly bound, probably as a result of anti-screening due to free gluons

• In the potential model, J/ψ dissociates spontaneously at about 2TC

• Below T=2TC, J/ψ dissociates by collision with gluons.. Its collision dissociation width is equal to its binding energy at T=1.2TC

• The potential model and the spectral analysis are qualitatively consistent with each other