Stability of Quarkonia in a Hot Medium

Cheuk-Yin Wong Oak Ridge National Laboratory & University of Tennessee

SQM Workshop, UCLA, March 26-30, 2006

• Introduction • How to extract the Q-Q potential from LGT results• Quarkonium bound states in a hot medium• Quark drip lines in quark-gluon plasma• Conclusions

C.Y.Wong,PRC65,034902(’02);PRC72,034906 (’05) C.Y.Wong, hep-ph/0509088

2

Why study quarkonia in a hot medium?

Successes of the recombination model suggest that heavy and light quarkonia may be bound in quark-gluon plasma.

Two new surprising results from lattice gauge calculations• Lattice spectral function analyses in quenched QCD

indicate that J/ψ may be stable up to 1.6Tc• Lattice static Q-Q “potential” appears to be very

strong between 1 and 2 Tc

3

We need • to confirm these lattice gauge results• to examine the stability of quarkonia • to study effects of dynamical quarks on

quarkonium stability

4

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)

S. Datta, F. Karsch, P. Petreczky, and I. Wetzorke, Phys. Rev. D69,094507(04)

The drastic change of the spectral function suggests the occurrence of spontaneous dissociation between 1.62 and 1.70Tc.

322x48x128

403x40483x24

5

T)(R,1S TT)(R,1FT)(R,1UT

T)(R,1FTT)(R,1FT)(R,1U

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

+=∂

∂−=

−=+

Kaczmarek et al. calculated the color-singlet F1 and U1 in the quenched approximation [hep-lat/0309121]

F1(r,T) was calculated in the Coulomb gauge

Rσ1/2

6

UU1 1 is much deeper and broader than Fis much deeper and broader than F11

and can hold many more bound statesand can hold many more bound states

O. Kaczmarek et al. hep-lat/0506019

U1

F1

Using U1 as the potential,, Shuryak, Zahed, Brown, Lee, and Rho suggested that even light quarkonia may be bound in quark-gluon plasma

T/Tc=1.3

R

7

What is the Q-Q potential?

As ansatzes:1. F1(r,T), the free energy (Digal et.al `01, Wong `02, Blaschke `05)

2. U1(r,T)=F1(r,T)+TS1(r,T), the internal energy (Kaczmarek et al.`02, Shuryak et al `04, Alberico `05)

With theoretical justifications:3. A linear combination of F1 and U1

(Wong ,PRC 72,034906`05)

),()(3

)(),(

)(3

3),( 11

)1( TRUTa

TaTRF

TaTRU QQ +

++

=

8

• We need to understand the meaning of U1. • We need to understand the meaning of TS1=U1-F1.

T/Tc =1.3

Why such behavior?

? Uand F gauge lattice from

potential Q-Qextract To

11

R (fm)

O. Kaczmarek et al. hep-lat/0506019

9

Implications of S1(R) increases as R increases

increases? as increases energy, internalgluon ,

increases? as increases gluons, ofnumber ,

:Questions

increases as increases

increases as increases

. Therefore,

. so fixed, held are Q and Q But,

gluons and ,QQ, of system a have We

RU

RN

R(R)S

R(R)S

(R) S(R) S

(R) S

(R) S(R) S(R)S

gluon

gluon

gluon

gluon

QQ

gluonQQ

⇒

⇒

=

=

+=

1

1

1

0

10

Simple model of charge screening

• Q (charge +q) at -R/2• Q (charge –q) at R/2

• medium: e+ (charge +q), e- (charge –q)

• particles interact with an e1e2/r interaction

We assume e+ and e- are massless and are fermions.

We also assume local thermal equilibrium

11

{ }

{ }{ }

{ }

{ } [e e

e

[e e

[e e

e

equlibrium thermallocal and at potential Under the

medium. charge theand ,Q Q, todue is at potential The

22

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]/),(),(/)(1

]),([2

),,(2

),(

]/),(/),(1

)1ln()1(ln2

),(

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),,()2/(),(

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,

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r

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TRrVbTRrVb

ffffdppg

Rr

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RprfdppgRrn

TRrVpRprf

r)R,rV(

)R,rV(r

ó

ó

ó

′+′+−=

⎭⎬⎫

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+−=

=

++=

±±±

−+

±±±

±±±

±±±±±

±±±

±±

±±

∫

∫

∫

rr

rrrrrrr

rrrr

rr

rrrr

rrrrr

rrrrr

rrr

rrr

π

σπ

σ

π

4444 84444 76

'V

12

{ {

( )

|2/

)exp()exp(

)(/

/)2/()()2/(4

0/0)(

)()2/()()2/(

?

,

22210

210

210

Rrr

r

rq

r

rq)R,rV(

Tqan

T)R,rV(qanRrqqRrq)R,rV(

T)R,rV(qan)R,r(nq)R,r(qn

)R,r(nq)R,r(qnRrqRrq)R,r(

)R,rV(

)R,r(u)R,r()R,r(n)R,rV(

rr

rr

rrrrrrrr

44 344 21

rrrrrr

rrrrrrrrrr

rr

rrrrrrrr

±=

−−

−=

==

+−−+−−=∇

++=−+

−++−−++=

±

−

−

+

+

−+

−+

±±±

|

isSolution

mass Debye 4 Define

:equationPoisson

:density Charge

determine tohow But,

,obtain to Need

2

order 2ndorder1st

orderlowest

μμ

μπ

δδπ

δδρ

σ

13

,

14

Total entropy, particle number,and increases and saturates

as R increases.

R

15

Total medium entropy, particle number, and Total medium entropy, particle number, and internal energy increase (and saturate) as R internal energy increase (and saturate) as R increases.increases.

R

16

)()()(

)()()(2

:

)(

|2/)exp()exp(

),2/()2/)(

)(2)(2

(22

2

2

2

22

22

RURUR

eqRU

RERRUp

statesboundQQforequationdingeroSchrR

eqRUTherefore,

Rrrr

rq

r

rq)R,rV(

RRrVRqRU

sources,ll charge , due to aQor Q and n energy fInteractio

RQQ

Up

mm

P

m

p

m

pH

Qd n for Q anHamiltonia

mediumtotal

R

QQ

QQQQ

R

R

QQ

QQ

QQ

R

QQ

CM

Q

Q

Q

Q

−=−=

=⎟⎟⎠

⎞⎜⎜⎝

⎛+

−=

±=−

−−

=

=×=

+++

=

++=

−

−

±−

−

+

+

| ,

ninteractio-self except - - at (

)Q and Q on acting ,energy ninteractio all

μ

μ

ψψμ

μμ

μ

&&

rrrr

rrrr

tes bound staQor Qequation fdingeroSchr &&

17C.Y.Wong,PRC72,034906 (’05)

18

{

11)1(

1111)1(

11

1)1(

33

3

)(3

3

)(3

3

3

3

,3

1

3)(

3)(

3

)()(

Ua

aF

aU

FUa

UUUU

FUa

TSa

U

dV

dST

dV

dUa(T)

pTa

dV

dST

Ta

p

dV

dSTp

SpdV

dST

dV

dU

(R)URURU

QQ

gQQ

gg

gg

g

g

ggg

gQQ

++

+=

−+

−=−=

−+

=+

=

=⎟⎠

⎞⎜⎝

⎛ +

=

=+

=+

−==

−=

,Hence

and

,So

state of equation thefrom takenbe can / on ninformatio

)entropy gluon theis (

,amics thermodynof law first By the

is potential Q-Q The

ε

εε

ε

ε

ε

How to separate out Ug from U1?

19

F1 and U1 fractions depend on T

Boyd et al. (Nucl. Phys. B ’96)

Quenched QCD equation of state

F1 fraction

U1 fraction

20

Solve for Q-Q bound states

T)|Å(T)|?(r,T)|?(r,

T),(r1UT)(r,1U

T),(r1FT)(r,1F

T),(rUT)(r,U

red2|Ì

2 QQQQ

=

⎪⎪⎪

⎭

⎪⎪⎪

⎬

⎫

⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

∞→−∞→−∞→−

+∇

−

)1()1(

(1)

21

(1)

T<Tc

T>Tc

C.Y.Wong, PRC65,034902 (`02)C.Y.Wong, PRC65,034906 (`05)

Quenched QCDFull QCD(2 flavors)

22

Spontaneous dissociation temperatures in quenched QCD

U QQ

)1(Heavy

Quarkonium

Spectral

Analysis Potential

F1

Potential

U1

Potential

J/ψ 1.62-1.70TC 1.62TC 1.40TC 2.60TC

χc , ψ ' below 1.1 TC unbound unbound 1.18TC

Υ 4.10TC 3.50 TC ~5.0 TC

χb 1.15-1.54 TC 1.19TC 1.10TC 1.73TC

23

Quenched QCD & Full QCD

• Quenched QCD is inadequate as it neglects the effects of dynamical quarks

• Dynamical quarks provide additional screening

• F1 and U1 for full QCD (with 2 flavors) have been obtained by Kaczmarek et al. ΄05

• The equation of state for full QCD (with 2 flavors) has been obtained by Karsch et al. ΄02.

24

Spontaneous dissociation temperatures in quenched QCD & full QCD

Heavy

Quarkonium Quenched

QCD

2-flavor

QCD

Spectral

Analysis

Quenched QCD

J/ψ 1.62TC 1.42TC ~ 1.6 TC

χc , ψ ' unbound unbound below 1.1 TC

Υ 4.10TC 3.30 TC

χb 1.18TC 1.22TC 1.15-1.54

U QQ

)1(

U QQ

)1(

25

Quarkonia in quark-gluon plasma We can treat the quark mass as a variable and obtain

the binding energies of a quarkonium as a function of the reduced mass μred and temperature T.

Stability represented by ‘quark drip lines’

• In the ( T, quark reduced mass μred ) space, the quark drip line is the line below which a

quarkonium is unbound.

• There are 1s drip line, and 1p drip line, etc,…

26

Quark drip lines in quark-gluon plasma

Unbound Region

27

Use quark drip lines to determine the stability of light quarkonia

• Because of the strong interaction, light quarks become quasiparticles and they acquire masses

• These masses can be estimated by studying the equation of state (Levai et al. `98, Szabo et al.`02, Iavanov et al.`05).

• They found that the quasi-particle masses of u, d, and s quarks are

mq~ 0.3-0.4 GeV for Tc<T<2Tc.

28

Light quark quarkonia

Szabo et al. JHEP 0306, 008 (`03) Results from Levai et al `98 and Ivanov et al `05 are similar.

For light quarks with For light quarks with a mass of 300-400 a mass of 300-400 MeV, the quark drip MeV, the quark drip line shows that line shows that quarkonia with light quarkonia with light quarks can be stable quarks can be stable up to 1.06Tc.up to 1.06Tc.

29

• The potential model is consistent with the spectral function analysis, if the Q-Q potential is a linear combination of F1 and U1,with coefficients that depend on the equation of state.

• The effects of the dynamical quarks modify J/ψ stability only slightly. In quenched QCD,. J/ψ dissociates spontaneously at 1.62 Tc. In full QCD with 2 flavors, J/ψ dissociates spontaneously at 1.42 Tc

• Light quarkonium states may be stable up to ~1.06 Tc.

The stability of these light quarkonia near Tc provides support to the recombination model at temperatures just above Tc.

Conclusions

30