![Page 1: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/1.jpg)
Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong
Oak Ridge National Laboratory
Dubna July 14, 2008
• Introduction• Static properties of quarkonia in QGP• Reactions of quarkonia with hadrons and QGP • Conclusions
![Page 2: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/2.jpg)
Why study quarkonia in quark-gluon plasma ?
• Heavy quarkonia may be used as a plasma diagnostic tool
• Successes of the recombination model• Successes of the thermal mode
--- quarkonia with light quarks may be stable in quark-gluon plsama, at least near Tc
![Page 3: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/3.jpg)
Q-Qbar interaction in Quarkonia
• The screening between Q and Qbar in QGP is non-perturbative in nature and must be studied non-perturbatively.
• Need lattice gauge theory• Need to understand the results from lattice gauge
theory• Need to study dynamical effects in screening,
response and relaxation of the medium to Q-Qbar motion
![Page 4: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/4.jpg)
What kind of framework in lattice gauge theory?
• Lattice is a subsystem in a much large thermal bath
• Subsystem is in constant contact with bath • In the grand-canonical ensemble (which is
used in the lattices gauge calcualtions), the subsystem particle numbers and energy of the subsystem are adjusted to maintain the same temperature as the bath
![Page 5: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/5.jpg)
Types of lattice calcualtions
• Polyakov lines
• Meson correlators
Gauge invariant correlator
)'()'()()( 22112211 xOxxOx
)2/()2/(( rLrLtr
)0,0()0,0(),0(),0( 2121
OtOt
![Page 6: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/6.jpg)
Why study heavy quarkonia in a hot medium?
Two new surprising results from lattice gauge calculations• Lattice spectral function analyses in quenched QCD show
that J/ψ is stable up to 1.6Tc• Lattice static Q-Q “potential” appears to be very strong
between 1 and 2 Tc• Shuryak, Zahed, Brown, Lee, and Rho suggested that even
light quarkonia may be bound in quark-gluon plasma We need
• to confirm these lattice gauge results• to study effects of dynamical quarks on J/ψ stability • to assess the strength of the Q-Q potential• to examine the stability of quarkonia
![Page 7: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/7.jpg)
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 between 1.62-1.70Tc suggests the occurrence of spontaneous dissociation at 1.62-1.70Tc.
![Page 8: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/8.jpg)
Why mass of J/psi roughly constant of T?
• In Debye screening, the screening potential is
in order first oconstant t is system theof mass The
expexp)(
rr
rrr
rVD
![Page 9: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/9.jpg)
Questions:
1 What does the potential model say about the J/ψ spontaneous dissociation temperature?
2 What are the effects of dynamical quarks?
3 What is the strength of interaction between a static quark and antiquark?
![Page 10: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/10.jpg)
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
UU1 1 is much deeper than Fis much deeper than F11 and can hold many more bound states and can hold many more bound states
![Page 11: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/11.jpg)
What is the Q-Q potential?
Initial conjectures:
1. F1(r,T) is the Q-Q potential
(Digal et.al `01,Wong `02,Blaschke et.al 05)
2. U1(r,T) is the Q-Q potential
U1(r,T) = F1(r,T) + TS1(r,T)
(Kaczmarek et al.`02,Shuryak et al `04)
![Page 12: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/12.jpg)
• 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
![Page 13: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/13.jpg)
Thermodynamical Quantities U1,S1, F1
• Internal energy U1 (kinetic plus potential energies)
• Entropy S1 (the degree of different ordering)
TS1 is the energy associated with entropy
• Free energy F1 = U1 – TS1
( the internal energy minus the energy associated with entropy)
)1( ln)1(ln1 iiii nnnnS
![Page 14: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/14.jpg)
Thermodynamical Quantities
• Internal energy U (kinetic plus potential energies)• Entropy S (the degree of different ordering)
TS is the energy associated with entropy• Free energy F = U – TS
( the internal energy minus the energy associated with entropy)
)1(ln)1(ln iiii nnnnS
![Page 15: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/15.jpg)
Equilibrium condition• dU=T dS – P dV Define free energy F=U – TS, we get dF= – SdT – PdV If the temperature is held fixed (thermal bath) and
the volume does not change locally, then F is a constant.
• In a constant temperature environment, equilibrium is reached when dF=0,
i.e. the variation of F with respect to all degrees of freedom is zero in a thermal bath.
![Page 16: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/16.jpg)
Entropy increases as Q and Qbar move away from each other
The number of gluons increases as Q and Qbar move away from each other because the first order of screening cancels but thesecond order change of gluon number always increases.
We want Q-Qbar interaction without changing the gluon internal energy.
We therefore need to subtract out the increases in gluon energy when Q and Qbar changes separations.
![Page 17: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/17.jpg)
11)1(
1111)1(
11
1)1(
33
3
)(3
3
.3
3
,3
3
3)(3
)(3
3
Ua
aFa
U
FUa
UUUU
FUTSTSa
U
dV
dSTadV
dU
pTadV
dUTa
dV
dUpp
SpdV
dST
dV
dU
UUU
gQQ
ggg
gg
gg
ggg
gQQ
Hence,
But and
So,
state ofequation thefromknown is /
entropy)gluon theis (
amics, thermodynof lawfirst By the
is potential Q-Q that theprocedure in this find We
![Page 18: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/18.jpg)
F1 and U1 fractions depend on T
Boyd et al. (Nucl. Phys. B ’96)
![Page 19: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/19.jpg)
Solve for Q-Q bound states
T)ε(T)ψ(r,T)ψ(r,
T),(r1UT)(r,1U
T),(r1FT)(r,1F
T),(rUT)(r,U
red2μ
2 QQQQ
)1()1(
(1)
![Page 20: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/20.jpg)
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
![Page 21: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/21.jpg)
stability. quarkoniumstudy toQCD
fullin potential theuse alsomay We
stability. quarkoniumstudy to
potential eappropriat thebemay
potential, that theindicates
QCD quenchedin tureson temperadissociati
sspontaneou theof comparison The
)1(
11)1(
)1(
,33
3
U
Ua
aFa
U
U
![Page 22: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/22.jpg)
Quenched QCD & Full QCD
• Quenched QCD is inadequate as it neglects the effects of dynamical quarks
• We need to study full QCD with dynamical quarks
• Kaczmarek et al. (PRD 71, 114510 ΄05) have obtained F1 and U1 in full QCD (with 2 flavors)
• Karsch et al. has obtained a(T) (PLB 478, 447).
• We can use the potential model to study the stability of quarkonium in full QCD
![Page 23: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/23.jpg)
Full QCD with two flavors Kaczmarek et al (’05) ,3.0
1)(/))((
1)(
)](1)[()(3
4)(
0
1
s , exp
TdTrrrf
rfTCrfr
rF s
![Page 24: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/24.jpg)
Full QCD with two flavors ,3.0
1)(/))((
1)(
)](1)[()(3
4)(
0
1
s , exp
TdTrrrf
rfTCrfr
rU s
![Page 25: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/25.jpg)
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(
![Page 26: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/26.jpg)
Recent lattice calculations in 2-flavor QCD
J/ψ spectral function (~Tc)
(~2Tc)
J/ψ appears to have narrow width even up to ~2Tc in full QCD
Aarts et al., hep-lat/0511028
![Page 27: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/27.jpg)
Quarkonia in quark-gluon plasma
The Q-Qbar potential extracted from lattice calculations can be used to examine the stability of quarkonia of different quark masses.
We can treat the quark mass as a variable and obtain the spontaneous dissociation temperature as a function of the reduced mass.
![Page 28: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/28.jpg)
The quark drip line
• The quark drip line is the line in the (μ,T) space above which Q-Qbar is unbound.
• It can also be characterized by the nature of the Q-Qbar state: 1s drip line, 1p drip line,..
• Given the Q-Qbar potential, the drip line can be determined by locating the spontaneous dissociation temperature as a function of the reduced mass.
![Page 29: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/29.jpg)
Quark drip lines in quark-gluon plasma in quenched QCD
![Page 30: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/30.jpg)
Stability of quarkonia in quark-gluon plasma in full QCD
Dynamical quarks modifies the 1s drip line but not the 1p drip line.
)()1( rU
potential
![Page 31: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/31.jpg)
Can the potential model be applied to light quarkonia?
• Because of the strong coupling, light quarks becomes quasiparticles and acquire masses
• The quasiparticle masses of quarks in quark-gluon plasma can be estimated by looking at the equation of state (Levai et al.,
Szabo et al, Iavanov et al.). They found that the quasi-particle masses of u, d, and s quarks are 0.3-0.4 GeV for Tc<T<2Tc.
![Page 32: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/32.jpg)
Light quark quarkonia
Szabo et al. JHEP 0306, 008 (`03) Results from Levai et al and Ivanov et al are similar.
For light quarks with a massof 300-400 MeV, quarkonia with light quarks can be stable up to 1.06Tc.
![Page 33: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/33.jpg)
• The potential model is consistent with the lattice gauge spectral function analysis, if the Q-Qbar potential is a linear combination of F1 and U1,with coefficients depending on the equation of state.
• The effects of the dynamical quarks modifies only slightly the stability of J/ψ. J/ψ dissociates spontaneously at about 1.62 Tc in quenched QCD and at 1.42 Tc in 2-flavor QCD.
• The interaction between a static quark and antiquark is such that the quark drip lines limit possible quarkonium states with light quarks to T close to Tc.
Conclusions
![Page 34: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/34.jpg)
J/ψ-nucleon collisions
• J/ψ precursor collide with nucleons at high energy• J/ψ-nucleon cross section depends on root-mean-
square separation• J/ψ colides with comovers at low energy
![Page 35: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/35.jpg)
J/psi-nucleon high energy cross section
Zhang & Wong, PRC68,035211(03)
tQ
rVdzbV
klijjlVikVklijebdtsA
tsAs
T
IIITTIIIbQi
ijk
2
tot
)( )(
)()(|)()(|)()( ),(
)0,( Im1
![Page 36: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/36.jpg)
Zhang & Wong, PRC68,035211(03)
![Page 37: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/37.jpg)
![Page 38: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/38.jpg)
Cross section dependence on color-octet admixture & c-cbar separation
P8 = octet fraction
(c- cbar root-mean square separation)
Zhang & Wong, PRC68,035211(03)
For color-singlet C-Cbar, cross section increases with C-Cbar separation.
![Page 39: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/39.jpg)
Low-energy π-J/ψ cross section
Use the Barnes-Swanson quark-interchange model
Martins,Blaschke,Quack, PRC 51, 2723 (`95)C.Y.Wong, E. Swanson, T. Branes, PRC65,014903(`010
22
||||64
1fi
A
Mpsdt
d
![Page 40: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/40.jpg)
Test the formulation in π-π scattering
![Page 41: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/41.jpg)
Wong, Swanson, Barnes PRC 65 014903 (2001)
![Page 42: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/42.jpg)
J/ψ dissociation by collision with gluon
)( )(
energy binding energy,gluon
2 )22(3
4)(
11
2E1dis
rurrudrI
BE
EIBEE
pp
![Page 43: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/43.jpg)
J/ψdissociation in collision with gluons
Wong, PRC72, 034906(05)
![Page 44: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/44.jpg)
Inverse reaction
Wong, PRC72, 034906(05)
![Page 45: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/45.jpg)
![Page 46: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/46.jpg)
Spectral function analysis
+
![Page 47: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/47.jpg)
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)
![Page 48: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/48.jpg)
Thermodynamical Quantities U1,S1, F1
• Internal energy U1 (kinetic plus potential energies)
• Entropy S1 (the degree of different ordering)
TS1 is the energy associated with entropy
• Free energy F1 = U1 – TS1
( the internal energy minus the energy associated with entropy)
)1( ln)1(ln1 iiii nnnnS
![Page 49: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/49.jpg)
Thermodynamical Quantities
• Internal energy U (kinetic plus potential energies)• Entropy S (the degree of different ordering)
TS is the energy associated with entropy• Free energy F = U – TS
( the internal energy minus the energy associated with entropy)
)1(ln)1(ln iiii nnnnS
![Page 50: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/50.jpg)
Equilibrium condition• dU=T dS – P dV Define free energy F=U – TS, we get dF= – SdT – PdV If the temperature is held fixed (thermal bath) and
the volume does not change locally, then F is a constant.
• In a constant temperature environment, equilibrium is reached when dF=0,
i.e. the variation of F with respect to all degrees of freedom is zero in a thermal bath.
![Page 51: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/51.jpg)
We parameterize the color-singlet F1 and U1 as
),(1 TrF
re
3α(T) 4
- C(T) t)(r,U
t)(r,F r μ(T)-
1
1
),(1 TrF),(1 TrU
![Page 52: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/52.jpg)
![Page 53: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/53.jpg)
U )1(QQ
U )1(g
1 ST
![Page 54: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/54.jpg)
![Page 55: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/55.jpg)
Solve for Q-Q bound states
T)ε(T)ψ(r,T)ψ(r,
T),(r1UT)(r,1U
T),(r1FT)(r,1F
T),(rUT)(r,U
red2μ
2 QQQQ
)1()1(
![Page 56: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/56.jpg)
![Page 57: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/57.jpg)
![Page 58: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/58.jpg)
Heavy quakonia dissociation by collision with gluons at T>Tc
![Page 59: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/59.jpg)
Heavy quakonia dissociation by collision with gluons at T<Tc
![Page 60: Quarkonia in Quark-Gluon Plasma Cheuk-Yin Wong Oak Ridge National Laboratory](https://reader035.vdocuments.net/reader035/viewer/2022062321/56813f5b550346895daa2a83/html5/thumbnails/60.jpg)
1
1/
1
/
2
2
c
c
c
T/Tnear screening small and coupling strong
T/Tnear large very is that implies
T/Tnear of valueLarge
)S(R
)S(R