Images of Excited Condensates: Diagonal Dynamical Bogoliubov Vacuum
UARKONIA Q EAVY H D M - uni-bielefeld.de€¦ · MOTT DISSOCIATION OF HEAVY QUARKONIA David...
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MOTT DISSOCIATION OFHEAVY QUARKONIA
David Blaschke
Institute for Theoretical Physics, University of Wroclaw, Poland
Bogoliubov Laboratory for Theoretical Physics, JINR Dubna, Russia
Outline:
• Introduction: historical remarks
•Bound states in strongly correlated plasmas
•Quantum mechanical evolution of charmonium at the QCD transition
•Mott effect for D-mesons in a hot, dense medium
EMMI Workshop “Quarkonia in Deconfined Matter”, Acitrezza, 30.09.2011
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INTRODUCTION: SOME HISTORICAL REMARKS ...
• 1983: Mott effect and color deconfinement
• 1984: Mott effect and hadron-to-quark mattertransition
• 1986: Matsui-Satz; (Blaschke in N. P. Army)
• 1987: Mott dissociation; NA38 data
• 1989: Meeting H.S., J.H.; Wall breakup
• 1990: 1st Visit at CERN - NA38
• ...
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INTRODUCTION: SOME HISTORICAL REMARKS ...
Ropke & group (Ahrenshoop ∼ 1987)
• 1983: Mott effect and color deconfinement
• 1984: Mott effect and hadron-to-quark mattertransition
• 1986: Matsui-Satz; (Blaschke in N. P. Army)
• 1987: Mott dissociation; NA38 data
• 1989: Meeting H.S., J.H.; Wall breakup
• 1990: 1st Visit at CERN - NA38
• ...
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INTRODUCTION: SOME HISTORICAL REMARKS ...
• 1983: Mott effect and color deconfinement
• 1984: Mott effect and hadron-to-quark mattertransition
• 1986: Matsui-Satz; (Blaschke in N. P. Army)
• 1987: Mott dissociation; NA38 data
• 1989: Meeting H.S., J.H.; Wall breakup
• 1990: 1st Visit at CERN - NA38
• ...
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INTRODUCTION: SOME HISTORICAL REMARKS ...
D.B. (Rostock ∼ 1988)
• 1983: Mott effect and color deconfinement
• 1984: Mott effect and hadron-to-quark mattertransition
• 1986: Matsui-Satz; (Blaschke in N. P. Army)
• 1987: Mott dissociation; NA38 data
• 1989: Meeting H.S., J.H.; Wall breakup
• 1990: 1st Visit at CERN - NA38
• ...
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INTRODUCTION: SOME HISTORICAL REMARKS ...
D.B., Ropke, Schulz (Rathen 2006)
• 1983: Mott effect and color deconfinement
• 1984: Mott effect and hadron-to-quark mattertransition
• 1986: Matsui-Satz; (Blaschke in N. P. Army)
• 1987: Mott dissociation; NA38 data
• 1989: Meeting H.S., J.H.; Wall breakup
• 1990: 1st Visit at CERN - NA38
• ...
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INTRODUCTION: SOME HISTORICAL REMARKS ...
Hufner, Aichelin, Werner (Heidelberg 1991)
• 1983: Mott effect and color deconfinement
• 1984: Mott effect and hadron-to-quark mattertransition
• 1986: Matsui-Satz; (Blaschke in N. P. Army)
• 1987: Mott dissociation; NA38 data
• 1989: Meeting H.S., J. Hufner; Wall breakup
• 1990: 1st Visit at CERN - NA38
• ...
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INTRODUCTION: SOME HISTORICAL REMARKS ...
The Berlin Wall at Potsdamer Platz (Dec. 1989)
• 1983: Mott effect and color deconfinement
• 1984: Mott effect and hadron-to-quark mattertransition
• 1986: Matsui-Satz; (Blaschke in N. P. Army)
• 1987: Mott dissociation; NA38 data
• 1989: Meeting H.S., J. Hufner; Wall breakup
• 1990: 1st Visit at CERN - NA38
• ...
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INTRODUCTION: SOME HISTORICAL REMARKS ...
Schulz, Knoll, Satz, Heinz (CERN 1990)
• 1983: Mott effect and color deconfinement
• 1984: Mott effect and hadron-to-quark mattertransition
• 1986: Matsui-Satz; (Blaschke in N. P. Army)
• 1987: Mott dissociation; NA38 data
• 1989: Meeting H.S., J. Hufner; Wall breakup
• 1990: 1st Visit at CERN - NA38
• ...
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INTRODUCTION: SOME HISTORICAL REMARKS ...
Schulz, D.B., Knoll (CERN-NA38 1990)
• 1983: Mott effect and color deconfinement
• 1984: Mott effect and hadron-to-quark mattertransition
• 1986: Matsui-Satz; (Blaschke in National Peo-ples Army)
• 1987: Mott dissociation; NA38 data
• 1989: Meeting H.S., J. Hufner; Wall breakup
• 1990: 1st Visit at CERN - NA38
• ...
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A SNAPSHOP OF THE SQGP
The Picture: String-flip (Rearrangement) ⇐⇒ Pair correlation
1 2
Horowitz et al. PRD (1985), D.B. et al. PLB (1985),Ropke, Blaschke, Schulz, PRD (1986)
NNr r
g(r)
1
Thoma,[hep-ph/0509154]Gelman et al., PRC 74 (2006)
•Strong correlations present: hadronic spectral functions above Tc (lattice QCD)
•Finite width due to rearrangement collisions (higher order correlations)
• Liquid-like pair correlation function (nearest neighbor peak)
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WHAT HAPPENS ON“H APPY ISLAND”?
"Happy Island"
quarkyonic"beach"
"cliff"
“beach” : hadron resonances −→ QGP
“cliff” :
• (unmodified) vacuum bound state energies
• fast chemical equilibration
Explanation:
Strong medium dependence of ratesfor flavor (quark) exchange processes
Reason:
• lowering of thresholds
• increase of hadron size (Pauli principle)→ geometrical overlap (percolation)
D.B., Berdermann, Cleymans, Redlich,Part. Nucl. Phys. Lett. (2011), arxiv:1102.2908;Few Body Syst. (2011) arxiv:1109.5391
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HYBRID APPOACH: PNJL & MOTT-HAGEDORN RESONANCEGAS
Ptot(T, {µj}) = PPNJL(T, {µi})+∑
r=M,B
δrgr
∫ds Ar(s,mr;T )
∫d3p
(2π)3T ln
{1 + δr exp
(√p2 + s− µr
T
)}
0 100 200 300 400 500 600T [MeV]
0
3
6
9
12
P[T
4],
ε[T
4]
εQGP
= εPNJL
+ ε2
PQGP
=PPNJL
+P2
PMHRG,21
εMHRG,21
Ptot
= PMHRG,21
+ PQGP
εtot
= εMHRG,21
+ εQGP
Lattice data: Borsanyi et al. Spectral function for hadronic resonances:
Ar(s,m;T ) = NsmΓr(T )
(s−m2)2 +m2Γ2r(T )
Ansatz motivated by chemical freeze-out model:
Γr(T ) = τ−1r (T ) =
∑
h
λ < r2r >T< r2h >T nh(T )
Apparent phase transition at Tc ∼ 165 MeV
Hadron resonances present up to Tmax ∼ 250 MeV
Blaschke & Bugaev, Fizika B13, 491 (2004)
Prog. Part. Nucl. Phys. 53, 197 (2004)
Blaschke, Prorok & Turko, in preparation
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T-MATRIX APPROACH TO QUARKONIA IN THE QGP
Riek & Rapp, PRC 82 (2010);arxiv:1005.0769
Open question: Wich potential to use?
U = F − TdF
dTV (r;T ) = F (r;T )− F (∞, T ) or F ↔ U
Result: J/ψ good resonancebelow 1.5 Tc for F , and 2.5 Tc for U
Lattice:Kaczmarek et al. (left), Petreczky et al. (right)
Field theoretic input:Megias et al. JHEP (2006)
D00(~k) = DP00(~k) +DNP
00 (~k)
DP00(~k) =
1
~k2 +m2D
DNP00 (~k) =
m2G
(~k2 + m2D)
2
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BOUND STATES IN STRONGLY COUPLED PLASMAS(I)
Bethe-Salpeter Equation and Plasma Hamiltonan
= + = + TG Gab ab abK ab
Gab = G0ab +G0
ab Kab Gab = G0ab +G0
ab Tab G0ab
= +G G0 G0
Σ Ga a a aa
Ga = G0a +G0
aΣaGa
Equivalent Schrodinger equation [Zimmermann et al. (1978)]∑
q
{[εa(p1) + εb(p2)− z] δq,0 − Vab(q)}ψab(p1+q, p2−q, z) =∑
q
Hplab(p1, p2, q, z)ψab(p1+q, p2−q, z),
with Plasma Hamiltonian
Hplab(p1, p2, q, z) = Vab(q) [Nab(p1, p2)− 1]︸ ︷︷ ︸
(i) Pauli blocking
−∑
q′Vab(q
′) [Nab(p1 + q′, p2 − q′)− 1]
︸ ︷︷ ︸(ii) Exchange self−energy
δq,0
+ ∆Vab(p1, p2, q, z)Nab(p1, p2)︸ ︷︷ ︸(iii) Dynamically screened potential
−∑
q′∆Vab(p1, p2, q
′, z)Nab(p1 + q′, p2 − q′)
︸ ︷︷ ︸(iv) Dynamical self−energy
δq,0
In-medium modification of interaction: ∆Vab(p1, p2, q, z) = Kab(p1, p2, q, z)− Vab(q)
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BOUND STATES IN STRONGLY COUPLED PLASMAS(II)
2-particle wave function ψab and phase space occupation factor Nab
•Uncorrelated fermionic medium: Nab(p1, p2) = 1− fa(p1)− fb(p2)
•Correlated medium with two-particle clusters (ψab(p1, p2, EnP ))fa(p1) → fa(p1) = fa(p1) +
∑c,n,P |ψac(p1, P − p1, EnP )|2gac(EnP )
Discussion of the plasma Hamiltonian:
•Bound states localized in x-space, therefore:over a finite range Λin q-space wave function q-independent:ψab(p1 + q, p2 − q, z = EnP ) ≈ ψab(p1, p2, z = EnP ) , for q < Λ, and vanishes for q > Λ.
• flat momentum dependence of the Pauli blocking factors:Nab(p1 + q, p2 − q) ≈ Nab(p1, p2)
• approximate cancellations of:Pauli blocking term (i) by the exchange self-energy (ii), anddynamically screened potential (iii) by the dynamical self-energy (iv)result in stability of bound states against medium effects !
•Scattering states extended in x-space → no cancellations!,but shift of the continuum threshold !
SUMMARY: Mott effect for bound states possible due to cancellations of medium effects whichdo not apply for the continuum states.
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BOUND STATES IN STRONGLY COUPLED PLASMAS(III)
Application to heavy quarkonia in medium, where heavy quarks are rare
•Nab ≈ 1: Pauli blocking (i) and exchange selfenergy (ii) negligible
•medium effects due to dynamically screened potential (iii) and dynamical selfenergy (iv);from coupling of two-particle state to collective excitations (plasmons)
Screened potential (VS) approximation to interaction kernel K
V Sab(p1p2, q, z) = V S
ab(q, z)δP,p1+p2δ2q,p1−p2
V Sab(q, z) = Vab(q) + Vab(q)Πab(q, z)V
Sab(q, z) = Vab(q)[1− Πab(q, z)Vab(q)]
−1
Example: Heavy quarkonia in a relativistic quark plasma
ΠRPAab (q, z) = 2δab
∫d3p
(2π)3fa(E
ap)− fa(E
ap−q)
Eap − Ea
p−q − z.
Relativistic quark plasma described by a Polyakov-loop NJL model; evaluate the RPA polariza-tion function for Nc ×Nf massless quarks (Ea
p = |p|) in static (ω = 0), long wavelength (q → 0)case:
ΠRPAab (q → 0, 0) = 2δab
∫d3p
(2π)3dfa(E
ap)
dEap
= −2δab
∫ ∞
0
dp p
π2fΦ(p) = − δab
6π2I(Φ)T 2 ,
where I(Φ) = (12/π2)∫∞0 dxxfΦ(x) and fΦ(x) = [Φ(1+2e−x)e−x+e−3x]/[1+3Φ(1+e−x)e−x+e−3x]
is the generalized quark distribution function (Hansen et al 2006).
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BOUND STATES IN STRONGLY COUPLED PLASMAS(IV)
If bare potential a color singlet one-gluon exchange V (q) = −4πα/q2, α = g2/(3π),then Fourier transform of screened potential is a Debye potential V S(r) = −α exp(−mD(T )r)/r
with Debye mass mD(T ) = 4παI(Φ)T 2.Add a screened confinement potential V S
conf(r) = (σ/mD)(1 − exp(−mDr)), calculate Hartreeselfenergies [Rapp, DB, Crochet, arxiv:0807.2470] and solve the effective Schrodinger equa-tion for
VQQ(r;T ) = −αrexp(−mD(T )r)− αmD +
σ
mD[1− exp(−mDr)]
Here σ =const, mD = mD; see Riek/Rapp, PRC 82, 035201 (2010) for σ = σ(T ) and mD 6= mD
0.1 0.2 0.3 0.4T [GeV]
0
0.3
0.6
0.9
1.2
1.5
mD
[GeV
]
with Polyakov loopwithout Polyakov loop
0 0.5 1 1.5 2r [fm]
-1
0
1
VQ
barQ
[GeV
]
T=370 MeVT=303 MeVT=240 MeVT=206 MeVT=151 MeVT=70 MeV
Temperature dependent Debye mass (left) with PL-suppressed screening and correspondingstatically screened Cornell potential (right) [Jankowski, DB, Proceedings CPOD-2010].
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BOUND STATES IN STRONGLY COUPLED PLASMAS(V)
If bare potential a color singlet one-gluon exchange V (q) = −4πα/q2, α = g2/(3π),then Fourier transform of screened potential is a Debye potential V S(r) = −α exp(−µD(T )r)/rwith Debye mass µD(T ) = 4παI(Φ)T 2.Add a screened confinement potential V S
conf(r) = (σ/µD)(1−exp(−µDr)), calculate Hartree self-energies [Rapp, DB, Crochet, arxiv:0807.2470] and solve the effective Schrodinger equation
Hpl(r;T )φnl(r;T ) = Enl(T )φnl(r;T )
for the plasma Hamiltonian Hpl(r;T ) = 2mQ − αµD(T )− ~∇2/mQ + VQQ(r;T )
2.4
2.7
3
3.3
3.6
3.9
Enl
[GeV
]
0.1860.192
0.256
charmonium
J/ψχ
cψ’continuum edge
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4T [GeV]
-0.6
-0.3
0
EB [G
eV]
-Eth= -T
EB = E
nl - (σ/µ − µ α + 2 m
c)
Tc = 0.202 GeV
9.0
9.3
9.6
9.9
10.2
10.5
Enl
[GeV
]
0.2290.244
0.469
bottomonium
Υχ
bΥ’continuum edge
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5T [GeV]
-0.6
-0.3
0
EB [G
eV]
-Eth= -T
EB
= Enl - (σ/µ − µ α + 2 m
b)
Tc = 0.202 GeV
Two-particle energies of charmonia (left) and bottomonia (right) in a statically screened Cornellpotential, [Jankowski, DB, Grigorian, Acta Phys. Pol. B (PS) 3, 747 (2010)].
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BOUND STATES IN STRONGLY COUPLED PLASMAS(VI)
Two(three-)-particle states in the medium: cluster expansion
XX
XX
T
X
X
X
X
T
=K + +X
X
X
X
Σ
T
= +X
X XX
X X
X X X
X X
X X
X X
X
= + Π= +
Π
T2L
T2L
= + + ...
Diagram expansion for 1st and2nd Born order cluster-clusterinteractions
X
X X
X
T
T
T
X
X X
X
T
T
T
’
"
Resulting plasma Hamiltonian [Ebeling, DB, et al., arxiv:0810.3336 [physics.plasm-ph]]:
Hpl = HHartree +HFock +HPauli +HMW +HDebye +Hpp +HvdW + . . . ,
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QUANTUM EVOLUTION OF THE cc STATE: MATSUI’ S MODEL
Harmonic oscillator Hamiltonian
Hcc = 2mc +p2
mc+mc
4ω2x2
Time evolution operator
Uc(r, t0) =
(mcω
4πi sin(ωt0)exp
[imcω
4cot(ωt0)
])
Supression ratio (survival probability)
Rψ(t0) =|〈cc, ψ|Uc(t0)H2g→cc|2g, k0〉|2
|〈cc, ψ|H2g→cc|2g, k0〉|2
Result for pseudoscalar state
Rηc(t0, ω) =[cos2(ωt0) + (ω/ωψ)
2 sin2(ωt0)]−3/2
→ (ω2ψt
20)
−3/2 ; ω = 0, complete deconfinement
T. Matsui, Ann. Phys. 196 (1989) 182
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QUANTUM EVOLUTION OF THE cc STATE: MATSUI’ S MODEL
Harmonic oscillator Hamiltonian
Hcc = 2mc +p2
mc+mc
4ω2x2
Time evolution operator
Uc(r, t0) =
(mcω
4πi sin(ωt0)
)3/2
exp
[imcω
4cot(ωt0)
]
Supression ratio (survival probability)
Rψ(t0) =|〈cc, ψ|Uc(t0)H2g→cc|2g, k0〉|2
|〈cc, ψ|H2g→cc|2g, k0〉|2
Result for pseudoscalar state
Rηc(t0, ω) =[cos2(ωt0) + (ω/ωψ)
2 sin2(ωt0)]−3/2
→ (ω2ψt
20)
−3/2 ; ω = 0, complete deconfinement
Lower Fig.: ω 6= 0, r =√
2/(mcω) = 0.6 fm
T. Matsui, Ann. Phys. 196 (1989) 182
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EXTENDING THE cc OSCILLATOR MODEL TO COMPLEX
FREQUENCIES
Imaginary part in the potential (optical potential = disso-ciation) studied byCugnon/Gossiaux, ZPC 58 (1993) 77, 94Koudela/Volpe, PRC 69 (2004) 054904Harmonic oscillator with complex frequency ω2 = ω2
R+iω2I
Hcc = 2mc +p2
mc+mc
4ω2x2
Time evolution operator for infinitesimal time intervals ∆t
Uc(r,∆t) =
(mcω
4πi sin(ω∆t)
)3/2
exp
[imcω
4cot(ω∆t)
]
Supression ratio (survival probability) can oscillate ...Reasonable assumptions for time dependencies:
t ≤ t0 : ωR = ωψ; ωI = 0
t > t0 : ωR = ωR(t) : ωI = ωI(t)
→ results for the survival probability P (t), see Figureω2I = (ω0
I)2γ, γ = 1/
√1− v2rel (Lorentz factor)
K. Martins, PhD Thesis (1996), unpublished.
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TIME-DEPENDENCE OF COMPLEX FREQUENCY: T-EVOLUTION
0 200 400 600 800 1000T [MeV]
0
5
10
15
20
p[T
4 ], ε
[T4 ],
cs2 , s
[T3 ]
p/T4
ε/T4
s/T3
fit formula
Lattice data: Borsanyi et al., arxiv:1007.2580
2 4 6 8 10 12 14τ [fm/c]
0.15
0.2
0.25
0.3
T [G
eV]
PHENIX AuAu, T0= 311 MeV
PHENIX AuAu, T0= 199 MeV
NA60 PbPb, T0= 224 MeV
NA60 PbPb, T0= 190 MeV
S = const = s(T (t))V (t)
T (t) from V (t) - Bjorken scaling
Harmonic oscillator with time-dependent complex fre-quency ω(t)
H(t) = 4µ +p2
2µ+µ
2ω2(t)r2
Linear combination of two solutions
r(t) = ρ(t) exp(±iφ(t)) , φ(t) =
∫ t
ti
dt′
ρ2(t′).
ρ(t) fulfills Ermakov equation (exact solutions exist)
ρ(t) + ω2(t) ρ(t)− 1
ρ3(t)= 0 .
Time evolution operator
U(tf ; ti) =
[µ ρf ρ
−1i φf
2πi sin(φf − φi)
]3/2eiScl ,
Supression ratio (survival probability)
RAA
RCNMAA
=∣∣∣ ρf/ρi
cos(φf) +(
ρf
ρf φf+ i
ωψ
φf
)sin(φf)
∣∣∣3
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COMBINED DESCRIPTION OFRHIC AND SPSCENTRALITY
DEPENDENCE
0 0.1 0.2 0.3T [GeV]
0
0.5
1
1.5
2
ωR ,
ωI [ω
ψ]
ωI, γ = 2.0
ωI, γ = 1.0
ωI, γ = 0.5ωR
Td = 1.4 Tc
ωI=γ (1−ωR/ωψ)
0 100 200 300 400 500 600 700 800dN/dη|η = 0
0.4
0.6
0.8
1
1.2
RA
A /
RA
A(C
NM
)
PHENIX Au-Au, y=0NA60 In-InNA50 Pb=Pbγ = 0.0γ = 1.0γ = 2.0
EKS98 CNM baseline
Td = 1.4 Tc
D.B., C. Pena, Nucl. Phys. Proc. Suppl. 214 (2011) 137; arxiv:1106.2519
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THE NA60 IN-IN “D IP” - A HINT FOR SUBTLE CORRELATIONS?
0.1 0.15 0.2 0.25T [GeV]
0
0.5
1
1.5
2
ωR ,
ωI [ω
ψ]
ωR=ωa+ωbωaωb
ωI, γ=0.22
ωI, γ=0.40
Td = 1.4 Tc
0 100 200 300 400 500 600 700 800dN/dη|η = 0
0.2
0.4
0.6
0.8
1
1.2
RA
A /
RA
A(C
NM
)
γ=0.4γ=0.22, no feedingγ=0.22PHENIX Au-Au, y=0NA60 In-InNA50 Pb=Pb
EKS98 CNM baseline
Td = 1.4 Tc
D.B., C. Pena, Nucl. Phys. Proc. Suppl. 214 (2011) 137; arxiv:1106.2519
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THE NA60 IN-IN “D IP” - A CONJECTURE...
Close to Tc a resonant J/ψ - ρ interaction gives a contribution to the plasma Hamiltonian whichcould lead to a “pocket” in the effective interaction potential ...
J/ψ J/ψ J/ψ J/ψ J/ψJ/ψ J/ψ
UflipT TUflipρ ρ ρ ρ ρ ρ ρ
X X
J/ψ J/ψ J/ψ J/ψ
UflipM M*_
ρ D,D*
D,_* D
ρ ρ ρ X
X X
X
T
T
T
’
"+. . . =
X X
T
TX
X X
High density of ρ-like states in the medium is required for this contribution to be sizeable.
C. Pena, D.B., in preparation.
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EXTENSION TO THELHC CASE ...
0.1 0.15 0.2 0.25T [GeV]
0
0.5
1
ωR ,
ωI [ω
ψ]
ωaωb
ωI, γ=0.44
ωR, δ=1.0
ωR, δ=1.2
ωR, δ=0.44
Td = 1.4 Tc
0 200 400 600 800 1000 1200 1400 1600dN/dη|η = 0
0.2
0.4
0.6
0.8
1
1.2
RA
A /
RA
A(C
NM
)
PHENIX Au-Au, y=0NA60 In-InNA50 Pb=PbALICE Pb-Pb0.441.01.2
EKS98 CNM baseline
Td = 1.4 Tc
Where does the real part of the oscillator strength at high temperature come from?High density of D, D∗-meson like states in the medium would feed the X-state which con-tributes to the cc plasma Hamiltonian.
C. Pena, D.B., in preparation (2011)
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QUANTUM KINETIC APPROACH TO J/ψ BREAKUP (µB ≈ 0)
Gqq
GqQ
GQq
Uex Uex
GQQGQQ
J/ψJ/ψ_*D, D
_
D*M*
π, ρ
D,M
τ−1(p) = Γ(p) = Σ>(p)∓ Σ<(p)
Σ>
<(p, ω) =
∫
p′
∫
p1
∫
p2
(2π)4δp,p′;p1,p2 |M|2G<
>π (p
′) G>
<D1(p1) G
>
<D2(p2)
G>h (p) = [1± fh(p)]Ah(p) and G<
h (p) = fh(p)Ah(p)
low density approximation for the final states
fD(p) ≈ 0 ⇒ Σ<(p) ≈ 0
τ−1(p) =
∫
p′
∫
p2
∫
p2
(2π)4δp,p′;p1,p2 |M|2 fπ(p′) Aπ(p′) AD1
(p1) AD2(p2)
dσ
dt=
1
16π
|M(s, t)|2λ(s,M2
ψ, s′),
τ−1(p) =
∫d3p′
(2π)3
∫ds′ fπ(p
′, s′) Aπ(s′)vrel σ
∗(s)
In-medium breakup cross section
σ∗(s) =
∫ds1 ds2 AD1
(s1) AD2(s2) σ(s; s1, s2)
Medium effects in spectral functions Ah and σ(s; s1, s2)
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MOTT EFFECT: NJL MODEL PRIMER
0 50 100 150 200 250T [MeV]
0
100
200
300
Con
stite
nt q
uark
mas
s m
and
the
pion
con
stan
t Fπ
m
m (m0=0)
Fπ
Tc
0.5Mπ
0 50 100 150 200 250T [MeV]
0
100
200
300
Dec
ay w
idth
s [M
eV]
Γσ−>ππ
Γρ−>ππ
Γρ−>qq
Γπ−>qq
Γσ−>qq
Tc
Meson propagator: RPA-type resummation,
Dh(P ) ∼ [1−GΠh(P )]−1,
e.g. Pion Pseudoscalar polarization fuction (mq = mq = m)
Ππ(Mπ,~0) = − Nc
8π2
{2A(m)− (Mπ − iΓπ/2)
2 B(Mπ,~0;m,m)}
Finite temperature (Matsubara)
A(m) = −4
∫
Λ
dpp2√E(p)
tanh(E(p)/2T ) real
B(P0,~0;m,m) = 8
∫
Λ
dpp2 tanh(E(p)/2T )
E(p)[4E2(p)− P 20 ]
real for T < Tc
Complex polarization function⇒ Breit-Wigner type spectral function
⇐= Blaschke, Burau, Volkov, Yudichev: EPJA 11 (2001) 319
Charm meson sector, seeGottfried, Klevansky, PLB 286 (1992) 221
Blaschke, Burau, Kalinovsky, Yudichev,Prog. Theor. Phys. Suppl. 149 (2003) 182
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MOTT EFFECT: HEAVY MESON GENERALIZATION
ΠD(P2;T ) = 4IΛ1 (mu;T ) + 4IΛ1 (mc;T ) + 4
(P 2 − (mu −mc)
2)I(λP ,Λ)2 (P 2,mu,mc;T ),
I(λM ,Λ)2 (M,mu,mc;T ) =
Nc
8π2M
Λ∫
λP
dp p2
[Euc tanh(Eu/2T )
Eu(E2u − E2
uc)+Ecu tanh(Ec/2T )
Ec(E2c − E2
cu)
],
0 100 200 300T [MeV]
0
0.5
1
1.5
2
2.5
[Ge
V]
thresholdmasswidth
TMott
= 186 MeV
NJL with IR cutoff
K D D*
Eij = (m2i −m2
j +M2)/2M ,
Infrared cutoff (Mπ(Tc) = 2mu(Tc) = 2mcru )
λP = [mcru θ(mu −mcr
u ) +mu θ(mcru −mu)]
×θ(P 2 − 4(mcru )
2)√P 2/(2 mcr
u )2 − 1,
Meson spectral properties (mass M, width Γ)
G ReΠ(P 2 =M 2; T ) = 1
Γ(T ) = ImΠ(M2; T )/[M(T ) ReΠ′(M2; T )]
⇐= Blaschke, Burau, Kalinovsky, Yudichev,Prog. Theor. Phys. Suppl. 149 (2003) 182.
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J/ψ DISSOCIATION RATE IN A π/ρ RESONANCE GAS
60 80 100 120 140 160 180 200 220 240T [MeV]
10-4
10-3
10-2
10-1
100
<σv
> [m
b]
with Mott effect without Mott effect
J/ψ + π → D* + D (+ h.c.)
NJL with IR cutoff
TMott
=186 MeV
60 80 100 120 140 160 180 200 220 240T [MeV]
10-2
10-1
100
101
<σv
> [m
b]
with Mott effectwithout Mott effect
J/ψ + ρ → D* + D* (+ h.c.)
NJL with IR cutoff
TMott
=186 MeV
Dissociation rate for a J/ψ at rest in a hot resonance gas(h = π, ρ)
τ−1(T ) = τ−1π (T ) + τ−1
ρ (T )
τ−1h (T ) =
∫d3p
(2π)3
∫ds′Ah(s
′; T )fh(p, s′; T )jh(p, s
′)σ∗h(s; T )
= 〈σ∗hvrel〉nh(T ) ,
fh(p, s; T ) = gh{exp[(√p2 + s− µ)/T ]− 1}−1
s(p, s′) = s′ +M2ψ + 2Mψ
√p2 + s′
• Masses slightly rising below TMott
⇒ reduction of breakup rate
• Mott-effect for intermediate states at TMott
⇒ breakup enhancement - “subthreshold” process
• Structure in the breakup rate at T = TMott
• Additional J/ψ absorption channel opens⇒ “anomalous” suppression
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CHARM AND CHARMONIUM PRODUCTION @ RHIC
0 1 2 3 4 5p
T [GeV]
0
0.5
1
1.5
2
RA
A
c+b resoc+b pQCDc resoPHENIX prel.
Au-Au (√s=200 GeV)
0 1 2 3 4 5p
T [GeV]
0
5
10
15
20
25
-5
v 2 [%]
c+b resoc+b pQCDc reso
STAR prel.PHENIX
Au-Au (√s=200 GeV)
0 50 100 150 200 250 300 350N
part
0
0.2
0.4
0.6
0.8
1
1.2
1.4
R AA
PHENIXdirectregenerationsumτ
c
eq~5fm/c
Tdiss
=1.25Tc
Au-Au (200 A GeV)
Recombination of open charm (regeneration of ψ)
dNψ/dt = −Γψ[Nψ −N eqψ (T )]
Hees, Mannarelli, Greco, Rapp, PRL 100, 192301(2008)Nuclear modification factor RAA and elliptic flow v2 ofsemileptonic D− and B− meson decay-electrons inb = 7 fm Au-Au (
√s = 200 GeV) collisions at RHIC
⇐= Hees, Greco, Rapp, PRC 73, 034913 (2006)
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CHARM AND CHARMONIUM PRODUCTION @ FAIR-CBM
__ _GQq
Uex Uex
GQQ
GqqQ
Gqqq
GQQ
J/ψ dissociation process in dense baryonic matterat FAIR-CBM: spectral functions for open charmhadrons (D-meson, Λc) are essential inputs!⇐=
D-meson spectral function in cold dense nuclearmatter from a G-matrix approach ↓
1600 1700 1800 1900ωD (MeV)
0
1
2
3
4
5
6
7
8
S D(kD=0
,ω) (G
eV−2
)
ρ=0.5ρ0
ρ=ρ0
ρ=1.5ρ0
1600 1700 1800 1900 2000ωD (MeV)
Tolos et al., EPJC (2005); nucl-th/0501151
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QUANTUM KINETICS OF J/ψ DISSOCIATION @ CBM (µB 6= 0)
__ _GQq
Uex Uex
GQQ
GqqQ
Gqqq
GQQ
J/ψJ/ψ
M*
D_
Λ cM
N
Charmonium lifetime in a dense nuclear medium (fD ≈ 0)
τ−1(p) =
∫
p′
∫
p2
∫
p2
(2π)4δp,p′;p1,p2 |M|2 fN(p′) AN(p′) AΛ(p1) AD(p2)
Medium effects in hadronic spectral functions Ah and σ(s; s1, s2)D-meson spectral function in cold dense nuclear matter from a G-matrix approach ↓ (N, Λc similar)
1600 1700 1800 1900ωD (MeV)
0
1
2
3
4
5
6
7
8
S D(k D=0,ω)
(GeV
−2)
ρ=0.5ρ0
ρ=ρ0
ρ=1.5ρ0
1600 1700 1800 1900 2000ωD (MeV)
Tolos et al., EPJC (2005); PRC 80, 065202 (2009)
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QUANTUM KINETICS OF J/ψ DISSOCIATION @ CBM (µB 6= 0)
__ _GQq
Uex Uex
GQQ
GqqQ
Gqqq
GQQ
J/ψJ/ψ
M*
D_
Λ cM
N
Charmonium lifetime in a dense nuclear medium (fD ≈ 0)
τ−1(p) =
∫
p′
∫
p2
∫
p2
(2π)4δp,p′;p1,p2 |M|2 fN(p′) AN(p′) AΛ(p1) AD(p2)
Medium effects in hadronic spectral functions Ah and σ(s; s1, s2)D-meson spectral function in hot, dense quark matter from a NJLmodel approach ↓ (N, Λc similar)
1850
1900
1950
2000
2050
2100
mas
s [M
eV]
0 1 2 3 4 5 6density n [n
0]
0100200300400500
widt
h [M
eV]
T = µ/3
D+
D-
D-
D+
Mu(d)
+Mc
D.B., P. Costa, Yu. Kalinovsky, arxiv:1107.2913
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SUMMARY
•Diagram expansions in strongly correlated quark plasma guided by plasma physics
•Microscopic formulation of the hadronic Mott effect within a chiral quark model
•Mesonic (hadronic) correlations important for T > Tc
•Step-like enhancement of threshold processes due to Mott effect
•Reaction kinetics for strong correlations in plasmas applicable @ SPS and RHIC
•Prospects for CBM: Anomalous suppression expected, eventually (more) steplike!
PLANS FOR THE FUTURE
•Bridge Lattice QCD and Phenomenology: spectral functions
•Calculate J/ψ breakup with baryon impact =⇒ CBM @ FAIR GSI
•Mott effect in dense baryonic matter: nucleon dissociation!
•EoS for hot, dense matter with Mott-effect, encoded in hadronic spectral functions
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CONCLUSION: MOTT DISSOCIATION STILL INTERESTING...
• 1983: Mott effect and color deconfinement
• 1984: Mott effect and hadron-to-quark mattertransition
• 1986: Matsui-Satz; (Blaschke in N. P. Army)
• 1987: Mott dissociation; NA38 data
• 1989: Meeting H.S., J. Hufner; Wall breakup
• 1990: 1st Visit at CERN - NA38
• ...
• 2011: EMMI workshop Acitrezza
THANKS FOR YOUR INSPIRING WORK, HELMUT !
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INVITATION : V ISIT WROCŁAW & U NIVERSITY