UARKONIA Q EAVY H D M - uni-bielefeld.de€¦ · MOTT DISSOCIATION OF HEAVY QUARKONIA David...

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

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

• ...


Ropke & group (Ahrenshoop ∼ 1987)







• ...








• ...


D.B. (Rostock ∼ 1988)







• ...


D.B., Ropke, Schulz (Rathen 2006)







• ...


Hufner, Aichelin, Werner (Heidelberg 1991)





• 1989: Meeting H.S., J. Hufner; Wall breakup


• ...


The Berlin Wall at Potsdamer Platz (Dec. 1989)







• ...


Schulz, Knoll, Satz, Heinz (CERN 1990)







• ...


Schulz, D.B., Knoll (CERN-NA38 1990)



• 1986: Matsui-Satz; (Blaschke in National Peo-ples Army)




• ...

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)

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

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

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

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)

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.

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).

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].

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)].

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 + . . . ,

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

QUANTUM EVOLUTION OF THE cc STATE: MATSUI’ S MODEL

Harmonic oscillator Hamiltonian

Hcc = 2mc +p2

mc+mc

4ω2x2


Uc(r, t0) =

(mcω

4πi sin(ωt0)

)3/2

exp

[imcω

4cot(ωt0)

]


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

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.

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 .


U(tf ; ti) =

[µ ρf ρ

−1i φf

2πi sin(φf − φi)

]3/2eiScl ,


RAA

RCNMAA

=∣∣∣ ρf/ρi

cos(φf) +(

ρf

ρf φf+ i

ωψ

φf

)sin(φf)

∣∣∣3

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

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

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.

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)

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)

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

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.

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

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)

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

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)

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

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

CONCLUSION: MOTT DISSOCIATION STILL INTERESTING...







• ...

• 2011: EMMI workshop Acitrezza

THANKS FOR YOUR INSPIRING WORK, HELMUT !

INVITATION : V ISIT WROCŁAW & U NIVERSITY

UARKONIA Q EAVY H D M - uni-bielefeld.de€¦ · MOTT DISSOCIATION OF HEAVY QUARKONIA David...

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