J/ψ Suppression and Enhancement - Theory...

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP

The statisticalhadronizationmodelIntroduction to themodel

Grand canonicalformalism

Canonical formalism

J/ψsuppressionandenhancementTheoreticaldescription

Data analysis

Some new results

Summary andreference

J/ψ Suppression and EnhancementThe Statistical Hadronization Model

Jun Nian

Universität Heidelberg

Jan. 24, 2008

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Outline

1 Introduction to QGP

2 The statistical hadronization modelIntroduction to the modelGrand canonical formalismCanonical formalism

3 J/ψ suppression and enhancementTheoretical descriptionData analysisSome new results

4 Summary and reference

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Definition of QGP

Quark-Gluon Plasma (QGP):

A plasma of strongly interacting, deconfined quarks andgluons.

A thermodynamic system (a system, which can bedescribed by the equation of motion from statisticalphysics). For such a system there should be transition,eventually phase transition.

Hadronic ConstituentsTransition

QGP

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Canonical formalism


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A short history

• 1965: Hagedron observed that the mass density of hadronstates grows exponentially with energy, which led to theexistence of a phase transition.

• 1973: asymptotic freedom (Nobelprize 2004)D.J.Gross, F.Wilczek, Phys. Rev. Lett. 30 (1973) 1343H.D.Politzer, Phys. Rev. Lett. 30 (1973) 1346

• 1975: deconfined quarks and gluonsN.Cabibbo, G.Parisi, Phys. Lett. B 59 (1975) 67J.C.Collins, M.J.Perry, Phys. Rev. Lett. 34 (1975) 1353

• 1980: suggested by Shuryak, the new phase wasdenominated “Quark-Gluon Plasma” (QGP).

• · · · · · ·

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Phase diagrams - 1

(Source: N.Cabibbo, G.Parisi, Phys. Lett. B 59 (1975) 67)

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Canonical formalism


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Phase diagrams - 2

(Source: K.Yagi, T.Hatsuda, Y.Miake, (2005) Quark-Gluon Plasma)

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Canonical formalism


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Phase diagrams - 3

(Source:presentation given by M.Ries from the seminar “experimental particle and nuclear physics” in Uni. Heidelberg)

J/ψSuppression

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Introduction toQGP



Canonical formalism


Data analysis

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Phase diagrams - 4

(Source: W.Greiner, S.Schramm, E.Stein, (2002) Quantum Chromodynamics)

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Introduction toQGP



Canonical formalism


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Creation of QGP

The only prerequisite condition to create QGP:• Critical energy density: εc ≈ 0.7GeV/fm3


J/ψSuppression

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Introduction toQGP



Canonical formalism


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Possible places to find QGP

3 possible places to find QGP:• in the early universe (“Big Bang”)• at the center of compact stars• in the initial stage of colliding heavy nuclei at high

energies (“Little Bang”)


J/ψSuppression

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Introduction toQGP



Canonical formalism


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Experimental probes for QGP

Facility Location System√

sNN

SIS GSI, Darmstadt Au+Au 1-2 GeVAGS BNL, New York Au+Au 2.6-4.3 GeVSPS CERN, Geneva Pb+Pb 8.6-17.2 GeVRHIC BNL, New York Au+Au 130, 200 GeVLHC CERN, Geneva Pb+Pb 5.5 TeV

The expected effects which cannot be produced in a normalnuclear surrounding:

• J/ψ enhancement

• Very exotic objects, e.g. multibaryon states with a very largestrangeness content.(According to W.Greiner, S.Schramm, E.Stein, (2002) Quantum Chromodynamics)

J/ψSuppression

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Jun Nian

Introduction toQGP



Canonical formalism


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Some details of RHIC

Brookhaven National Laboratory

Relativistic Heavy Ion Collider (RHIC)

Experiments:

STAR, PHENIX,

PHOBOS, BRAHMS

Au-Au,√

sNN = 130 , 200 GeV

∼ 103 particles produced

(Source: www.bnl.gov/rhic)

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Outline





J/ψSuppression

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Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Some general information about the model

The statistical hadronization model (SHM):• mainly used to calculate particle production;• basic idea: all particles stem from a thermalized fireball

at temperature T and baryon chemical potential µb;• can be applied both to p+p collsions and to A+A

collisions;• a partition function (microcanonical, grand canonical,

canonical) is used;• with three parameters V , T and µb particle yields can

be explained.

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Introduction toQGP



Canonical formalism


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Space-time evolution of heavy ion collsions(Source: presentation given by M.Ries from theseminar “experimental particle and nuclear physics”in Uni. Heidelberg)


Space-time evolution of heavy ion collsions in the Bjorken model:

1 0 < τ < τ0: Pre-equilibrium stage and thermalization

2 τ = τ0: Thermal equilibrium

3 τ0 < τ < τf : Hydrodynamical evolution and freeze-out

4 τ = τf : Chemical freeze-out

5 τ > τf : Free-out and post-equilibrium

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Introduction toQGP



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All assumptions of the model

Some Assumptions:1 All heavy quarks (charm and bottom) are produced in

primary hard collisions.2 Their total number stays constant until hadronization.3 Thermal (but not chemical) equilibration takes place in

QGP, at least near the critical temperature Tc .4 The quarkonia are all produced (nonperturbatively)

when Tc is reached and the system hadronizes.5 The participating nucleons’ number Npart is sufficiently

large.

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Canonical formalism


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Assumptions of the model - 1


1. All heavy quarks (charm and bottom) are produced in primaryhard collisions.

- Hard QCD process −→ QGP −→ Hadron gas

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Introduction toQGP



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Assumptions of the model - 2


2. Their total number stays constant until hadronization.

- The cc and bb pairs are created at the early stage of A+Areaction, and the number of cc and bb pairs remainsapproximately unchanged during the further evolutionrespectively.

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Assumptions of the model - 3 & 4


3. Thermal (but not chemical) equilibration takes place in QGP, atleast near the critical temperature Tc .

4. The quarkonia are all produced (nonperturbatively) when Tc isreached and the system hadronizes.

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Canonical formalism


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Difference between grand canonical andcanonical formalism

Grand Canonical Ensemble (GC):- only valid in system with large number of produced particles;

- conservation of addtive quantum numbers (B, S, I3) can beimplemented on average by use of chemical potential µ;

- asymptotic realization of exact canonical approach.

Canonical Ensemble (C):- can be valid in system with small particle multiplicity;

- conservation law must be implemented locally on event-by-eventbasis, which leads to severe phase space reduction for particleproduction (“canonical suppression”);

- relevant in low energy A+A collisions, high energy p+p or e+e−

collisions.

J/ψSuppression

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Introduction toQGP



Canonical formalism


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Grand canonical formalism: concrete derivation- 1

Partition function: Z GC = Tr[e−β(H−µN)

], where H =

∑p εpa†pap , N =

∑p a†pap .

Another form: Z GC = Tr[e−β(H−

∑j µj Qj )

],

where Qj is some total quantum number (e.g. baryon number, electric charge, · · · )of the system.

=⇒ Z GC = Tr∏

pe−β(εp−µ)a†p ap =

∏p

∑np

e−β(εp−µ)np ≡∏

pZp,

where

Zp ≡∑np

e−β(εp−µ)np =

{ ∑∞np=0 e−β(εp−µ)np = 1

1−e−β(εp−µ) , for boson∑1np=0 e−β(εp−µ)np = 1 + e−β(εp−µ), for fermion

= (1∓ e−β(εp−µ))∓1 ≡ (1∓ λe−βεp )∓1,

where

λ ≡ eβµ = exp(

µ

kBT

)= exp

(BiµB + SiµS + QiµQ

T

). (set kB = 1)

Bi , Si , Qi : baryon number, strangeness and electric charge of one i-th particle.

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For the i-th particle:considering the degeneracy factor gi , the partition function becomes(the upper sign for boson, and the lower sign for fermion)

ln Zi = gi∑

pln Zp = gi

V(2π~)3

∫d3p ln

(1∓ λi e−βεi

)∓1

(set ~ = 1) =gi V2π2

·∫ ∞

0dp (∓p2) · ln

(1∓ λi e−βεi

)=

gi V2π2

· (Integral I)

Integral I =

∫ ∞

0(∓p2) ·

∞∑k=1

(−1)k−1

k

(∓λi e−βεi

)k

=∞∑

k=1

(−1)k−1 · (∓1)k+1

k· λk

i ·∫ ∞

0dp p2e−βεi k

=∞∑

k=1

(±1)k+1

k· λk

i ·∫ ∞

0dp p2e−βεi k

=∞∑

k=1

(±1)k+1

k· λk

i · (Integral II)

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Integral II =∫∞

0 dp p2 · e−βεi k =∫∞

0 dp p2 · e−kT

√p2+m2

i

=∫∞

0 dp p2 · e− kmi

T

√1+

(p

mi

)2

=∫∞

0 dp p2 · e−z·cosh(t) (z ≡ kmiT , cosh(t) ≡

√1 +

(p

mi

)2)

(* see below) =∫∞

0 dt mi cosh(t) ·m2i sinh2(t) · e−z·cosh(t)

=∫∞

0 dt m3i

4 [cosh(3t)− cosh(t)] · e−z·cosh(t)

=∫∞

0 dt m3i

4 cosh(3t) · e−z·cosh(t) −∫∞

0 dt m3i

4 cosh(t) · e−z·cosh(t)

=m3

i4 (K3(z)− K1(z)) =

m3i

4 · 4Tkmi

· K2

(kmiT

)=

m2i Tk · K2

(kmiT

)[

Kn(z) =

∫ ∞

0dt cosh(nt) · e−z·cosh(t),Kn+1 − Kn−1 =

2nz

Kn(z)

]

* cosh(t) =et + e−t

2=

√1 +

(pmi

)2⇔

e2t + e−2t + 24

= 1 +

(pmi

)2

⇔(

et − e−t

2

)2

=

(pmi

)2⇔ sinh(t) =

pmi

⇔ p = mi · sinh(t)

⇔ p2 = m2i · sinh2(t) & dp = mi · cosh(t) dt

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Introduction toQGP



Canonical formalism


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ln Zi = gi V2π2 · (Integral I)

= gi V2π2 ·

∑∞k=1

(±1)k+1

k · λki · (Integral II)

= gi V2π2 ·

∑∞k=1

(±1)k+1

k · λki ·

m2i Tk K2

(kmiT

)= VTgi

2π2 ·∑∞

k=1(±1)k+1

k2 · λki ·m2

i K2

(kmiT

)⇒ 〈Ni〉 = 1

β∂lnZi∂µ

= 1β· VTgi

2π2 ·∑∞

k=1(±1)k+1

k2 · ∂(λki )

∂µ·m2

i K2

(kmiT

)[λi ≡ exp

(µT

)]= 1

β· VTgi

2π2 ·∑∞

k=1(±1)k+1

k2 · kλk−1i · λi

T ·m2i K2

(kmiT

)= VTgi

2π2 ·∑∞

k=1(±1)k+1

k λki m2

i K2

(kmiT

)⇒ ni(T , ~µ) =

〈Ni〉V

=Tgi

2π2 ·∞∑

k=1

(±1)k+1

kλk

i m2i K2

(kmi

T

)An important consequence:there is a relation between the one-particle partition function and theone-particle density: (k = 1)

ni =ln Zi

V

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Introduction toQGP



Canonical formalism


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Grand canonical formalism: summary

For a large number of particles:Partition function: Z GC(T ,V , µQ) = Tr [e−β(H−

∑i µQi

Qi)]For particle i of strangeness Si , baryon number Bi , electric charge Qi

and spin-isospin degeneracy factor gi :(the upper sign for boson, and the lower sign for fermion)

lnZi(T ,V , ~µ) =Vgi

2π2

∫ ∞

0∓p2dp ln[1∓ λi exp(−βεi)],

whereλi(T , ~µ) = exp

Bi µB + Si µS + Qi µQ

T.

=⇒ lnZi(T ,V , ~µ) =VTgi

2π2

∞∑k=1

(±1)k+1

k2 λki m2

i K2

(kmi

T

),

where K2 is the modified Bessel function of the second kind.

=⇒ ni(T , ~µ) =〈Ni〉V

=Tgi

2π2

∞∑k=1

(±1)k+1

kλk

i m2i K2

(kmi

T

)

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Canonical formalism


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Grand canonical formalism: input parameters -1

Zi(T ,V , µB, µS, µQ) =⇒ ni(T , ~µ)

In order to compare with the experimental data, we must:1 fix some input parameters:

Strangeness conservation 〈S〉V = 0 =⇒ fix µS

Initial condition 〈Q〉/V〈B〉/V = const =⇒ fix µQ

2 cosider relevant decays:

nthi ≡ ntot

i (T , µB) = ni(T , µB) +∑

j

B(j → i) · nj(T , µB)

3 only consider the relative densities:

nthi

nthref

=〈Ni〉/V〈Nref 〉/V

=〈Ni〉〈Nref 〉

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Canonical formalism


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Grand canonical formalism: input parameters -2

Zi(T ,V , µB, µS, µQ) =⇒ ni(T , ~µ)

To determine the input parameters T and µB:

• measure the multiplicities of three particles (e.g. π, ρand K ), then solve

nthρ

nthπ

=〈ρ〉/V〈π〉/V

=〈ρ〉〈π〉

,nth

Knthπ

=〈K 〉/V〈π〉/V

=〈K 〉〈π〉

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Compare with the experimental data - 1SPS, Pb-Pb collisions at

√sNN = 40 GeV,

T = 148MeV, µB = 400MeV:

χ2 =∑

i

(Rexp.

i − Rmodeli

)2

σ2i

= 1.1

(Source: P.Braun-Munzinger, K.Redlich, J.Stachel, arXiv: nucl-th/0304013v1)

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Compare with the experimental data - 2

SPS, Pb-Pb collisions at√

sNN = 158 GeV,T = 170MeV, µB = 255MeV:

Excluding φ and d : χ2 = 2.0;Considering different efficiencies of Λ and π− from weak decays: χ2 = 1.5

(Source:P.Braun-Munzinger, I.Heppe, J.Stachel, Phys. Lett. B 465 (1999) 15 + reanalysis in 2003 with more data)

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RHIC, Au-Au collisions at√

sNN = 130 GeV,T = 174MeV, µB = 46MeV:

(Source: P.Braun-Munzinger, D.Magestro, K.Redlich, J.Stachel, Phys. Lett. B 518 (2001) 41)

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RHIC, Au-Au collisions at√

sNN = 130 and 200 GeV,T = 176MeV, µB = 41MeV for

√sNN = 130 GeV, T = 177MeV,

µB = 29MeV for√

sNN = 200 GeV:

χ2 = 0.8 χ2 = 1.1(Source: P.Braun-Munzinger, D.Magestro, K.Redlich, J.Stachel, Phys. Lett. B 518 (2001) 41, updated byD.Magestro in 2002)

J/ψSuppression

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Introduction toQGP



Canonical formalism


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Why canonical formalism?

Grand Canonical Ensemble (GC):- only valid in system with large number of produced particles;

- conservation of addtive quantum numbers (B, S, I3) can beimplemented on average by use of chemical potential µ.

Canonical Ensemble (C):- can be valid in system with small particle multiplicity;

- conservation law must be implemented locally on event-by-eventbasis.

From experiments (SPS, RHIC): the heavy quarks’ multiplicitiesare very small in A+A collisions.

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Introduction toQGP



Canonical formalism


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Canonical formalism: concrete derivation - 1

Aim: find an expression of particle density, in which some quantumnumber is exactly conserved.Start from the grand canonical partition function:Z GC(T ,V , µC) = Tr [e−β(H−µC C)]

Eigenstates of H and C: H|C〉 = EC |C〉, C|C〉 = C|C〉

=⇒ Z GC(T ,V , µC) =+∞∑

C=−∞

e−βEC · eβµC C =+∞∑

C=−∞

ZC · (λC)C ,

where ZC ≡ TrC [e−βH ], λC ≡ eβµC .

1 If the value of C is fixed, ZC ≡ TrC [e−βH ] is a canonical partitionfunction.ZC=C0(T ,V ) = TrC0 [e

−βH ] = Tr [e−βH · PC0 ],where PC0 = P2

C=0 = δCC0 is the projection operator.

2 Z GC(T ,V , µC) ⇒ Z GC(T ,V , λC)Define eiφ ≡ λC :Z GC(T ,V , µC) ⇒ Z GC(T ,V , λC) ⇒ Z (T ,V , φ)

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ZC=C0(T ,V ) = Tr [e−βH · δCC0 ] =1

2π

∫ 2π

0dφ e−i(C−C0)φ · Z (T ,V , φ)

Redefine: Znew(T ,V , φ) ≡ eiφ · Zold(T ,V , φ), then for fixed C

ZC(T ,V ) =1

2π

∫ 2π

0dφ e−iCφ · Z (T ,V , φ)

Consider a system consisting of m “C = 0”, n −m “C = 1” and p −m

“C = −1” particles, but without multicharm particles:(All Zk ’s are one-particle partition functions.)

Z (T ,V , φ) = exp(m∑

k=1

ln Z C=0k +

n∑k=m+1

ln Z C=1k · eiφ +

p∑k=n+1

ln Z C=−1k · e−iφ)

≡ exp(∑

k

ln Z C=0k ) · exp(eiφ · C1) · exp(e−iφ · C−1)[

Z =∏

i

Zi = eln Z1 · eln Z2 · · · eln Zn = eln Z1+ln Z2+···+ln Zn

]

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⇒ ZC = 12π

∫ 2π0 dφ e−iCφ · Z

= 12π

∫ 2π0 dφ e−iCφ · e

∑k ln Z C=0

k · eeiφ·C1 · ee−iφ·C−1

≡ Z0 · 12π

∫ 2π0 dφ e−iCφ · eeiφ·C1+e−iφ·C−1

= Z0 · 12π

∫ 2π0 dφ e−iCφ · e

√C1C−1(eiφ

√C1

C−1+e−iφ

√C−1C1

)

(see below ∗) = Z0 · 12π

∫ 2π0 dφ e−iCφ ·

∑+∞C′=−∞

(eiφ ·

√C1

C−1

)C′

· IC′ (2√

C1C−1)

= Z0 · 12π∑+∞

C′=−∞∫ 2π

0 dφ e−iCφ · eiC′φ ·(

C1C−1

)C′/2· IC′ (2

√C1C−1)

= Z0 ·(

C1C−1

)C/2· IC(2

√C1C−1)

* For the modified Bessel function of the first kind:

ex2 (t+ 1

t ) =+∞∑

C=−∞tC · IC(x).

Here x = 2√

C1C−1, t = eiφ√

C1C−1

:

⇒ e2√

C1C−12 (eiφ

√C1

C−1+e−iφ

√C−1C1

)=

+∞∑C=−∞

(eiφ

√C1

C−1

)C

· IC(2√

C1C−1)

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Canonical formalism: concrete derivation - 4We implement a transformation by introducing fugacity parameters:(The same particle species has the same λk .)

Z (T ,V , φ) = exp(m∑

k=1

ln Z C=0k +

n∑k=m+1

ln Z C=1k · eiφ +

p∑k=n+1

ln Z C=−1k · e−iφ)

⇒ Z (T ,V , φ) = exp(m∑

k=1

λk ·ln Z C=0k +

n∑k=m+1

λk ·ln Z C=1k ·eiφ+

p∑k=n+1

λk ·ln Z C=−1k ·e−iφ)

The density of the k-th particle: (assuming Nk terms has the same λk )

nGCk =

λk

V·∂

∂λkln Z |λk =1 = Nk ·

ln Zk

V

If we consider the conservation of the charm:

nCk =

λk

V·∂

∂λkln ZC |λk =1

with

ZC =1

2π

∫ 2π

0dφ e−iCφ · Z = Z0 ·

(C1

C−1

)C/2· IC(2

√C1C−1)

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Canonical formalism


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nCk =

λk

V·∂

∂λkln ZC |λk =1, ZC = Z0 ·

(C1

C−1

)C/2· IC(2

√C1C−1),

C1 ≡n∑

k=m+1

λk · ln Z C=1k , C−1 ≡

p∑k=n+1

λk · ln Z C=−1k

First we calculate the density of a particle with C = 1:

=⇒∂

∂λkln ZC =

C2·

1C1

· Nk ln Zk +1

IC(2√

C1C−1)·∂IC(2

√C1C−1)

∂λk

=C2·

1C1

· Nk ln Zk +1

IC(2√

C1C−1)·∂IC∂x

|x=2√

C1C−1·∂(2√

C1C−1)

∂λk

=C2·

1C1

· Nk ln Zk +1

IC(2√

C1C−1)·∂IC(x)

∂x|x=2

√C1C−1

·C−1 · Nk ln Zk√

C1C−1

= Nk ln Zk

[C

2C1+

1IC(x0)

·C−1√C1C−1

·IC−1(x0) + IC+1(x0)

2

](x0 ≡ 2

√C1C−1)

= Nk ln Zk

[√C1C−1

2C1·

IC−1(x0)− IC+1(x0)

IC(x0)+

1IC(x0)

·C−1√C1C−1

·IC−1(x0) + IC+1(x0)

2

]

= Nk ln Zk ·C−1√C1C−1

·IC−1(x0)

IC(x0)(∗ see next page)

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Canonical formalism: concrete derivation - 6The modified Bessel function of the first kind In(x) has the properties:

In(x) = I−n(x), In−1(x)− In+1(x) = 2nx In(x), In−1(x)+ In+1(x) = 2I′n(x).

In the last page we derived

∂

∂λkln ZC = Nk ln Zk ·

C−1√C1C−1

· IC−1(x0)

IC(x0).

This yields

nCk =

Nk ln Zk

V· C−1√

C1C−1· IC−1(x0)

IC(x0).

Similarly for a particle with C = −1:

nCk =

Nk ln Zk

V· C1√

C1C−1· IC+1(x0)

IC(x0),

and for a particle with C = 0:

nCk =

Nk ln Zk

V.

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results



C = 1:nC

k =Nk ln Zk

V· C−1√

C1C−1· IC−1(x0)

IC(x0).

C = −1:

nCk =

Nk ln Zk

V· C1√

C1C−1· IC+1(x0)

IC(x0),

C = 0:nC

k =Nk ln Zk

V.

In QGP there are only open c and c quarks, whose quantum number isC = 1 or C = −1, and C1 = C−1:

=⇒ nCc = nC

c =Nk ln Zc

V· I1(2nc · V )

I0(2nc · V )

=⇒ nCc = nGC

c · I1(2NGCc )

I0(2NGCc )

= nGCc · I1(NGC

oc )

I0(NGCoc )

I.e. using canonical formalism, the open charm densities (or yields) aresuppressed by a factor I1

I0.

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Charm quarks’ evolution in heavy-ion collisions(in a not completely correct picture)

(Source: notes of the lecture “standard model” by Prof. Uwer from Uni. Heidelberg)

More precisely, what must be exactly conserved, is

the number of open charms at the phase boundary.

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Canonical formalism of charm quarks - 1

In grand canonical formalism:

Ndircc =

12

N thoc + N th

cc

1. Modification: canonical suppression factor I1/I0

Ndircc =

12

N thoc

I1(N thoc)

I0(N thoc)

+ N thcc ,

where I0 and I1 are modified Bessel functions of the firstkind.

2. Modification: fugacity parameter gc(Npart ,T , µB), to account fordeviations from chemical equilibrium.

Ndircc =

12

gc N thoc

I1(gcN thoc)

I0(gcN thoc)

+ g2c N th

cc

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Canonical formalism of charm quarks - 2

The yields of different charm hadrons produced in heavy ioncollisions:

• For open charm mesons and hyperons:

Ni = gc N thi

I1(gcN thoc)

I0(gcN thoc)

• For charmonia:Nj = g2

c N thj

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Explanation of the 5. assumption

5. The participating nucleons’ number Npart is sufficiently large.

We’ve just got for charmonia: Nj = g2c N th

j

=⇒ Nψ′ = gc(Npart)2 N th

ψ′ , NJ/ψ = gc(Npart)2 N th

J/ψ

=⇒ Nψ′NJ/ψ

=N thψ′

N thJ/ψ

,

which doesn’t depend on Npart .

(Source: P.Braun-Munzinger, J.Stachel, Phys. Lett. B490 (2000) 196-202)

⇒ “Corona Effect”

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Outline





J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Some concepts in relativistic kinematics - 1

• Rapidity:

y =12

ln(

E + pl

E − pl

)• Pseudo-rapidity:

η =12

ln(|p|+ pl

|p| − pl

)= −ln(tan

θ

2)

-��

��>

��

��=

6

-θ~p1 ~p2

~p3

~p4

~pl

1 When β ≡ vc → 1, y ≈ η.

2 η = 0 ⇔ pl = 0 ⇔ ~p3 ⊥ ~p1

An example:|η| 6 1

2⇔ −1

26 ln(tan

θ

2) 6

12⇔ e−

12 6 tan

θ

26 e

12

⇔ arctan(e−12 ) 6

θ

26 arctan(e

12 ) ⇔ 62.4762 ◦ 6 θ 6 117.5238 ◦

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Some concepts in relativistic kinematics - 2

(Source: Notes of the lecture “compressed nuclear matter”by C.Höhne in GSI Summer Student Program 2007)

• Centrality:

- describes quantitatively, how central (or peripheral) acollision is.

- is related to the concept “impact parameter”.

• Centrality class: (non)overlapping percentage of collidingions, e.g. 0 ∼ 20%, 20 ∼ 40%, · · ·

• Centrality dependecne: a physical quantity as a function ofNpart or ET .

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


What is J/ψ suppression?

(Source: C.Lourenco, Nucl.Phys. A 685 (2001) 384c)

• X-Axis: ET , Npart , · · ·

• Y-Axis: dNJ/ψ/dyNpart

, RJ/ψAA ≡ dNAA

J/ψ/dyNcoll ·dNpp

J/ψ/dy , Bµµ·σ(J/ψ)σ(DY ) , · · ·

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Qualitative description of J/ψ suppression andenhancement

(Source: notes of the lecture “standard model” by Prof. Uwer from Uni. Heidelberg)

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Quantitative description of J/ψ suppressionusing SHM: Calculation procedure

Under the assumptions mentioned before:

Ndircc =

12

gc N thoc

I1(gcN thoc)

I0(gcN thoc)

+ g2c N th

cc , NJ/ψ = g2c N th

J/ψ

• From pQCD: σ(pp → cc); nuclear overlap function TAA(Npart)Ndir

cc = σ(pp → cc) · TAA(Npart)

• From grand canonical formalism: nthoc , nth

cc , nthch;

measure dNch/dy |y=0;dNch/dy |y=0 = nth

ch · V∆y=1 =⇒ V∆y=1;N th

oc = nthoc · V∆y=1, N th

cc = nthcc · V∆y=1

• Ndircc , N th

oc ,N thcc =⇒ gc

• J/ψ yields: NJ/ψ = g2c · N th

J/ψ

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


When suppression? When enhancement?

Ndircc =

12

gc N thoc

I1(gcN thoc)

I0(gcN thoc)

+ g2c N th

cc

(Source: A.Andronic, P.Braun-Munzinger, K.Redlich, J.Stachel, nucl-th/0611023v2)

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Centrality dependence of NJ/ψ /Npart at SPS

(Source: A.Andronic, P.Braun-Munzinger, K.Redlich, J.Stachel, Phys. Lett. B 571 (2003) 36-44)

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Centrality dependence of RJ/ψAA at RHIC and

LHC


J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Influence of the input parameters at RHIC


J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Rapidity dependence of RJ/ψAA at RHIC


• In other models (e.g. melting model, co-moving model, · · · ):constant or minimum at midrapidity

• Only in the statistical hadronization model: maximum at midrapidity

The first direct evidence for generation of J/ψ mesons at the phase boundary!

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Recent revision of the SHM - 1: “Corona Effect”

⇒ ⇒

(Source: A.Andronic, P.Braun-Munzinger, K.Redlich,J.Stachel, nucl-th/0611023v2)

NJ/ψ = NcoreJ/ψ + Ncorona

J/ψ ,

where

NJ/ψ = g2c · nth

J/ψ · Vcore,

NcoronaJ/ψ = Ncorona

coll ·σppJ/ψ/σ

ppinel .

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Recent revision of the SHM - 2: cc annihilationin QGP

• QGP not in chemical equilibrium.⇒ c + c → g + g and g + g → c + c are asymmetric.

• Production of cc pairs in QGP is negligible when T < 1GeV.(see hep-ph/0001008)

• We can estimate:

Nannicc =

∫ τc

τ0

drcc

dτV (∆y = 1, τ)dτ,

where

drcc

dτ= ncnc〈σcc→gg · vr 〉, V (∆y = 1, τ) = A⊥τ,

nc =dNc/dy(τ)

V (∆y = 1, τ)6

dNc/dy(τ0)

V (∆y = 1, τ).

=⇒ Nannicc 6

(dNc

dy(τ0)

)2 1A⊥

∫ τc

τ0

dττ〈σcc→gg · vr 〉

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Recent revision of the SHM - 2: cc annihilationin QGP


Consequences:• Charm quark annihilation in QGP can be safely neglected.• Charmonia are not likely to be formed in QGP, and not before QGP

formation, either.• The statistical hadronization model (SHM) and the recombination

model (RM) are different, because

σ(cc → J/ψ)RM > σ(cc → gg)SHM .

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


New analysis of centrality dependence at SPS


J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


New analysis of centrality dependence at RHIC(Source: A.Andronic, P.Braun-Munzinger, K.Redlich, J.Stachel, nucl-th/0611023v2)

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Revised predictions for centrality and rapiditydependence at LHC


J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Outline





J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Summary

• Statistical hadronization model (SHM):assumptions, grand canonical formalism, canonicalformalism.

• To J/ψ suppression:SHM is quite successful (centrality dependene at SPS andRHIC, rapidity dependence at RHIC).

• To J/ψ enhancement:SHM gives predictions (centrality and rapidity dependene atLHC).

• Recent revision of SHM:Corona Effect, cc annihilation in QGP.

• Next generation of SHM:maybe to think about continuous transition from core regionnto pp region.

J/ψSuppression

andEnhancement

Jun Nian

Introduction toQGP



Canonical formalism


Data analysis

Some new results


Reference

• Books:K.Yagi, T.Hatsuda, Y.Miake, (2005) Quark-Gluon PlasmaR.C.Hwa(Editor), X.N.Wang(Editor) (2004) Quark-Gluon Plasma 3W.Greiner, S.Schramm, E.Stein, (2002) Quantum ChromodynamicsO.Nachtmann, (1991) Phänomene und Konzepte der Elementarteilchenphysik

• Papers:P.Braun-Munzinger, K.Redlich, J.Stachel, nucl-th/0304013v1P.Braun-Munzinger, J.Stachel, Phys. Lett. B 490 (2000) 196-202M.I.Gorenstein, A.P.Kostyuk, L.McLerran, H.Stöcker, W.Greiner, Journal of Physics G 28 (2002)2151-2167A.Andronic, P.Braun-Munzinger, K.Redlich, J.Stachel, Phys. Lett. B 571 (2003) 36-44A.Andronic, P.Braun-Munzinger, K.Redlich, J.Stachel, Phys. Lett. B 652 (2007) 259-261A.Andronic, P.Braun-Munzinger, K.Redlich, J.Stachel, nucl-th/0611023v2J.Cleymans, H.Oeschler, K.Redlich, Phys. Rev. C Vol.59, Num.3 1663

• Scripts:Notes of the lecture “quark-gluon plasma physics” by Prof. Stachel and Prof. Braun-Munzinger inCERN Summer Student Program 2005:

http://indico.cern.ch/getFile.py/access?resId=0&materialId=5&confId=a054063http://indico.cern.ch/getFile.py/access?resId=0&materialId=4&confId=a054064http://indico.cern.ch/getFile.py/access?resId=1&materialId=4&confId=a054065http://indico.cern.ch/getFile.py/access?resId=0&materialId=4&confId=a054065

Notes of the lecture “compressed nuclear matter” by C.Höhne in GSI Summer Student Program 2007:http://www-linux.gsi.de/∼hoehne/2007-hoehne.pdf

Notes of the lecture “standard model” by Prof. Uwer from Uni. Heidelberg:http://www.physi.uni-heidelberg.de/∼uwer/lectures/StandardModel/Notes/QGP.pdf

Presentation given by M.Ries from the seminar “experimental particle and nuclear physics” in Uni.Heidelberg:

http://www.physi.uni-heidelberg.de/∼uwer/lectures/Seminar/KeyExp/2007/qgp.pdf

J/ψ Suppression and Enhancement - Theory...

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