relativistic heavy-ion collisions Taesoo Song (Texas A&M Univ.) - - PowerPoint PPT Presentation

Quarkonium production in relativistic heavy-ion collisions

Taesoo Song (Texas A&M Univ.)

• 1. Introduction

QCD phase diagram

Electromagnetic probe : photon, dilepton Hard probe : jet, heavy quark, quarkonium Bulk property : elliptic flow, HBT

3

J/ψ suppression

• J/ψ suppression was suggested as a signature of quark-

gluon plasma (QGP) formation in relativistic heavy-ion collisions by Matsui and Satz. (If QGP is created in relativistic heavy-ion collisions, Debye color screening suppresses quarkonium production)

• Recent lattice QCD studies claim that J/ψ can survive in

QGP . (a thermometer of hot dense nuclear matter)

c

c c

4

• 2. Quarkonium dissociation

in hadronic nuclear matter

Bethe-Salpeter vertex

Multiplying ∆ 𝑞1 to the left and ∆ −𝑞2 to the right, and assuming 𝑞0∆ 𝑞1 Γ

𝜈 𝑞1, −𝑞2 Δ −𝑞2 ~ (1 + 𝛿0)𝛿𝑗𝑕𝜈 𝑗 (1 − 𝛿0)𝜔( 𝑞

) where 𝑞 ≡ (𝑞1 − 𝑞2)/2, in heavy quark limit

NR Schrodinger equation for the Coulombic bound state

6

Order counting in heavy-quark limit

• Binding energy 𝜁0 = 𝑛

𝑂𝑑𝑕2 16𝜌2

~𝑃(𝑛𝑕4)

2

• From energy conservation (Φ + 𝑕 → 𝑅 + 𝑅

), 𝑛Φ + 𝑙0 = 2𝑛 + |𝑞

1|2 2𝑛 + |𝑞 2|2 2𝑛 ,

𝑞 1 ~ 𝑞 2 ~𝑃 𝑛𝑕2 , 𝑙0 = 𝑙 ~𝑃 𝑛𝑕4 Heavy quark propagator Bethe-Salpeter vertex

Γ

𝜈 𝑞1, −𝑞2 =

𝑛Φ 𝑂𝑑 𝜁0 + 𝑞 2 𝑛 × 1 + 𝛿0 2 𝛿𝑗𝑕𝜈

𝑗 1 − 𝛿0

2 𝜔 𝑞

𝑛Φ: quarkonium mass 𝑛 : heavy quark mass

7

Leading-order dissociation Φ + 𝑕 → 𝑅 + 𝑅

→ Suppressed in large Nc limit

8

Quark-induced next-to-leading-order dissociation Φ + 𝑟 → 𝑅 + 𝑅 + 𝑟

9

Gluon-induced next-to-leading-order dissociation Φ + 𝑕 → 𝑅 + 𝑅 + 𝑕

10

LO

Transition amplitudes

quark-induced NLO gluon-induced NLO

Current conservation 𝑟𝜈𝑁𝜈𝜉 = 𝑙𝜉𝑁𝜈𝜉 = 0 𝑟𝜈𝑁𝜈 = 0 𝑟𝜈𝑁𝜈𝜉𝜇 = 𝑙1

𝜉𝑁𝜈𝜉𝜇

= 𝑙2

𝜇𝑁𝜈𝜉𝜇 = 0

11

Quark-induced next-to-leading-order dissociation Φ + 𝑟 → 𝑅 + 𝑅 + 𝑟

Collinear divergence 12

Gluon-induced next-to-leading-order dissociation Φ + 𝑕 → 𝑅 + 𝑅 + 𝑕

Collinear divergence Soft divergence 13

Mass factorization for collinear divergence

→ the divergence moves to parton distribution function(PDF) Dj (x,Q2) ; Renormalization of PDF 14

One-loop diagrams for soft divergence

|𝑁Φ+𝑕→𝑅+𝑅|2 = |𝑁𝑢𝑠𝑓𝑓

Φ+𝑕→𝑅+𝑅 + 𝑁𝑝𝑜𝑓−𝑚𝑝𝑝𝑞 Φ+𝑕→𝑅+𝑅 + ⋯ |2

= |𝑁𝑢𝑠𝑓𝑓

Φ+𝑕→𝑅+𝑅|2 + 2𝑁𝑢𝑠𝑓𝑓 Φ+𝑕→𝑅+𝑅*𝑁𝑝𝑜𝑓−𝑚𝑝𝑝𝑞 Φ+𝑕→𝑅+𝑅 + ⋯

|𝑁Φ+𝑕→𝑅+𝑅+𝑕|2 = |𝑁𝑢𝑠𝑓𝑓

Φ+𝑕→𝑅+𝑅+𝑕|2 + ⋯

Soft (infrared) divergences are cancelled

15

Introducing the effective four-point vertex Ultraviolet divergence from loop is cured by renormalization

16

Cross section for bottomonium (1S) dissociation by partons

LO gluon-NLO quark-NLO 17

Bottomonium-hadron dissociation cross section

• Factorization formula

𝜏Φ+ℎ 𝑡 = 𝑒𝑦 𝐸𝑗(𝑦, 𝑅)𝜏Φ+𝑗(𝑦𝑡, 𝑅)

𝑗=𝑟,𝑟 ,𝑕

Y(1S)+nucleon dissociation cross section (MRST PDF, Q2=1.25 GeV2) LO LO+NLO 18

• 3. Quarkonium dissociation

in partonic nuclear matter

Leading Ord rder (LO (LO) qua uark-induced Next xt to to Leading Ord rder (q (qNLO) glu luon-in induced Next xt to to Leading Ord rder (g (gNLO) Temperature- dependent wavefunction Introduce thermal mass

• f partons:

all divergences disappear 20

Screened Cornell potential

• 𝑊 𝑠, 𝑈 =

𝜏 𝜈(𝑈) 1 − 𝑓−𝜈 𝑈 𝑠 − 𝛽 𝑠 𝑓−𝜈 𝑈 𝑠

• 𝜏 = 0.192 GeV2: string tension
• 𝛽 = 0.471 : Coulomb-like potential constant
• 𝜈 𝑈 =

𝑂𝑑 3 + 𝑂𝑔 6 𝑕𝑈: screening mass in pQCD

• lim

𝜈 𝑈 →0𝑊 𝑠, 𝑈 = 𝜏𝑠 − 𝛽 𝑠

21

Charmonia wavefunctions from the screened Cornell potential

Screening mass 289 MeV 298 MeV 306 MeV 315 MeV 323 MeV 332 MeV 340 MeV

J/ψ (1S) χc (1P) Ψ’(2S)

P (GeV) 22

Thermal mass of quark and gluon (Quasi-particle method)

Lattice equation of state

Thermal masses of partons

23

Thermal decay width

• Γ 𝑈 =

𝑒𝑗

𝑒3𝑙 (2𝜌)3 𝑜𝑗(𝑙, 𝑈)𝑤𝑠𝑓𝑚.𝜏Φ+𝑗 𝑗=𝑟,𝑟 ,𝑕

• Survival probability from

thermal decay 𝑇 = 𝑓𝑦𝑞 − 𝑒𝜐

𝜐 𝜐0

Γ(𝑈)

0.001 0.01 0.1 1 10 0.13 0.23 0.33 0.43 0.53

Y(1S) Y(2S) Y(3S) X(1P) X(2P) Temperature (GeV) Thermal width (GeV)

24

• 4. Relativistic heavy-ion

collisions

Number of participants: number of nucleons participating heavy-ion collisions (total number of nucleons =number of participants + number of spectators) Number of binary collisions: number of N+N primary collisions in heavy-ion collisions

26

2+1 ideal hydrodynamics

(boost invariant in longitudinal direction)

• Coordinate (τ≡ 𝑢2 − 𝑨2, x, y, η=

1 2 ln 𝑢+𝑨 𝑢−𝑨 )

∂τ(τT00)+∂x(τT0x)+∂y(τT0y)=-p ∂τ(τT0x)+∂x(τTxx)+∂y(τTxy)=0 ∂τ(τT0y)+∂x(τTxy)+∂y(τTyy)=0 where Tμν=(e+p)uμuν-pgμν, uμ=γ(1,v) + initial conditions + equation of state

27

Initial local entropy density

𝑒𝑡 𝑒𝜃 𝑦, 𝑧, 𝜐0 = 𝐵 1 − 𝛽 𝑜𝑞𝑏𝑠𝑢 2 + 𝛽𝑜𝑑𝑝𝑚𝑚 where 𝑜𝑞𝑏𝑠𝑢=

𝑂𝑞𝑏𝑠𝑢 τ0Δ𝑦Δ𝑧 , 𝑜𝑑𝑝𝑚𝑚= 𝑂𝑑𝑝𝑚𝑚 τ0Δ𝑦Δ𝑧

A and α are determined from particle multiplicities Equation of state

• From lattice results

28

Time-evolution of hot nuclear matter

τ=0.6 fm/c τ=2.0 fm/c

• 14.85
• 12.75
• 10.65
• 8.55
• 6.45
• 4.35
• 2.25
• 0.15

1.95 4.05 6.15 8.25 10.35 12.45 14.55

• 14.85
• 12.45
• 10.05
• 7.65
• 5.25
• 2.85
• 0.45

1.95 4.35 6.75 9.15 11.55 13.95 0.4-0.5 0.3-0.4 0.2-0.3 0.1-0.2 0-0.1

• 14.85
• 12.75
• 10.65
• 8.55
• 6.45
• 4.35
• 2.25
• 0.15

1.95 4.05 6.15 8.25 10.35 12.45 14.55

• 14.85
• 12.45
• 10.05
• 7.65
• 5.25
• 2.85
• 0.45

1.95 4.35 6.75 9.15 11.55 13.95 0.4-0.5 0.3-0.4 0.2-0.3 0.1-0.2 0-0.1

• 14.85
• 12.75
• 10.65
• 8.55
• 6.45
• 4.35
• 2.25
• 0.15

1.95 4.05 6.15 8.25 10.35 12.45 14.55

• 14.85
• 12.45
• 10.05
• 7.65
• 5.25
• 2.85
• 0.45

1.95 4.35 6.75 9.15 11.55 13.95 0.3-0.4 0.2-0.3 0.1-0.2 0-0.1

• 14.85
• 12.75
• 10.65
• 8.55
• 6.45
• 4.35
• 2.25
• 0.15

1.95 4.05 6.15 8.25 10.35 12.45 14.55

• 14.85
• 12.45
• 10.05
• 7.65
• 5.25
• 2.85
• 0.45

1.95 4.35 6.75 9.15 11.55 13.95 0.2-0.3 0.1-0.2 0-0.1

τ=1.0 fm/c τ=3.0 fm/c

29

Hypersurfaces at chemical/kinetical freezeout temperatures

T=160 MeV T=130 MeV

30

pT spectra from Pb+Pb collisions at √sNN=2.76 TeV

• Initial thermalization

time, τ0=0.6 fm/c

• Chemical freezeout

temperature=160 MeV

• Kinetic freezeout

temperature=130 MeV

31

Bottomonia suppression at LHC

27.1, 10.5, 10.7, and 0.8 % of 1S state come from the decay

• f 1P

, 2P , 2S, and 3S states, respectively 32

• 5. Quarkonium regeneration

RAA of J/ψ at RHIC ( 𝑡𝑂𝑂 = 200 GeV) and at LHC ( 𝑡𝑂𝑂 = 2.76 TeV)

Forward rapidity Mid-rapidity

34

Statistical model

j C j s I j B j cfo j j j j

C S I B T E dpp d n                              





3 3 1 2 2

1 exp 2

Statistical model successfully describes particle ratios ni/nj, where ni, nj is particle number density in grand canonical ensemble

j C j s I j B j cfo j j j j

C S I B T E dpp d n                              





3 3 1 2 2

1 exp 2

A.Andronic et al. NPA 772, 167 (2006) 35

Chemical nonequilibrium

• Initially many heavy quark pairs 𝑅𝑅

are produced in relativistic heavy-ion collisions.

• Because the cross section for 𝑅𝑅

annihilation is small, chemical thermalization of heavy quarks takes much longer time than the lifetime of fireball.

• excessive heavy quarks is expressed by fugacity in the

statistical model .

• If the number of 𝑅𝑅

pairs is small, we should use canonical ensemble rather than grandcanonical

• ensemble. → canonical suppression

V n V n I V n I V n N

hidden hidden

• pen
• pen

AA c c C 2 C C 1 C

) ( ) ( 2 1      

36

5 10 15 20 25 30 35 40 45 100 200 300 400

Fugacity of charm quarks in Au+Au collisions at √sNN

NN=200 GeV

GeV

0.2 0.4 0.6 0.8 1 1.2 100 200 300 400

canonical suppression

• No. of participant
• No. of participant

37

Kinetic nonequilibrium

Tsallis distribution function for heavy quarks

[1+λE/T]-1/λ ↓λ=0 e–E/T : Boltzman distribution

38

2 2 1 2 1 4 4 2 3 2 3 1 3 1 3 3 3 / 3 / 3

) ( ) ( ) ( ) 2 ( 2 ) 2 ( 2 ) 2 ( 2 ) 2 ( 2 1 ) 2 ( M p f p f k q p p E p d E p d E k d E q Vd dN

c c k J J

   

  

     

 

Production rate of quarkonium

2 2 ) ( 2 1 2 1 2 1 4 4 2 3 2 3 1 3 1 3 3 2 3 3 1 3 / 3 / 3

) ( ) ( ) ( ) ( ) 2 ( 2 ) 2 ( 2 ) 2 ( 2 ) 2 ( 2 ) 2 ( 2 1 ) 2 (

2 1

M k f p f p f k q k p p E p d E p d E k d E k d E q Vd dN

g q c c g g J J

     

   

      

  2 2 1 2 1 2 1 4 4 2 3 2 3 1 3 1 3 3 2 3 3 1 3 / 3 / 3

) ( ) ( ) ( ) 2 ( 2 ) 2 ( 2 ) 2 ( 2 ) 2 ( 2 ) 2 ( 2 1 ) 2 (

2 1

M p f p f k k q p p E p d E p d E k d E k d E q Vd dN

c c g g J J

     

   

      

 

Q + + Q → ф + + g Q + + Q + + q(g (g) → ф + + q(g (g) Q + + Q → ф + + q + + q(g (g + + g) 39

Leading Ord rder (LO (LO) Q + + Q → ф + + g qua uark-induced Next to to Leadin ing Ord rder (qNLO) Q + + Q + + q → ф + + q

Quarkonium production in pQCD

40

glu luon-in induced Next to to Leading Ord rder (gNLO) Q + + Q Q + + g → ф + + g 41

J/ψ production rate & spectra

42

Cascade method

43

QGP (1 Tc, 1.5 Tc)

Initial charm spectrum from PHYTIA

parton cross section σcq=1 mb σcg=2 mb

The change of charm spectra with time

44

RHIC λ=0.013 T=650 MeV LHC λ=0.033 T=680 MeV RHIC λ=0.072 T=140 MeV LHC λ=0.097 T=90 MeV RHIC λ=0.078 T=190 MeV LHC λ=0.107 T=140 MeV RHIC λ=0.058 T=150 MeV LHC λ=0.081 T=100 MeV

Reduced J/ψ production rate due to the kinetic nonequilibrium of charm & anticharm quarks at RHIC & LHC

45

RAA of J/ψ at SPS, RHIC and LHC

(LHC) (LHC)

46

summary

• Quarkonium production in relativistic heavy-ion

collisions is explained by using thermal decay and regeneration.

• Thermal decay of quarkonia is calculated by using the

screened Cornell potential, pQCD and hydrodynamics background.

• Large fugacity of heavy flavor enhances regeneration
• f quarkonia but kinetic nonequilibrium suppresses it.
• There are still many uncertainties such as the

formation time of each quarkonium.

47