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) c c c Recent lattice QCD studies claim that J/ ψ can survive in • QGP . (a thermometer of hot dense nuclear matter) 4

2. Quarkonium dissociation in hadronic nuclear matter

Bethe-Salpeter vertex Multiplying ∆ 𝑞 1 to the left and ∆ −𝑞 2 to the right, and assuming 𝑗 (1 − 𝛿 0 )𝜔( 𝑞 𝜈 𝑞 1 , −𝑞 2 Δ −𝑞 2 ~ (1 + 𝛿 0 )𝛿 𝑗 𝑕 𝜈 ) 𝑞 0 ∆ 𝑞 1 Γ where 𝑞 ≡ (𝑞 1 − 𝑞 2 )/2 , in heavy quark limit NR Schrodinger equation for the Coulombic bound state 6

Order counting in heavy-quark limit 𝑛 Φ : quarkonium mass 𝑛 : heavy quark mass 𝑂 𝑑 𝑕 2 Binding energy 𝜁 0 = 𝑛 2 ~𝑃(𝑛𝑕 4 ) • 16𝜌 2 ) , From energy conservation ( Φ + 𝑕 → 𝑅 + 𝑅 • 1 | 2 2 | 2 𝑛 Φ + 𝑙 0 = 2𝑛 + |𝑞 2𝑛 + |𝑞 2𝑛 , 𝑙 0 = 𝑙 ~𝑃 𝑛𝑕 4 2 ~𝑃 𝑛𝑕 2 , 𝑞 1 ~ 𝑞 Heavy quark propagator Bethe-Salpeter vertex 2 𝑛 Φ 𝜁 0 + 𝑞 Γ 𝜈 𝑞 1 , −𝑞 2 = 𝑛 𝑂 𝑑 × 1 + 𝛿 0 𝑗 1 − 𝛿 0 𝛿 𝑗 𝑕 𝜈 𝜔 𝑞 2 2 7

Leading-order dissociation Φ + 𝑕 → 𝑅 + 𝑅 → Suppressed in large N c limit 8

Quark-induced next-to-leading-order dissociation + 𝑟 Φ + 𝑟 → 𝑅 + 𝑅 9

Gluon-induced next-to-leading-order dissociation + 𝑕 Φ + 𝑕 → 𝑅 + 𝑅 10

Transition amplitudes Current conservation LO 𝑟 𝜈 𝑁 𝜈𝜉 = 𝑙 𝜉 𝑁 𝜈𝜉 = 0 quark-induced NLO 𝑟 𝜈 𝑁 𝜈 = 0 gluon-induced NLO 𝑟 𝜈 𝑁 𝜈𝜉𝜇 = 𝑙 1 𝜉 𝑁 𝜈𝜉𝜇 𝜇 𝑁 𝜈𝜉𝜇 = 0 = 𝑙 2 11

Quark-induced next-to-leading-order dissociation + 𝑟 Φ + 𝑟 → 𝑅 + 𝑅 Collinear divergence 12

Gluon-induced next-to-leading-order dissociation + 𝑕 Φ + 𝑕 → 𝑅 + 𝑅 Soft divergence Collinear divergence 13

Mass factorization for collinear divergence → the divergence moves to parton distribution function(PDF) D j (x,Q 2 ) ; Renormalization of PDF 14

One-loop diagrams for soft divergence Φ+𝑕→𝑅+𝑅 + 𝑁 𝑝𝑜𝑓−𝑚𝑝𝑝𝑞 Φ+𝑕→𝑅+𝑅 + ⋯ | 2 |𝑁 Φ+𝑕→𝑅+𝑅 | 2 = |𝑁 𝑢𝑠𝑓𝑓 Φ+𝑕→𝑅+𝑅 + ⋯ Φ+𝑕→𝑅+𝑅 | 2 + 2𝑁 𝑢𝑠𝑓𝑓 Φ+𝑕→𝑅+𝑅 * 𝑁 𝑝𝑜𝑓−𝑚𝑝𝑝𝑞 = |𝑁 𝑢𝑠𝑓𝑓 |𝑁 Φ+𝑕→𝑅+𝑅+𝑕 | 2 = |𝑁 𝑢𝑠𝑓𝑓 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 𝜏 Φ+ℎ 𝑡 = 𝑒𝑦 𝐸 𝑗 (𝑦, 𝑅)𝜏 Φ+𝑗 (𝑦𝑡, 𝑅) ,𝑕 𝑗=𝑟,𝑟 Y(1S)+nucleon dissociation cross section (MRST PDF, Q 2 =1.25 GeV 2 ) LO+NLO LO 18

3. Quarkonium dissociation in partonic nuclear matter

Temperature- Leading Ord rder (LO (LO) dependent wavefunction qua uark-induced Next xt to to Leading Ord rder (q (qNLO) Introduce thermal mass of partons: all divergences disappear glu luon-in induced Next xt to to Leading Ord rder (g (gNLO) 20

Screened Cornell potential 𝜈(𝑈) 1 − 𝑓 −𝜈 𝑈 𝑠 − 𝜏 𝛽 𝑠 𝑓 −𝜈 𝑈 𝑠 • 𝑊 𝑠, 𝑈 = • 𝜏 = 0.192 GeV 2 : string tension • 𝛽 = 0.471 : Coulomb-like potential constant 𝑂 𝑔 𝑂 𝑑 • 𝜈 𝑈 = 3 + 6 𝑕𝑈 : screening mass in pQCD 𝜈 𝑈 →0 𝑊 𝑠, 𝑈 = 𝜏𝑠 − 𝛽 𝑠 lim • 21

Charmonia wavefunctions from the screened Cornell potential J/ ψ (1S) χ c (1P) Ψ’(2S) Screening mass 289 MeV 298 MeV 306 MeV 315 MeV 323 MeV 332 MeV 340 MeV P (GeV) 22

Thermal mass of quark and gluon (Quasi-particle method) Lattice equation of state Thermal masses of partons 23

Thermal decay width Thermal width (GeV) 10 Γ 𝑈 = • 𝑒 3 𝑙 𝑒 𝑗 (2𝜌) 3 𝑜 𝑗 (𝑙, 𝑈)𝑤 𝑠𝑓𝑚. 𝜏 Φ+𝑗 1 ,𝑕 𝑗=𝑟,𝑟 0.13 0.23 0.33 0.43 0.53 Temperature (GeV) Survival probability from • 0.1 thermal decay Y(1S) 𝜐 Γ(𝑈) Y(2S) 𝑇 = 𝑓𝑦𝑞 − 𝑒𝜐 𝜐 0 Y(3S) 0.01 X(1P) X(2P) 0.001 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) 1 𝑢+𝑨 • Coordinate ( τ ≡ 𝑢 2 − 𝑨 2 , x, y, η = 2 ln 𝑢−𝑨 ) ∂ τ ( τ T 00 )+ ∂ x ( τ T 0x )+ ∂ y ( τ T 0y )=-p ∂ τ ( τ T 0x )+ ∂ x ( τ T xx )+ ∂ y ( τ T xy )=0 ∂ τ ( τ T 0y )+ ∂ x ( τ T xy )+ ∂ y ( τ T yy )=0 where T μν =(e+p)u μ u ν -pg μν , u μ = γ (1,v) + initial conditions + equation of state 27

Equation of state Initial local entropy density • From lattice results 𝑒𝑡 𝑒𝜃 𝑦, 𝑧, 𝜐 0 = 1 − 𝛽 𝑜 𝑞𝑏𝑠𝑢 𝐵 + 𝛽𝑜 𝑑𝑝𝑚𝑚 2 𝑂 𝑞𝑏𝑠𝑢 where 𝑜 𝑞𝑏𝑠𝑢 = τ 0 Δ𝑦Δ𝑧 , 𝑜 𝑑𝑝𝑚𝑚 = 𝑂 𝑑𝑝𝑚𝑚 τ 0 Δ𝑦Δ𝑧 A and α are determined from particle multiplicities 28

Time-evolution of hot nuclear matter 14.55 14.55 12.45 12.45 10.35 10.35 8.25 8.25 τ =0.6 fm/c τ =1.0 fm/c 6.15 6.15 4.05 4.05 0.4-0.5 0.4-0.5 1.95 1.95 0.3-0.4 0.3-0.4 -0.15 -0.15 0.2-0.3 0.2-0.3 -2.25 -2.25 -4.35 -4.35 0.1-0.2 0.1-0.2 -6.45 -6.45 0-0.1 0-0.1 -8.55 -8.55 -10.65 -10.65 -12.75 -12.75 -14.85 -14.85 14.55 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 -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 12.45 12.45 10.35 10.35 8.25 8.25 6.15 6.15 4.05 4.05 τ =3.0 fm/c 1.95 0.3-0.4 1.95 τ =2.0 fm/c 0.2-0.3 -0.15 -0.15 0.2-0.3 0.1-0.2 -2.25 -2.25 0.1-0.2 -4.35 -4.35 0-0.1 0-0.1 -6.45 -6.45 -8.55 -8.55 -10.65 -10.65 -12.75 -12.75 -14.85 -14.85 -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 -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 29

Hypersurfaces at chemical/kinetical freezeout temperatures T=160 MeV T=130 MeV 30

p T spectra from Pb+Pb collisions at √s NN =2.76 TeV • Initial thermalization time, τ 0 =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 of 1P , 2P , 2S, and 3S states, respectively 32

5. Quarkonium regeneration

R AA of J/ ψ at RHIC ( 𝑡 𝑂𝑂 = 200 GeV) and at LHC ( 𝑡 𝑂𝑂 = 2.76 TeV) Forward rapidity Mid-rapidity 34

Statistical model Statistical model successfully describes particle ratios n i /n j , where n i , n j is particle number density in grand canonical ensemble  1       d E     1     j  j j    2   n dpp exp 1   d E  j 2   2 T            j j j 2 cfo n dpp exp 1             j 2   B I S C 2 T     j B j I 3 3 s j C j cfo          B I S C j B j I 3 3 s j C j A.Andronic et al. NPA 772, 167 (2006 ) 35

Chemical nonequilibrium are produced in • Initially many heavy quark pairs 𝑅𝑅 relativistic heavy-ion collisions. annihilation is small, • Because the cross section for 𝑅𝑅 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 . pairs is small, we should use • If the number of 𝑅𝑅 canonical ensemble rather than grandcanonical ensemble. → canonical suppression  I n V ( ) 1     1 open C AA 2 N n V n V  c c open C hidden C 2 I ( n V ) 0 hidden C 36

Fugacity of charm quarks in Au+Au collisions at √ s NN GeV NN =200 GeV canonical suppression 45 1.2 40 1 35 30 0.8 25 0.6 20 0.4 15 10 0.2 5 0 0 0 100 200 300 400 0 100 200 300 400 No. of participant No. of participant 37

Kinetic nonequilibrium Tsallis distribution function for heavy quarks [1+ λ E/T] -1/ λ ↓ λ =0 e – E/T : Boltzman distribution 38