Quarkonium dissociation and regeneration · 2020. 1. 10. · Quark-gluon plasma (QGP) •Early...
Transcript of Quarkonium dissociation and regeneration · 2020. 1. 10. · Quark-gluon plasma (QGP) •Early...
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Quarkonium dissociation and regeneration
Juhee HongYonsei University
Phys. Rev. C 99, 034905 (2019) JH, Su Houng LeePhys. Lett. B 801, 135147 (2020) JH, Su Houng Lee
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Simulation for Heavy IoN Collision with Heavy-quark and ONia(SHINCHON)
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Quark-gluon plasma (QGP)• Early universe before 10-6 s after the Big Bang• Relativistic heavy ion collisions
• Heavy quarks created in hard processes at the beginning, remain frozen
dissociation, regeneration hadronic effects
T0 ⁓ 550 MeV TC ⁓ 192 MeV TF ⁓ 115 MeV
quark-gluon
plasma
hadron gas
pre-equilibrium hadronization freeze-out
t0 ⁓ 0.3fm/c tC⁓ 7fm/c tF⁓ 17fm/c
hadronsg, q, ϒ
the expansion rate > the scattering rate
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Quarkonium
• Bound states of a heavy quark (b, c) and its antiquark
• Quark-gluon plasma formation, thermal properties
• Color screening
• Interaction length ↔ bound state radius
• Melting at Tdiss
H. Satz (2006)
T. Matsui, H. Satz (1986)
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Quarkonium suppression
• Nuclear modification factor (RAA)
RAA ⁓ 𝑁𝐴𝐴
ϒ
𝑁𝑐𝑜𝑙𝑙
𝑁𝑝𝑝
ϒ
• Quarkonium dissociation by in-medium interaction
• Quarkonium regeneration
• Feed-down
• Cold nuclear matter effects
CMS Collaboration (2019)
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Finite temperature QCD
• Heavy quark-antiquark static potential: screened Coulomb
• The imaginary part of the singlet potential: thermal width
• Quarkonium dissociation by scattering processes
- Gluo-dissociation (LO) - Inelastic parton scattering (NLO)
M. Laine, O. Philipsen, M. Tassler, P. Romatschke (2007)N. Brambilla, J. Ghiglieri, A. Vairo, P. Petreczky (2008)
hard thermal loop (HTL) resummation
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g≪ 1 for high Thard ⁓ Tsoft ⁓ gT
perturbative
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Outline
• Quarkonium dissociation in a partonic picture:
Gluo-dissociation, inelastic parton scattering
- Numerical analysis for ϒ(1S)
• Quarkonium regeneration
Inverse gluo-dissociation, inelastic parton scattering
• Boltzmann equation for quarkonium transverse momentum spectra:
Nuclear modification factor RAA, elliptic flow v2
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Quarkonium dissociation
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Gluo-dissociation
• g+ϒ →
• Interactions between partons and HQ bound state:dipole interaction of color charge with gluon
• Bethe-Salpeter amplitude in ϒ rest frame:
q, p1,p2»k
G. Bhanot, M. E. Peskin (1979)
Y. Oh, S. Kim, S. H. Lee (2002)
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• Coulombic bound state:
the relative momentum p=(p1-p2)/2
• Bohr radius:
• Dissociation cross section:
• Thermal width:
k≥E
n(k)=1
𝑒𝑘/𝑇−1
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• LO: k,k0 »mD
• NLO transverse dispersion for k«T: k02 - k2 - ReПT =0
HTL self-energy in Coulomb gauge:
• NLO cross section:
agrees with potential nonrelativistic QCD (pNRQCD) for mv » T » E » mDpNRQCD: m » mv » E (nonrelativistic)
T » mD (thermal)
N. Brambilla, M. A. Escobedo, J. Ghiglieri, A. Vairo (2013)
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the imaginary part using the octet propagator
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Inelastic parton scattering• p + ϒ → p + (p=g, )
• Effective vertex:
• ϒ dissociation at NLO:
T. Song, S. H. Lee (2005)
→+
gluo-dissociation at LO
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k0≈0 for small energy transfer ⁓ the singlet-octet chromoelectric
dipole vertex in pNRQCD
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• Small energy transfer for weakly coupled quarkonia: k10 ≈ k20
• Hard thermal loop (HTL) propagator:
• Dissociation cross section:
• Collinear breakup:
• Thermal width:
N. Brambilla, M. A. Escobedo, J. Ghiglieri, A. Vairo (2013)
agrees with pNRQCD for mv » T » mD » E
T ⁓
⁓mD
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nF(k1)=1
𝑒𝑘1/𝑇+1, nB(k1) =
1
𝑒𝑘1/𝑇−1
small anglescattering
Landau damping
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Higher order corrections
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O(g) corrections
• Higher order expansion with the effective vertex
• Same order for soft(⁓gT) gluons:
• Bose enhancement in the presence of soft gluons: αsn(k) ⁓ g2 T/k ⁓ g
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gT ⁓ gT ⁓
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⁓ g2
⁓ 1
𝑔2
4π
1
𝑒𝑘/𝑇 − 1
T ⁓hard
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Heavy quark diffusion
• Momentum diffusion coefficient of a HQ:the mean-squared momentum transfer per unit time
• Thermal width:
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bath particles
G. D. Moore, D. Teaney (2005)
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• κNLO with soft gluons
• κNLO is useful to obtain O(g) corrections to ΓNLO: ΓO(g) ⁓ κNLO
•Other O(g) corrections induced by heavy quark-antiquark interactions
S. Caron-Huot, G. D. Moore (2008)
ΓNLO with hard partons
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Numerical analysis for ϒ(1S)
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• ϒ(1S) survives up to Tdiss⁓ 600MeV
• Transitional behavior in QGP at Tc ≤ T ≤ Tdiss
• Binding energy from lattice QCD
• Debye screening mass: 𝑚𝐷2 =
𝑔2𝑇2
3𝑁𝑐 +
𝑁𝑓
2
A. Mocsy, P. Petreczky (2007)
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ϒ(1S)
Tc
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Numerical calculations
• Gluo-dissociation:
- NLO slightly smaller
• Inelastic parton scattering by numerical integral over the phase space:
- depends on binding energy
- approach the asymptotic formula
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E
log
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Dissociation cross section
• Numerical integration over the phase space:
• Gluo-dissociation peak depending on EInelastic parton scattering decreases with large mD at high T
• Low k1: gluo-dissociation is efficientHigh k1: inelastic parton scattering is dominant
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Thermal width
• Phase space: larger at high T, peak at higher k
• Gluo-dissociation/inelastic parton scattering is dominant at low/high T• Total thermal width increases with T: dissociation when Γtot ≥ E• Larger width at weaker αs (smaller mD, larger a0)
E»T tunnellingD. Khareev et al. (1995)
21⁓ 1/g2⁓ gT
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Quarkonium moving through QGP
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Kinetic approach
• Rate equation with absorption and production:
𝑑𝑁
𝑑𝑡= −Γ𝑁 + (production)
• Boltzmann equation:
𝜕
𝜕𝑡+ 𝑣 ∙
𝜕
𝜕𝑥𝑓 𝑝
= −∫𝑝2,𝑝3,𝑝4𝑀 2 𝑓𝑓2 1 ± 𝑓3 1 ± 𝑓4 − 𝑓3𝑓4 1 ± 𝑓 1 ± 𝑓2
× (2π)4δ4(𝑝 +𝑝2 −𝑝3−𝑝4)
p
p2
p3
p4
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Hadronic models
P. Braun-Munzinger, J. Stachel (2000)V. Greco, C. M. Ko, R. Rapp (2004)
• Recombination by hadronic processes near the phase transition
• Statistical hadronization: 𝑁𝑒𝑞 = 𝑔γ𝑉 ∫𝑑3𝑝
2𝜋 3𝑓(𝑝)
• Coalescence: 𝑑2𝑁
𝑑2𝑝𝑇⁓ ∫𝑑2𝑝1𝑇𝑑
2𝑝2𝑇𝑑2𝑁𝑏
𝑑2𝑝1𝑇
𝑑2𝑁ഥ𝑏𝑑2𝑝2𝑇
δ2( Ԧ𝑝𝑇 − Ԧ𝑝1𝑇 − Ԧ𝑝2𝑇)
• Continuous regeneration by the Boltzmann equation
(dof)(fugacity)(volume)
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thermal widththermal widththermal width regenerationregeneration
Quarkonium transport
b
b−ϒ b
b−ϒ
• Boltzmann equation with dissociation and regeneration
• Dissociation:
• Regeneration by b+b → ϒ+g , b+b+p → ϒ+p
• Quarkonium regeneration depends on HQ density, Nϒ/NQ
Nϒ/Nb « NJ/ψ/Nc
− −
⁓ 10-2σpp→ϒ/σpp→b ⁓ 10-3 ⁓ 10-2
ϒ velocity = q/q0
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Thermal width for ϒ(1S) moving in QGP
• Calculate the scattering amplitudes in the ϒ rest frame
• Partons move w.r.t. ϒ(1S): f k =1
𝑒𝑝·𝑢/𝑇±1, 𝑢μ = γ 1, 𝑣 , γ =
1
𝑣2−1
• Thermal width by convoluting the parton distributions with the cross section
• Thermal width at the plasma rest frame, dividing by the Lorentz factor
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thermal bath velocity
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• Higher q: smaller thermal width by gluo-dissociationlarger width by inelastic parton scattering
• The total thermal width increases with ϒ(1S) momentum
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Quarkonium regeneration
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Quarkonium regeneration
• Inverse gluo-dissociation, inelastic parton scattering
• Regeneration depends on HQ distribution function
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b
b− b
b−
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Heavy quark distribution
• Boltzmann equation with elastic scattering (p+b → p+b)
• Small energy transfer: Fokker-Planck equation
• Langevin equation: 𝑑𝑥
𝑑𝑡=
𝑝
𝑚
• Random walk suffering many collisions
• HQ approach to the equilibrium slowly by ⁓ m/T
⁓mD
drag momentum diffusion
B. Svetitsky (1988)H. van Hees, R. Rapp (2005)
G. D. Moore, D. Teaney (2005)
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⁓ 𝑇
𝑚suppressed
random momentum kicks
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• Heavy quark distribution
• At leading-log order (vHQ=0):
• Einstein relation: spatial diffusion
• Green function:
• Solution:
initial: differential cross section in pp collisions
H. van Hees, R. Rapp (2005) G. D. Moore, D. Teaney (2005)
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Thermal medium evolution
• Viscous hydrodynamics:
• A longitudinal motion by a Bjorken expansion
- ideal gas equation of state: e=3P ⁓ T4
- local equilibrium at t0=0.3 fm/c with T0=550 MeV
T ≤ 7fm for QGP
R ⁓ 7fm
ideal
shear viscosityenergy density, pressureequation of state
J. D. Bjorken (1983)
⁓ T2
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• Conservation of bottom: fugacity by a statistical model (Nϒ«Nb)
• Evolution of b quarks:
⁓ 1
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Heavy quark distribution
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Regeneration term
• Inverse gluo-dissociation is efficient at low TInelastic parton scattering is dominant at high T
• Higher q: smaller regeneration by inverse gluo-dissociationlarger regeneration by inelastic parton scattering
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• Regeneration is stronger for smaller diffusion
• Inverse gluo-dissociation is sensitive to D at low T
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ϒ(1S) transverse momentum spectra
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Dynamic evolution of ϒ(1S)• In the central rapidity region with the Lorentz boost invariance
• Initial distribution: differential cross section in pp collisions
• Dominant dissociation: Nϒ reduces to 40%• Small fϒ at high qT: regeneration effects
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Nuclear modification factor
• Tf ≈ Tc at tf ≈ 7fm/c:
• Low qT: suppression by dissociationHigh qT: suppression, enhancement by regeneration
• Less suppression for smaller D
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• Significant uncertainties in the initial stage of heavy ion collisions
• RAA curves depend on b,ϒ initial distributions:
• Softer spectrum with larger α, smaller Λ: stronger regeneration at high qT
• Higher T0: longer QGP lifetime, smaller RAA
Dependence on initial conditions
, Λb=6.07GeV
, Λϒ=6.05GeV, α=2.44
softer bsofter ϒ
harder bharder ϒ
⁓ smaller diffusion
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•Higher energy collisions with larger T0: smaller RAA
• Significant regeneration effects on RAA at high qT
• Sum of gluo-dissociation and inelastic parton scattering: RAA⁓ 0.4
• RAA data appear to be independent of qT: suppression by dissociation and enhancement by regeneration
CMS Collaboration (2017, 2019)
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Comparison to experiment
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Feed-down
State Tdiss (MeV)
ϒ(1S) 593
ϒ(2S) 228
ϒ(3S) < 192
Χb1 265
Χb2 < 192
A. Mocsy, P. Petreczky, M. Strickland (2013)
feed-down fractions
ϒ(1S) → ϒ(1S) 0.668
ϒ(2S) → ϒ(1S) 0.086
ϒ(3S) → ϒ(1S) 0.010
χb(1P) → ϒ(1S) 0.170
χb(2P) → ϒ(1S) 0.051
χb(3P) → ϒ(1S) 0.015
B. Krouppa, A. Rothkopf, M. Strickland (2018)
• Inclusive RAA = σ𝑠 𝑓𝑠𝑅𝐴𝐴
𝑠 Dissociation temperatures
• Gluo-dissociation is important for excited states
• If 𝑅𝐴𝐴2𝑆 ⁓ 𝑅𝐴𝐴
1𝑃, 𝑅𝐴𝐴3𝑆 , 𝑅𝐴𝐴
2𝑃, 𝑅𝐴𝐴3𝑃 ∶
feed-down effects ⁓ 10% of 𝑅𝐴𝐴1𝑆
CMS Collaboration (2019)
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Elliptic flow
• 𝑣2 =𝑝𝑥2−𝑝𝑦
2
𝑝𝑥2+𝑝𝑦
2
• Azimuthal angular anisotropy: b quark v2
• Elliptic flow induced by regeneration:
•With the same initial conditions, RAA and v2 are comparable to experiment
M. He, R. J. Fries, R. Rapp (2017)
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y
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Other approaches
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Langevin simulationJ. P. Blaizot, D. De Boni, F. Faccioli, G. Garberoglio (2016)
• Dynamics of heavy quarks including bound state formation and dissociation
• Generalized Langevin equation with the force and noise determined from correlation functions of the equilibrium plasma
• Dissociation by a screened potential and collisions with partons, regeneration when enough heavy quarks are present
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Open quantum system
S. Kajimoto, Y. Akamatsu, M. Asakawa, A. Rothkopf (2018)
• Quarkonium dynamics by a Schrodinger equation with an in-medium potential and noise terms describing HQ-medium interactions
• Noise correlation: wave decoherence
• For short lcorr , the initial ground state is easily excited and mixed with excited states
noise
inelastic parton scattering
⁓
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Summary
• Quarkonium dissociation and regeneration by scattering processes:
For collinear breakup with small energy transfer, NLO dissociation cross sections agree with pNRQCD
• Thermal width increases with T, qRegeneration depends on HQ diffusion: stronger regeneration for smaller D
• ϒ(1S) transverse momentum spectra by the Boltzmann equation
• Nuclear modification factor: suppression by dissociation at low qTsuppression and enhancement by regeneration at high qT
• Elliptic flow induced by regeneration
• With the same initial conditions, both RAA and v2 are comparable with the CMS, ALICE data
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Thank you for your attention!
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