Quarkonia Production in Heavy Ion Collisions: Coupled Boltzmann Transport Equations
Xiaojun Yao
Collaborators: Berndt Mueller, Steffen Bass, Weiyao Ke, Yingru Xu
Duke UniversityMay 16 2018, Quark Matter 2018
Introduction• Debye (static) screening on heavy quark bound state, not enough explain
quarkonia production suppression
• Production complicated by many factors:
• Cold nuclear matter (CNM) initial production
• Static screening (real part potential suppressed) v.s. dynamical screening (imaginary part potential, related to dissociation)
• In-medium evolution (dissociation and recombination)
• Feed-down, etc.
• Include all factors consistently!2 Xiaojun Yao (Duke)
b
b
Dynamical Evolution: Dissociation
1S
b
b
1) not exist due to static screening
2) dissociate due to dynamical screening
propagateb
diffuse
b
b
b
1S
B
hadronization
hadronization
initial production QGP medium expands and cools
time
hadron gas
B
!3 Xiaojun Yao (Duke)
b
b
Dynamical Evolution: Recombination
1S
b
b
propagate
b
b
nLdiffuse
recombine T < melting T
b
1Sb
1S,2S,1P…
nL
melting temperature: above which a specific bound state 1) ill defined (thermal width too large) 2) not exists (potential not supports bound state)
dissociate
RL. Thews, M. Schroedter, J. Rafelski Phys.Rev.C 63, 054905 (2001)
in-medium formation
Xiaojun Yao (Duke)!4
initial production QGP medium expands and cools
time
hadron gas
1) not exist due to static screening
2) dissociate due to dynamical screening
Coupled Boltzmann Equations
(@
@t+ x ·r
x
)fQ(x,p, t) = �C+Q + C�
Q + CQ
(@
@t+ x ·r
x
)fQ(x,p, t) = �C+Q+ C�
Q+ CQ
(@
@t+ x ·r
x
)fnl(x,p, t) = +C+nl � C�
nl
heavy quark
anti-heavy quark
each quarkonium statenl = 1S, 2S,1P etc.
!5Xiaojun Yao (Duke)
Coupled Boltzmann Equations
(@
@t+ x ·r
x
)fQ(x,p, t) = �C+Q + C�
Q + CQ
(@
@t+ x ·r
x
)fQ(x,p, t) = �C+Q+ C�
Q+ CQ
(@
@t+ x ·r
x
)fnl(x,p, t) = +C+nl � C�
nl
heavy quark
anti-heavy quark
each quarkonium statenl = 1S, 2S,1P etc.
!6Xiaojun Yao (Duke)
phase space evolution of distribution function
recombination quarkonium gain heavy quark loss
dissociation quarkonium loss heavy quark gain
f
heavy Q energy loss
Heavy Quark Energy Loss: Linearized Boltzmann
• Specific implementation: Duke LBT describe open heavy and developed by Weiyao Ke, Yingru Xu, Steffen Bass
• See posters for details ID: 288 (W. Ke) 300 (Y. Xu)
(@
@t+ x ·r
x
)fQ(x,p, t) = �C+Q + C�
Q + CQ
0.0
0.5
1.0
1.5
R AA
3E+3E 0-10%
DAL,CE, D
0.0
0.5
1.0
1.53E+3E 30-50%
100 101 102
pT [GeV]
0.0
0.5
1.0
1.5
R AA
3E+3E 60-80%
100 101 102
pT [GeV]
0.0
0.5
1.0
1.53E+3E 0-100%
%C06, B±
• Collision terms: gQ—>gQ, qQ—>qQ, gQ—>gQg, qQ—>qQg, gQg—>gQ, qQg—>qQ (LPM effect) Gossiaux, Aichelin Phys.Rev.C78,014904(2008)
Gossiaux, Bierkandt, Aichelin Phys.Rev.C79,044906(2009)Uphoff, Fochler, Xu, Greiner J.Phys.G42,no.11,115106(2015)
!7
RAA v2
Dissociation, Recombination, pNRQCD(@
@t+ x ·r
x
)fnl(x,p, t) = +C+nl � C�
nl
LpNRQCD =
Zd3rTr
⇣S†(i@0 �H
s
)S + O†(iD0 �Ho
)O + VA
(O†r · gES + h.c.) +VB
2O†{r · gE,O}+ · · ·
⌘
Hs,o
=P 2c.m.
4M+
p2relM
+ V (0)s,o
+V
(1)s,o
M+
V(2)s,o
M2+ · · ·
no imaginary potential
Brambilla, Ghiglieri, Vairo, Petreczky, Phys. Rev. D 78, 014017 (2008) Brambilla, Escobedo, Ghiglieri, Vairo, JHEP1112,116(2011)JHEP1305,130(2013)
ϵ∗λ,q, a
k1, nl k2,prel, a
q
k1, nl k2,prel, c
q1, ϵ∗1, a q2, ϵ2, b
k1, nl k2,prel, a
p1, s1, i p2, s2, j
q
gluon absorption/emission inelastic scattering w/ light quark inelastic scattering w/ gluon
light quark
quarkoniumquarkonium quarkonium
unbound pairunbound pair
unbound pair
M � Mv � Mv2, T,mD• Separation of scales (bound state exists)1
M, r ⇠ 1
Mv• Systematic expansion in
V (0)s
= �CF
↵s
rV (0)o
=1
2NC
↵s
r
virial theorem
!8
10−3
10−2
10−1
NΥ/N
b,tot
thermal w/o HQ energy loss
non-relativistic equilibrium
relativistic equilibrium
0 10 20 30 40 50 60
t (fm/c)
0.000
0.002N
Υ/N
b,tot
uniform w/ HQ energy loss
uniform w/o HQ energy loss
Approach Equilibrium XY, B.Mueller, Phys. Rev. C 97, no. 1, 014908 (2018)
!9
Setup: QGP box, 1S state, b quarkTotal b flavor = 50 (fixed) Initial momenta thermal or uniform
Recombination from QCD effective field theory
Dissociation-recombination interplay drives to detailed balance
Heavy quark energy loss necessary to drive kinetic equilibrium of quarkonium
Xiaojun Yao (Duke)
Collision Event Simulation
• Initial production:
PYTHIA 8.2
Nuclear PDF (cold nuclear matter effect)
Trento, sample position, hydro. initial condition
• Medium background: 2+1D viscous hydrodynamics
• Include 1S 2S, 2S feed-down 1S ~ 26% (from PDG)
Bernhard, Moreland, Bass, Liu, Heinz, Phys.Rev.C94,no.2,024907(2016)
Eskola, Paukkunen, Salgado,JHEP 0904 (2009) 065
Song, Heinz, Phys.Rev.C77,064901(2008)Shen, Qiu, Song, Bernhard, Bass, Heinz,Comput. Phys. Commun.199,61 (2016)
!10
Sjostrand, et al, Comput. Phys.Commun.191 (2015) 159
Xiaojun Yao (Duke)
0 100 200 300 400Npart
0.0
0.5
1.0
1.5
RA
A
1S
2S
5 10 15pT (GeV)
0.0
0.2
0.4
0.6
0.8
1.0
RA
A
1S
2S
CMS Phys.Lett. B 770 (2017) 357-379
!11 Xiaojun Yao (Duke)
↵s = 0.3
Tmelt(2S) = 210 MeV
Vs = �CF0.42
r
0.5 1.0 1.5 2.0y
0.0
0.2
0.4
0.6
0.8
1.0
RA
A
1S
2S
Upsilon in 2760 GeV PbPb Collision
Upsilon in 200 GeV AuAu Collision
0 100 200 300Npart
0.0
0.2
0.4
0.6
0.8
1.0
RA
A
1S
2S
2 4 6pT (GeV)
0.0
0.2
0.4
0.6
0.8
1.0
RA
A
0-60%
1S
2S
STAR Talks at QM 17&18
!12
Upsilon(1S) Azimuthal Anisotropy in 2760 GeV PbPb
Better understand recombination from
measurementsv2
Develop azimuthal momentum anisotropy from heavy quark
recombination
Xiaojun Yao (Duke)
0.0 2.5 5.0 7.5 10.0 12.5 15.0pT (GeV)
0.00
0.01
0.02
0.03
v 2
30-50%
!13
Doubly Charmed Baryon• LHCb observed a new baryon (ccu): u bound around cc core
• Pair of heavy Q in anti-triplet forms bound state (diquark)
• Heavy diquark in QGP: dissociation, recombination (similar to quarkonium), carry color, energy loss different from quarkonium
• Hadronize into doubly charmed baryon
LHCb, Phys. Rev. Lett. 119, no.11,112001 (2017) ⌅++cc
!14 Xiaojun Yao (Duke)
cc
J/
cc
cc diquark (1S)
singletcolor neutralexist in vacuum
QQ anti-tripletcolorednot exist in vacuumexist in QGP
0 1 2 3 4 5pT (GeV)
0.0
0.1
0.2
0.3
0.4
0.5
dN
⌅+
+cc
dp2 T
Doubly Charmed Baryon Production in Heavy Ion Collisions
XY, B.Mueller, Phys.Rev.D97 (2018) no.7, 074003
Study recombination from measurements
!15
Predicted production rate in 2760 GeV PbPb, -1<y<1, 0<pT<5 GeV,
0.02 per collision with melting temperature = 250 MeV:
0.0125 per collision
⌅++cc
⌅++cc
Xiaojun Yao (Duke)
Setup: coupled Boltzmann for charm quark and diquark (add energy loss of diquark)assume only charm quark produced initially, diquark comes from (re)combination
Summary
• Describe both open and hidden heavy flavors: coupled Boltzmann equation
• Consistent dissociation and recombination from pNRQCD
• Extract potential and melting temperature from data
• Future: include 1P 2P 3S states, temperature-dependent potential, systematic extraction procedure (e.g. Bayesian)
• Heavy diquarks and doubly heavy baryons / tetraquarks
!16 Xiaojun Yao (Duke)
Acknowledgements
• I would like to thank my collaborators and colleagues: Berndt Mueller, Steffen Bass, Weiyao Ke, Yingru Xu, Jean-Francois Paquet, Jonah Bernhard, J. Scott Moreland
• Research funded by U.S. Department of Energy
Xiaojun Yao (Duke)
Backup: Thermal Equilibrium
N eqi = giVol
Zd3p
(2⇡)3�ie
�Ei(p)/T
Ei(p) =q
M2i + p2, Mi +
p2
2Mi
gb = gb = 3⇥ 2 = 6
g⌥(1S) = 3 + 1 = 4
�b = �b
�2b = �⌥(1S)
N eq
b +N eq
⌥(1S)
= Nb,tot
hyperfine splitting not considered
0 10 20 30 40 50 60
t (fm/c)
10�5
10�4
10�3
Nb,
hid
den/N
b,to
t
simulation w/ uniform initial momenta
relativistic equilibrium
non-relativistic equilibrium
0 10 20 30 40 50 60
t (fm/c)
10�5
10�4
10�3
Nb,
hid
den/N
b,to
t
simulation w/ uniform initial momenta
relativistic equilibrium
non-relativistic equilibrium
Backup: Thermal Equilibrium
gluon
0 10 20 30 40 50 60
t (fm/c)
10�5
10�4
10�3
Nb,
hid
den/N
b,to
t
simulation w/ uniform initial momenta
relativistic equilibrium
non-relativistic equilibrium
inelastic quarkinelastic gluon
0 10 20 30 40 50 60
t (fm/c)
10�5
10�4
10�3
Nb,
hid
den/N
b,to
t
simulation w/ uniform initial momenta
relativistic equilibrium
non-relativistic equilibrium
all
initial p uniform in 10 GeV
c
c
J/ψ
• Quarkonium production in pp collisions NRQCD factorization
• short-distance production of heavy quarks ~ 1/M
• long-distance coalescence into quarkonium ~ 1/E
Bodwin, Braaten, Lepage Phys. Rev. D 51, 1125 (1995)
p p
Backup: Initial Production
Backup: Initial Production
c
c
c
c
J/ψQGP
Initially no quarkonium enters QGP quarkonium is formed (recombined)
inside QGP or later (re)combination dominates
Initially quarkonium is generated and enters QGP
suppressed due to screening dissociation dominates
QGP
Backup: Numerical Implementation• Test particle Monte Carlo
• Each time step: consider diffusion, dissociation, recombination
• If specific process occurs, sample incoming medium particles and outgoing particles conserving energy momentum
• Recombination term contains
Two delta at same x ill-defined, almost never at same point
Enhance sampling for recombination
fQ(x,p1, t)fQ(x,p2, t)
fQ(x,p1, t)fQ(x,p2, t) !X
i,j
e�(yi�yj)2/2a2
B
(2⇡a2B)3/2
�3✓x�
yi + yj
2
◆�3(p1 � ki)�
3(p2 � kj)
f(x,p, t) =X
i
�3(x� yi(t))�3(p� ki(t))
Backup: Imaginary Part More Important
C. Miao, A. Mocsy, P. Petreczky arXiv:1012.4433
Backup: Diquark pNRQCD, Rates
