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Jet quenching in the hadronic phasewithin a hybrid approach
Sangwook Ryu
Transport meeting (Nov 30, 2016)
• By colliding heavy nuclei (at RHIC and the LHC), we can ➤ create quark-gluon plasma (QGP) and ➤ study its properties (e.g. transport coefficients).
• This can be done by creating a realistic dynamical model of heavy ion collisions
• Different aspects of QGP and hadronic matter influence each other. e.g.,➤ non-zero alters the estimate of➤ jet quenching in hadronic phase changes determination of the jet-medium interaction in QGP
• Goal : hybrid model covering all these different aspects.
Introduction
⌘/s⇣/s
Jet production and energy lossfor hard (high- ) physics
PART 2
Hybrid approach anddescription of soft (low- ) physics
PART 1
pT
pT
Jet production and energy lossfor hard (high- ) physics
PART 2
Hybrid approach anddescription of soft (low- ) physics
PART 1
pT
pT
Hybrid approach
Jet production andenergy lossCollective
dynamics(hydrodynamics)
Pre-thermalizationdynamics
Collision geometry
Hadronic re-scattering (microscopic transport) figure bySteffen Bass
Model Structure
Collision Geometry
IP-Glasma Initial Condition
MUSIChydrodynamics
Cooper-Fryeparticlization
MARTINIjet
PYTHIA/LUNDstring fragmentation
UrQMDcascade
Hadronic E-loss
Collision Geometry
IP-Glasma Initial Condition
MUSIChydrodynamics
Cooper-Fryeparticlization
MARTINIjet
PYTHIA/LUNDstring fragmentation
UrQMDcascade
Hadronic E-loss
Model Structure
Model : IP-Glasma I.C.B. Schenke, P. Tribedy and R. Venugopalan (2012)
Classical YM dynamics with color sources in nuclei
Ai(1,2)(xT )
=i
gU(1,2)(xT ) @iU
†(1,2)(xT )
U(1,2)(xT ) = P exp
�ig
Zdx
± ⇢(1,2)(xT , x±)
r2T �m
2
�
Ai(⌧ = +0) = Ai(1) +Ai
(2)
h⇢a(x0T ) ⇢
a(x00T )i
= g2µ2A�
ab�2(x0T � x
00T )
color charge distribution
initial gluon field after collision
gluon field from each nucleus
Tµ⌫(⌧ = ⌧0)u
⌫ = ✏uµ
energy density profile at ⌧ = ⌧0
A⌘(⌧ = +0) =ig
2[Ai
(1), Ai(2)]
@µFµ⌫ � ig[Aµ, F
µ⌫ ] = 0
Model : IP-Glasma I.C.
well describes distributionvn
C. Gale, S. Jeon, B. Schenke,P. Tribedy and R. Venugopalan (2012)
B. Schenke, P. Tribedy and R. Venugopalan (2012)Classical YM dynamics with color sources in nuclei
Collision Geometry
IP-Glasma Initial Condition
MUSIChydrodynamics
Cooper-Fryeparticlization
MARTINIjet
PYTHIA/LUNDstring fragmentation
UrQMDcascade
Hadronic E-loss
Model Structure
Model : MUSIC hydroB. Schenke, S. Jeon, and C. Gale (2010)
@µTµ⌫ = 0
hydrodynamic equations of motion
�µ⌫ = gµ⌫ � uµu⌫
bulk shear
Conservation equation
Decomposition
Local 3-metric
Local 3-gradient rµ = �µ⌫@⌫
Tµ⌫ = ✏0uµu⌫ � (P0(✏0) +⇧)�µ⌫ + ⇡µ⌫
EoS
equation of motion for viscous corrections
shear viscosity relaxation equation
✓ = rµuµ
expansion rate
shear tensor
�µ⌫ =1
2
rµu⌫ +r⌫uµ � 3
2�µ⌫ (r↵u
↵)
�⌘ rhµu⌫i
⇡̇hµ⌫i = �⇡µ⌫
⌧⇡+
1
⌧⇡
⇣2⌘ �µ⌫ � �⇡⇡⇡
µ⌫✓ + '7⇡hµ↵ ⇡⌫i↵
�⌧⇡⇡⇡hµ↵ �⌫i↵ + �⇡⇧⇧�µ⌫
⌘
Model : MUSIC hydroB. Schenke, S. Jeon, and C. Gale (2010)
shear⌘
s= const
equation of motion for viscous corrections
shear viscosity relaxation equation
⇡̇hµ⌫i = �⇡µ⌫
⌧⇡+
1
⌧⇡
⇣2⌘ �µ⌫ � �⇡⇡⇡
µ⌫✓ + '7⇡hµ↵ ⇡⌫i↵
�⌧⇡⇡⇡hµ↵ �⌫i↵ + �⇡⇧⇧�µ⌫
⌘
Model : MUSIC hydroB. Schenke, S. Jeon, and C. Gale (2010)
equation of motion for viscous corrections
shear viscosity relaxation equation
⌘
⌧⇡=
1
5(✏0 + P0)
�⇡⇧
⌧⇡=
6
5
�⇡⇡⌧⇡
=4
3
⌧⇡⇡⌧⇡
=10
7
G. Denicol, S. Jeon, and C. Gale (2014)
second-order transport coefficients
⇡̇hµ⌫i = �⇡µ⌫
⌧⇡+
1
⌧⇡
⇣2⌘ �µ⌫ � �⇡⇡⇡
µ⌫✓ + '7⇡hµ↵ ⇡⌫i↵
�⌧⇡⇡⇡hµ↵ �⌫i↵ + �⇡⇧⇧�µ⌫
⌘
14-moment approximation in the small mass limit
Model : MUSIC hydroB. Schenke, S. Jeon, and C. Gale (2010)
equation of motion for viscous corrections
bulk viscosity relaxation equation
Tc = 180MeV
F. Karsch,D. Kharzeev andK. Tuchin (2008)
J. Noronha-Hostler,J. Noronha andC. Greiner (2009)
bulk
⇧̇ = � ⇧
⌧⇧+
1
⌧⇧(�⇣ ✓ � �⇧⇧⇧ ✓ + �⇧⇡⇡
µ⌫�µ⌫)
Model : MUSIC hydroB. Schenke, S. Jeon, and C. Gale (2010)
equation of motion for viscous corrections
bulk viscosity relaxation equation
14-moment approximation in the small mass limitG. Denicol, S. Jeon, and C. Gale (2014)
⇣
⌧⇧= 15
✓1
3� c2s
◆2
(✏0 + P0)
�⇧⇧
⌧⇧=
2
3
�⇧⇡
⌧⇧=
8
5
✓1
3� c2s
◆second-order transport coefficients
⇧̇ = � ⇧
⌧⇧+
1
⌧⇧(�⇣ ✓ � �⇧⇧⇧ ✓ + �⇧⇡⇡
µ⌫�µ⌫)
Model : MUSIC hydroB. Schenke, S. Jeon, and C. Gale (2010)
P. Huovinen, and P. Petreczky (2010)
Cross over phase transition around T = 180 MeV
Initial condition + Hydro equation + EoS
Up to the isothermal hypersurface at to switch from hydrodynamics to transport
Model : Equation of state
Only those included in UrQMD
Equation of state : hadron gas + lattice data
Hydrodynamic evolution
Tsw = 145MeV
Collision Geometry
IP-Glasma Initial Condition
MUSIChydrodynamics
Cooper-Fryeparticlization
MARTINIjet
PYTHIA/LUNDstring fragmentation
UrQMDcascade
Hadronic E-loss
Model Structure
f0(x,p) =1
exp [(p · u)/T ]⌥ 1
sampling particles according to the Cooper-Frye formula
�fshear(x,p) = f0(1± f0)p
µp
⌫⇡
µ⌫
2T 2(✏0 + P0)
dN
d
3p
����1-cell
= [f0(x,p) + �fshear(x,p) + �fbulk(x,p)]p
µ�3⌃µ
Ep
1
Cbulk=
1
3T
X
n
m2n
Zd3k
(2⇡)3Ekfn,0(1± fn,0)
✓c2sEk � |k|2
3Ek
◆
P. Bozek (2010)
�fbulk(x,p) = �f0(1± f0)Cbulk⇧
T
c
2s(p · u)�
(�p
µp
⌫�µ⌫)
3(p · u)
�
Model : Cooper-Frye samplingF. Cooper and G. Frye (1974)
Collision Geometry
IP-Glasma Initial Condition
MUSIChydrodynamics
Cooper-Fryeparticlization
MARTINIjet
PYTHIA/LUNDstring fragmentation
UrQMDcascade
Hadronic E-loss
Model Structure
Model : UrQMD cascadeUltra-relativistic Quantum Molecular Dynamics
S. A. Bass et al. (1998)Monte-Carlo implementation of transport theory
Which species? : 55 baryons + 32 mesonswith masses up to 2.25 GeV
Cross sections : based on experimental dataJet-hadron interaction by PYTHIA
Keeps track of particle trajectories
pµ�
�xµfi(x, p) = Ci[f ]
Description of soft physicsPRL 2015 (arXiv:1502.01675)
S. Ryu, J-F, Paquet, G. Denicol, C. Shen, B. Schenke, S. Jeon and C. Gale
Parameters are tuned to fit multiplicity, mean and integrated flow coefficients .
pTvn
The shear viscosity is favored. ⌘
s= 0.095
The bulk viscosity is crucial to describe those observables.
Spectra at the LHC
The low- spectra are well described.pT
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
0 2 4 6 8 10
(1/2
π)(
1/p
T)
dN
/dp
T (
GeV
-2)
pT (GeV)
0-5%shear+bulkη/s = 0.095Tsw = 145 MeV
X0.5
X0.1
Pb+Pb2.76 TeV
IP-Glsma + MUSIC + UrQMD ALICE π+/-
K+/-
proton/pbar
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
0 2 4 6 8 10
(1/2
π)(
1/p
T)
dN
/dp
T (
GeV
-2)
pT (GeV)
0-5%shear+bulkη/s = 0.095Tsw = 145 MeV
X0.5
X0.1
Pb+Pb2.76 TeV
IP-Glsma + MUSIC + UrQMD
UrQMD w/ collfeeddown
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
0 2 4 6 8 10
(1/2
π)(
1/p
T)
dN
/dp
T (
GeV
-2)
pT (GeV)
0-5%shear+bulkη/s = 0.095Tsw = 145 MeV
X0.5
X0.1
Pb+Pb2.76 TeV
IP-Glsma + MUSIC + UrQMD ALICE π+/-
K+/-
proton/pbar
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
0 2 4 6 8 10
(1/2
π)(
1/p
T)
dN
/dp
T (
GeV
-2)
pT (GeV)
0-5%shear+bulkη/s = 0.095Tsw = 145 MeV
X0.5
X0.1
Pb+Pb2.76 TeV
IP-Glsma + MUSIC + UrQMD
UrQMD w/ collfeeddown
Jet production and energy-loss are necessary.
Spectra at the LHC
Jet production and energy-loss are necessary.
0
0.1
0.2
0.3
0.4
0 1 2 3 4 5 6
v 2{2
} (p
T)
pT (GeV)
20-30%shear+bulkη/s = 0.095Tsw = 145 MeV
π
IP-Glasma+ MUSIC + UrQMD
UrQMD w/ collfeeddown
ALICE π+/-
Spectra at the LHC
Jet production and energy-loss are necessary.
0
0.1
0.2
0.3
0.4
0 1 2 3 4 5 6
v 2{2
} (p
T)
pT (GeV)
20-30%shear+bulkη/s = 0.095Tsw = 145 MeV
proton
IP-Glasma+ MUSIC + UrQMD
UrQMD w/ collfeeddown
ALICE p/pbar
Spectra at the LHC
Jet production and energy lossfor hard (high- ) physics
PART 2
Hybrid approach anddescription of soft (low- ) physics
PART 1
pT
pT
Collision Geometry
IP-Glasma Initial Condition
MUSIChydrodynamics
Cooper-Fryeparticlization
MARTINIjet
PYTHIA/LUNDstring fragmentation
UrQMDcascade
Hadronic E-loss
Model Structure
Hard process at the position ofbinary collision (PYTHIA)
Energy loss- Radiation (AMY)- Collision (with thermal partons)
Fragmentation into hadrons(PYTHIA / LUND string model)
Model : MARTINI jetsB. Schenke, C. Gale and S. Jeon (2010)
Modular Algorithm for Relativistic Treatment of heavy IoN Interaction
Energy loss- Radiation (AMY)- Collision (with thermal partons)
Fragmentation into hadrons(PYTHIA / LUND string model)
Hard process at the position ofbinary collision (PYTHIA)
Model : MARTINI jetsB. Schenke, C. Gale and S. Jeon (2010)
Modular Algorithm for Relativistic Treatment of heavy IoN Interaction
Model : MARTINI jets
Energy loss- Radiation (AMY)- Collision (with thermal partons)
B. Schenke, C. Gale and S. Jeon (2010)Modular Algorithm for Relativistic Treatment of heavy IoN Interaction
Fragmentation into hadrons(PYTHIA / LUND string model)
Hard process at the position ofbinary collision (PYTHIA)
Energy loss- Radiation (AMY)- Collision (with thermal partons)
Fragmentation into hadrons(PYTHIA / LUND string model)
Hard process at the position ofbinary collision (PYTHIA)
Model : MARTINI jetsB. Schenke, C. Gale and S. Jeon (2010)
Modular Algorithm for Relativistic Treatment of heavy IoN Interaction
Collinear emission
Nearly on-shell intermediate propagator
Infinite number of diagrams> Integral equations
figures by G-Y. Qin
Model : jet energy lossRadiative energy loss (AMY)
P. Arnold, G. Moore and L. Yaffe (2002)
Model : jet energy lossCollisional energy loss (soft approximation)
B. Schenke, C. Gale and G-Y. Qin (2009)
dE
dt
=2
9nf⇥�
2sT
2
ln
ET
m2g
+ cf23
12+ cs
�
dE
dt
����qg
=4
3⇥�2
sT2
ln
ET
m2g
+ cb13
6+ cs
�
dE
dt
����gq
=1
2nf⇥�
2sT
2
ln
ET
m2g
+ cf13
6+ cs
�
dE
dt
����gg
= 3⇥�2sT
2
ln
ET
m2g
+ cb131
48+ cs
�
G-Y. Qin et al. (2008)
Spectra with MARTINI
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
0 2 4 6 8 10
(1/2
π)(
1/p
T)
dN
/dp
T (
GeV
-2)
pT (GeV)
0-5%shear+bulkη/s = 0.095Tsw = 145 MeV
X0.5
X0.1
Pb+Pb2.76 TeV
IP-Glsma + MUSIC + UrQMD+ MARTINI
αS = 0.23
ALICE π+/-
K+/-
proton/pbar
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
0 2 4 6 8 10
(1/2
π)(
1/p
T)
dN
/dp
T (
GeV
-2)
pT (GeV)
0-5%shear+bulkη/s = 0.095Tsw = 145 MeV
X0.5
X0.1
Pb+Pb2.76 TeV
IP-Glsma + MUSIC + UrQMD+ MARTINI
αS = 0.23
UrQMD w/ collfeeddown
It can be extended toward the higher range.pT
Collision Geometry
IP-Glasma Initial Condition
MUSIChydrodynamics
Cooper-Fryeparticlization
MARTINIjet
PYTHIA/LUNDstring fragmentation
UrQMDcascade
Hadronic E-loss
Model Structure
Model : Jet quenching
soft hardmicroscopic transport
hydrodynamics
?partonic
jet quenching(AMY + collision)
t
z
Tsw
Tc
Model : Jet quenching
soft hardmicroscopic transport
hydrodynamics
?partonic
jet quenching(AMY + collision)
“coarse-grained” hadronic jet quenching in medium
t
z
Tsw
Tc
Model : Jet quenching
PDF (zcoll
) = � exp (��zcoll
)
Probability that the jet has collision after travelling is .�x ��x
Does the jet experience collisions?
Scale the probability to take 1. formation time (out of string) 2. different quark contents (AQM) into account
Determine the process (mostly elastic or string excitation)
0
0.2
0.4
0.6
0 2 4 6 8
Tmedium = 160 MeV
π+ (pz = 10 GeV)
λcoll. = 0.48 fm-1
Pstring = 66%
PD
F (
z co
ll) (
fm-1
)
zcoll (fm)
Model : Jet quenchingString excitation and fragmentation
pµjet =⇣q
m2jet + P 2
jet,0, Pjet
⌘
pµth,f =⇣q
m2th + p2? + p2k,p?, pk
⌘
pµth,i = (mth,0, 0)
pµstring =�Estring,�p?, Pjet � pk
�
Model : Jet quenchingString excitation and fragmentation
PDF (p?) =1
⇡�2exp
✓�p2?�2
◆
2. determine string mass
1. determine transverse momentum transfer
Mmin
= mjet
Mmax
=⇥(ps�m?,th)
2 � p2?⇤1/2
where m?,th =�m2
th + p2?�1/2
PDF (Mstring) ⇠ Mstring ⇠ density of state
Model : Jet quenchingString excitation and fragmentation
3. determine momenta of the string and (thermal) hadron
yth = asinh
✓Pjetps
◆� acosh
s+m2
th �M2string
2m?,thps
!
pk = m?,th sinh yth
Estring =hM2
string + p2? +�Pjet � pk
�2i1/2
p±string =1p2
⇥Estring±
�Pjet � pk
�⇤
4. fragment string based on LUND/PYTHIA model : TBD
• A hybrid model, involving both the soft and hard physics of heavy ion collisions, is presented.
• The low- distribution is well reproduced, while we need jet production and energy-loss to extend toward the higher regime.
• Jet quenching in hadronic phase is currently under investigation to improve this hybrid approach.
Conclusion
pT
pT
Backup Slides
Model : Cooper-Frye samplingsampling particles according to the Cooper-Frye formula
F. Cooper and G. Frye (1974)
�nbulk(x) = d
Zd
3k
(2⇡)3�fbulk(k)
n0(x) = d
Zd
3k
(2⇡)3f0(k)
¯
N |1-cell =(
[n0(x) + �nbulk(x)]uµ�⌃µ if u
µ�⌃µ � 0
0 otherwise
1. sample number of particles based on Poisson distribution
2. sample momentum of each particlesaccording to the Cooper-Frye formula shown in the main slide
Model : jet energy lossRadiative energy loss (AMY)
P. Arnold, G. Moore and L. Yaffe (2002)
d�
dk(p, k) =
Cs
g2
16�p7ek/T
ek/T ⇥ 1
e(p�k)/T
e(p�k)/T ⇥ 1
8>>><
>>>:
1+(1�x)2
x
3(1�x)2 q ⇤ qg
Nf
x
2+(1�x)2
x
2(1�x)2 g ⇤ qq̄
1+x
4+(1�x)4
x
3(1�x)3 g ⇤ gg
9>>>=
>>>;
�Z
d2h
(2�)22h · ReF(h, p, k)
2h = i �E(h, p, k)F(h, p, k) + g2s
Zd2q?(2⇥)2
m2D
q2?(q
2? +m2
D)
⇥�(Cs � CA/2)[F(h)� F(h� k q?)] + (CA/2)[F(h)� F(h+ pq?)]
+ (CA/2)[F(h)� F(h� (p� k)q?)]
�E(h, p, k) =h2
2pk(p� k)+
m2k
2k+
m2(p�k)
2(p� k)�
m2p
2ph ⌘ (k⇥ p)⇥ e||
Spectra with MARTINI
0
0.1
0.2
0.3
0.4
0 1 2 3 4 5 6
v 2{2
} (p
T)
pT (GeV)
20-30%shear+bulkη/s = 0.095Tsw = 145 MeV
αS = 0.23
π
IP-Glasma+ MUSIC + UrQMD+ MARTINI
UrQMD w/ collfeeddown
ALICE π+/-
It can be extended toward the higher range.pT
Spectra with MARTINI
0
0.1
0.2
0.3
0.4
0 1 2 3 4 5 6
v 2{2
} (p
T)
pT (GeV)
20-30%shear+bulkη/s = 0.095Tsw = 145 MeV
αS = 0.23
proton
IP-Glasma+ MUSIC + UrQMD+ MARTINI
UrQMD w/ collfeeddown
ALICE p/pbar
It can be extended toward the higher range.pT