jet quenching in the hadronic phase - uni-frankfurt.de · 2016-12-14 · introduction ⇣ /s ⌘/s....

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

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


MUSIChydrodynamics


MARTINIjet


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


MUSIChydrodynamics


MARTINIjet


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⌫

⌘


shear⌘

s= const



⇡̇hµ⌫i = �⇡µ⌫

⌧⇡+

1

⌧⇡

⇣2⌘ �µ⌫ � �⇡⇡⇡

µ⌫✓ + '7⇡hµ↵ ⇡⌫i↵

�⌧⇡⇡⇡hµ↵ �⌫i↵ + �⇡⇧⇧�µ⌫

⌘




⌘

⌧⇡=

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



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⌫)



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⌫)


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


MUSIChydrodynamics


MARTINIjet


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


MUSIChydrodynamics


MARTINIjet


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)


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)


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)


X0.5

X0.1

Pb+Pb2.76 TeV

IP-Glsma + MUSIC + UrQMD


Jet production and energy-loss are necessary.

Spectra at the LHC


0

0.1

0.2

0.3

0.4

0 1 2 3 4 5 6

v 2{2

} (p

T)

pT (GeV)


π

IP-Glasma+ MUSIC + UrQMD


ALICE π+/-

Spectra at the LHC


0

0.1

0.2

0.3

0.4

0 1 2 3 4 5 6

v 2{2

} (p

T)

pT (GeV)


proton

IP-Glasma+ MUSIC + UrQMD


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


MUSIChydrodynamics


MARTINIjet


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

Model : MARTINI jets


B. 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

��qq

=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)


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)


X0.5

X0.1

Pb+Pb2.76 TeV

IP-Glsma + MUSIC + UrQMD+ MARTINI

αS = 0.23


It can be extended toward the higher range.pT

Collision Geometry


MUSIChydrodynamics


MARTINIjet


UrQMDcascade

Hadronic E-loss

Model Structure

Model : Jet quenching

soft hardmicroscopic transport

hydrodynamics

?partonic

jet quenching(AMY + collision)

t

z

Tsw

Tc


soft hardmicroscopic transport

hydrodynamics

?partonic

jet quenching(AMY + collision)

“coarse-grained” hadronic jet quenching in medium

t

z

Tsw

Tc


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

�


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


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||


0

0.1

0.2

0.3

0.4

0 1 2 3 4 5 6

v 2{2

} (p

T)

pT (GeV)


αS = 0.23

π

IP-Glasma+ MUSIC + UrQMD+ MARTINI


ALICE π+/-



0

0.1

0.2

0.3

0.4

0 1 2 3 4 5 6

v 2{2

} (p

T)

pT (GeV)


αS = 0.23

proton

IP-Glasma+ MUSIC + UrQMD+ MARTINI


ALICE p/pbar


jet quenching in the hadronic phase - uni-frankfurt.de · 2016-12-14 · introduction ⇣ /s ⌘/s....

Documents