Constraining the QCD equation of state in hadron collidersnfqcd2018/Slide/Monnai.pdf · Akihiko...

Constraining the QCD equation of state in hadron colliders

Akihiko Monnai (KEK, Japan)

with Jean-Yves Ollitrault (IPhT Saclay, France)

New Frontiers in QCD 2018

7th June 2018, Yukawa Institute for Theoretical Physics, Kyoto, Japan

AM and J.-Y. Ollitrault, Phys. Rev. C 96, 044902 (2017)

2 / 24Akihiko Monnai (KEK), NFQCD 2018, June 7th 2018

Introductionn  The quark-gluon plasma (QGP) Transverse momentum spectra

A high-temperature phase of QCD where quarks are deconfined from hadrons (> 2×1012 K)

It can be created in relativistic nuclear collider experiments

One can study the properties of the hot matter under strong interaction quantitatively


Introductionn  Relativistic nuclear colliders: a gateway to the QGP Transverse momentum spectra

Relativistic Heavy Ion Collider (RHIC)@BNL, √sNN = 5.5-200 GeV (2000-)

Large Hadron Collider (LHC)@CERN, √sNN = 2.76-5.44 TeV (2010-)

FAIR@GSI, NICA@JINR, SPS@CERN, J-PARC@JAEA/KEK … ?


Introductionn  A “standard model” of heavy-ion collisions

Graphics by AM

z

t

Colliding nuclei Color glass condensate (< 0 fm/c)

Gluons are emitted in an accelerated nucleusgluongluon

gluon

gluon

gluongluon

gluon

gluon

gluongluon

Gluons eventually overlap and saturate(called color glass condensate)


Introductionn  A “standard model” of heavy-ion collisions n  momentum spectra

Glasma (~0-1 fm/c)Graphics by AM

z

t

”Little bangs”

(Color) glass + plasma = glasma

Details of equilibration is not known

Longitudinal color electric and magnetic fields

Colliding nuclei Color glass condensate (< 0 fm/c)



Hydrodynamic model (~1-10 fm/c)

QGP fluid

Hadronic fluid

Graphics by AM

z

t

Local equilibration

Hydrodynamic evolution

Colliding nuclei

The hot QCD matter behaves as a relativistic fluid

Glasma (~0-1 fm/c)”Little bangs”

Color glass condensate (< 0 fm/c)



Hadronic transport (> 10 fm/c)Hadronic gas

Graphics by AM

z

t

Freeze-out

Hadronic decay and transport

Interaction becomes weaker when cold QCD liquid to QCD gas

Hydrodynamic model (~1-10 fm/c)Local equilibration

Glasma (~0-1 fm/c)”Little bangs”

Color glass condensate (< 0 fm/c)

QGP fluid

Hadronic fluid

Colliding nuclei

Freeze-out


Motivation and goals

To understand (I) the macroscopic evolution of the QCD matter and (II) the microscopic properties such as the equation of state (EoS) & transport coefficients

Goals

Motivation

To investigate the QGP dynamics using hydrodynamic models (the first principle calculations are difficult at finite T and μ)

First principle calculations

EoS, transport coefficients

Experimental data

Hydrodynamic models

THIS WORK


Relativistic hydrodynamicsn  Energy-momentum tensor (in the local rest frame)

Matching condition or AM, 1803.03318

Landau frame

: energy density

: pressure

: bulk pressure

: shear stress tensor

In a general frame

: flow (four-velocity)

where


Overview of the modeln  Constraining the QCD equation of state in hadron colliders

Initial conditions

Relativistic hydrodynamics

Observables

Equation of state

Transport coefficients ,

Information of QCD

Hadronic transport

Experimental dataComparison

Indirect constraining


QCD equation of state (EoS)n  Static relation among thermodynamic variables; sensitive to

degrees of freedom in the system

HotQCD, PRD 90, 094503 (2014) Wuppertal-Budapest, PLB 730, 99 (2013)

We have lattice QCD calculations at μB = 0

Is it what we see in heavy-ions collisions?


QCD equation of state (EoS)n  We may see something different in HIC for various reasons:

Finite size effect Chemical equilibration

Strong magnetic field

p

zp

(1 − z)p

… B


QCD equation of state (EoS)n  We systematically generate variations of EoS at μB= 0:

We estimate observables using hydrodynamic models for each EoS and find the correspondence between them and the EoS

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7T (GeV)

0

1

2

3

4

5

6

7

4P/

T

EOS AEOS BEOS LEOS C

(a)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7T (GeV)

0

1

2

3

4

5

6

4P/

T

EOS DEOS EEOS LEOS F

(b)

Varying DOF

Varying Tc

Finite size?

Fewer quarks?

B field?


Observable sensitive to EoSn  Particle spectra

Rapidity : related to momentum in the beam axis direction

(I) Integrate pT out → particle number at y = 0

(II) Integrate pT out with pT as weight → momentum per particle

PHENIX, PRC 69, 034909 (2004)


Observable sensitive to EoSn  Particle spectra

(I) Integrate pT out → particle number at y = 0

(II) Integrate mT out with mT as weight → energy per particle

Transverse mass : effective mass of a particle where is “incorporated”

*At , except for thermal blurring

PHENIX, PRC 69, 034909 (2004)


Rough picture of hydro expansionn  Transverse expansion and τeff

Longitudinal expansion is dominant ( )

Transverse expansion is relevant ( )

Effective radius of the medium:

Cf: J.-Y. Ollitrault, PLB 273, 32 (1991)


Imprint of the EoSn  Entropy density vs. Particle number

: freeze-out temperature (constant) : dimensionless constant factor

Particle number at

Effective entropy per volume

: effective temperature when transverse expansion starts : effective radius of the medium where

Total entropy conservation


Imprint of the EoSn  Energy density over entropy density vs. Mean mT

: dimensionless constant factor

Energy per number at

Effective energy per entropy

Once transverse expansion sets in ( ), longitudinal work becomes smaller and total energy is conserved


Input for hydrodynamic modeln  Transport coefficients

*Minimalistic choices from the gauge-string correspondence

Shear viscosity

Bulk viscosity

P. Kovtun et al., PRL 94, 111601 (2005)

A. Buchel, PLB 663, 286 (2008)

n  Initial conditions

Monte-Carlo Glauber model

Monte-Carlo KLN model H.-J. Drescher and Y. Nara, PRC 75, 034905 (2007)

M. L. Miller et al., ARNPS 57, 205 (2007); AM, 1408.1410

We show the results of the MC Glauber model here The scaling relations not affected; may affect comparison to data


Determination of a and bn  Ideal hydro calculations, Au-Au collisions, 0-5% central events

A single set of fits hydro results on to all the EoS

0 10 20 30 40 50 60 70 80)-3s (fm

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

/s (G

eV)

∈

a = 4.534, b = 0.202

(b)

EOS DEOS EEOS LEOS Fideal (w/o dec.) (EOS D)ideal (w/o dec.) (EOS E)ideal (w/o dec.) (EOS L)ideal (w/o dec.) (EOS F)

0 10 20 30 40 50 60 70 80)-3s (fm

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

/s (G

eV)

∈

a = 4.534, b = 0.202

(a)

EOS AEOS BEOS LEOS Cideal (w/o dec.) (EOS A)ideal (w/o dec.) (EOS B)ideal (w/o dec.) (EOS L)ideal (w/o dec.) (EOS C)

Hydro calculations for 5 different energies (scaled)

central peripheral

There is correspondence between the EoS and observables


Before comparing to datan  Must considered are the effects of hadronic decay and viscosity

can be determined so that all the EoS are satisfied

0 2 4 6 8 10 12 14 16 18 20 22)-3)dN/dy (fm3

0(1/R

0

0.2

0.4

0.6

0.8

1

1.2

1.4

> (G

eV)

T


Comparisons to experimental data n  Viscous hydro results with hadronic decays, Au-Au, 0-5% events

0 2 4 6 8 10 12 14 16)-3)dN/dy (fm3

0(1/R

00.10.20.30.40.50.60.70.80.9

1

> (G

eV)

T


Summary and outlookn  We have probed collective properties of the hot QCD matter

QCD equation of state is constrained using dN/dy and

The EoS with the effective number of DOF equal to or larger than that of lattice QCD is favored

We may extract the finite-density EoS out of Beam Energy Scan experimental data

? 0

10

20

30

40

50

60

0 0.5 1 1.5 2 2.5 3

dN/d

p tdy

(GeV

-1)

pT (GeV)

STAR 7.7 GeVSTAR 11.5 GeVSTAR 19.6 GeV

STAR 27 GeVSTAR 39 GeV

AM and J.-Y. Ollitrault, in preparation


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