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Hydrodynamic approach to nuclear collisions at beam energy scan - - PowerPoint PPT Presentation

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Hydrodynamic approach to nuclear collisions at beam energy scan energies Akihiko Monnai (KEK) In collaboration with: Bjrn Schenke (BNL) and Chun Shen (Wayne) AM, B. Schenke, C. Shen, arXiv:1902.05095 [nucl-th] Hadron Interactions and

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Hydrodynamic approach to nuclear collisions at beam energy scan energies

Akihiko Monnai (KEK)

In collaboration with: Björn Schenke (BNL) and Chun Shen (Wayne)

Hadron Interactions and Polarization from Lattice QCD, Quark Model, and Heavy Ion Collisions 28th March 2019, Yukawa Institute for Theoretical Physics, Kyoto, Japan

AM, B. Schenke, C. Shen, arXiv:1902.05095 [nucl-th]

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Introduction

n The quark-gluon plasma (QGP)

Transverse momentum spectra A high-temperature phase of QCD (> 21012 K) Well-established theoretically by lattice QCD at vanishing μB and experimentally by nuclear collisions

  • BNL Relativistic Heavy Ion Collider (RHIC)
  • CERN Large Hadron Collider (LHC)

LHC

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Introduction

n Little is known at finite density (“sign problem” of lattice QCD)

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Introduction

n Little is known at finite density (“sign problem” of lattice QCD) Nuclear collisions

Beam Energy Scan @RHIC and FAIR, NICA, J-PARC…

Use nuclear collisions to: Determine the quark matter properties at finite T, μB Verify the existence of a QCD critical point (QCP)

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Introduction

n Modeling nuclear collisions

QCD properties

10 20 30 40 50 60 0.5 1 1.5 2 2.5 3 dN/dptdy (GeV-1) pT (GeV) STAR 7.7 GeV STAR 11.5 GeV STAR 19.6 GeV STAR 27 GeV STAR 39 GeV

Experimental data

We need a “link” between fundamental QCD properties and experimental data of nuclear collisions

?

We consider the relativistic hydrodynamic model

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Introduction

n Relativistic nuclear collisions

Nuclei (saturated gluons)

Local equilibration Collision

Color glass condensate Hadronic transport

Freeze-out

Hydrodynamic evolution Glasma

τ < 1 fm τ = 1-10 fm τ > 10 fm τ < 0 fm

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Introduction

n Relativistic nuclear collisions

Nuclei (saturated gluons)

Local equilibration

Color glass condensate Hadronic transport

Freeze-out

Hydrodynamic evolution Glasma

τ < 1 fm τ = 1-10 fm τ > 10 fm τ < 0 fm

Collision

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Introduction

n Relativistic nuclear collisions

Glasma (Longitudinal color magnetic & electric fields)

Local equilibration Collision

Color glass condensate Hadronic transport

Freeze-out

Hydrodynamic evolution Glasma

τ < 1 fm τ = 1-10 fm τ > 10 fm τ < 0 fm

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Introduction

n Relativistic nuclear collisions Local equilibration Collision

Color glass condensate Hadronic transport

Freeze-out

Hydrodynamic evolution Glasma QGP fluid (After local thermalization)

τ < 1 fm τ = 1-10 fm τ > 10 fm τ < 0 fm

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Introduction

n Relativistic nuclear collisions Local equilibration Collision

Color glass condensate Hadronic transport

Freeze-out

Hydrodynamic evolution Glasma Thermal hadrons

τ < 1 fm τ = 1-10 fm τ > 10 fm τ < 0 fm

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Introduction

n Relativistic nuclear collisions Local equilibration Collision

Color glass condensate Hadronic transport

Freeze-out

Hydrodynamic evolution Glasma Decay hadrons Thermal hadrons

τ < 1 fm τ = 1-10 fm τ > 10 fm τ < 0 fm

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Introduction

n Evidence for the QGP fluid

Momentum anisotropy Spatial anisotropy

py px y x

In-medium Interaction Characterized by Fourier harmonics of azimuthal distribution : elliptic flow

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Introduction

n Experimental data

Kolb et al., PLB 500, 232 (2001)

Consistent with the nearly-perfect liquid picture up to pT ~ 2 [GeV]

Gas Gas Gas

Liquid: strong-coupling limit Gas: weak-coupling limit

✓

  • The QGP is strongly-coupled near the quark-hadron transition
  • We may use hydrodynamics for an effective theory of QGP

✗

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Is it good at BES energies?

n A historical point of view

√sNN Year 2000 2010 100 10 1000 2018 1990 1980 1

Bevalac AGS SPS RHIC

Not hydro

LHC

Hydro

Discovery of a nearly-perfect fluid

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Is it good at BES energies?

n A historical point of view

√sNN Year 2000 2010 100 10 1000 2018 1990 1980 1

Bevalac AGS SPS RHIC

?

RHIC-BES

Not hydro

LHC

Hydro

Discovery of a nearly-perfect fluid

Hydro

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Is it good at BES energies?

n A historical point of view (around 2000)

√sNN Year 2000 2010 100 10 1000 2018 1990 1980 1

Bevalac AGS SPS RHIC

Not hydro Ideal hydro

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Is it good at BES energies?

n A historical point of view (around 2018)

√sNN Year 2000 2010 100 10 1000 2018 1990 1980 1

Bevalac AGS SPS RHIC

Not hydro Viscous hydro

RHIC-BES LHC

Shear viscosity: Csernai, Kapusta & McLerran, PRL 97, 152303 (2006)

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Small systems and beam energy scan

n Similar but different physics

Temperature: large Volume: small Temperature: small Volume: large

Small systems Beam energy scan

“Evidence of the QGP” such as jet quenching is more sensitive to volume, thermal photons to temperature

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Λ polarization and beam energy scan

n Vorticity converted into spin

Spin-orbit coupling + (possible) magnetic field effects More prominent at lower collision energies; a complete understanding of the background medium evolution is required

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Overview

  • 1. Introduction
  • 2. Multiple charges
  • 3. Summary and outlook
  • 4. Diffusion and dissipation

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Akihiko Monnai (KEK), “Phenomenology and experiments at RHIC and the LHC”, 16th February 2019

  • 2. Multiple charges

AM, B. Schenke, C. Shen, arXiv:1902.05095 [nucl-th]

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Conserved charges

n in relativistic nuclear collisions

Baryon number (B) (> 0 in total) Strangeness (S) (= 0 in total) Electric charge (Q) (> 0 in total)

p n

+1 +1

p n

+1

p n

Dunlop et.al., PRC 84 044914

Essential in understanding particle-antiparticle ratios

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Overview of hydro model

n with multiple charges

Relativistic hydrodynamic model Initial conditions Hadronic transport Equation of state Transport coefficients

We start with construction of the QCD equation of state

Information of QCD

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Equation of state

n Construction

Lattice QCD: expansion up to the 4th order

HotQCD: PRD 86, 034509 (2012); PRD 90, 094503 (2014); PRD 92, 073743 (2015)

Match to hadron resonance gas (HRG) at lower T

Wuppertal-Budapest: PLB 730, 99 (2013); JHEP 01, 138 (2012); PRD 92, 114505 (2015)

  • 1. Taylor expansion is not reliable when the fugacity is large
  • 2. Agreement between lattice QCD and HRG is good in hadronic phase

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Equation of state

n Construction

(Cont’d)

  • 3. EOS of hydrodynamic model should match EOS of kinetic theory

Freezeout

Hydrodynamics Kinetic transport t

for correct energy-momentum/charge conservation

Stefan-Boltzmann limits are used as anchors at very high T where lattice QCD data are scarce

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Equation of state

n Construction

where

Connect to HRG at low T Parameters are chosen to satisfy thermodynamic conditions: ,

Crossover-type EOS The dependences on sub-leading μ’s are approximated to be small

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Strangeness and charge densities

n Strange neutrality condition (nS = 0)

μS is finite positive at μB > 0 because of s quarks (or strange baryons) s quark chemical potential: u d s u d s _ _ _

density

μS = 0 leads to nS ≠ 0 The condition can be modified by initial fluctuations and diffusion

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Strangeness and charge densities

n Charge-to-baryon ratio (nQ = c nB)

μQ is finite negative at μB > 0 for neutron rich nuclei (Z/A < 1/2) d quark abundance: c ≃ 0.4 for Au and Pb nuclei relevant for background of isobars proton rich/neutral nuclei; μQ ≥ 0 for μB > 0

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Equation of state

n μS = μQ = 0 (conventional; denoted as NEOS B)

0.1 0.2 0.3 0.4 0.5 0.6 0.1 0.2 0.3 0.4 0.5 0.6 1 2 3 4 5

P/T4

(a) NEOS B

s/nB = 420 s/nB = 144 s/nB = 51 s/nB = 30 µB (GeV) T (GeV) P/T4

0.5 1 1.5 2 2.5 3 3.5 4 4.5

0.1 0.2 0.3 0.4 0.5 0.6 0.1 0.2 0.3 0.4 0.5 0.6 0.2 0.4 0.6 0.8 1

  • nS/T3

(b) NEOS B

s/nB = 420 s/nB = 144 s/nB = 51 s/nB = 30 µB (GeV) T (GeV)

  • nS/T3

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Thermodynamically consistent smooth EoS is obtained The strangeness neutrality condition is violated (nS < 0)

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Equation of state

n nS = 0, μQ = 0 (strangeness neutral; denoted as NEOS BS)

A visible modification is observed at larger μB/T

0.1 0.2 0.3 0.4 0.5 0.6 0.1 0.2 0.3 0.4 0.5 0.6 0.05 0.1 0.15 0.2 0.25

µS (GeV)

(b) NEOS BS

s/nB = 420 s/nB = 144 s/nB = 51 s/nB = 30 µB (GeV) T (GeV) µS (GeV)

0.05 0.1 0.15 0.2

0.1 0.2 0.3 0.4 0.5 0.6 0.1 0.2 0.3 0.4 0.5 0.6 1 2 3 4 5

P/T4

(a) NEOS BS

s/nB = 420 s/nB = 144 s/nB = 51 s/nB = 30 µB (GeV) T (GeV) P/T4

0.5 1 1.5 2 2.5 3 3.5 4 4.5

Finite positive μS is seen owing to the neutrality condition μB is becomes larger at large T for a given nB

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Equation of state

n Where you can probe on the μB-T plane

s/nB is constant when entropy and net baryon number are conserved s/nB = 420 s/nB = 144 s/nB = 51 s/nB = 30 √sNN = 200 GeV √sNN = 62.4 GeV √sNN = 19.6 GeV √sNN = 14.5 GeV

  • J. Gunther et. al., Nucl. Phys. A 967, 720 (2017)

If conformal, it is a straight line because s ~ T3 and nB ~ μBT2 Larger μB is required to fix the s/nB ratio when pions are dominant

0.1 0.2 0.3 0.4 0.5 0.6 0.1 0.2 0.3 0.4 0.5 0.6

T (GeV) µB (GeV)

NEOS B, s/nB=420 NEOS B, s/nB=144 NEOS B, s/nB=51 NEOS B, s/nB=30 NEOS BS, s/nB=420 NEOS BS, s/nB=144 NEOS BS, s/nB=51 NEOS BS, s/nB=30

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Equation of state

n nS = 0, nQ = 0.4nB (realistic in HIC; denoted as NEOS BQS)

Finite negative μQ owing to the condition nQ = 0.4nB The overall system is positively charged; μQ turns positive around nQ = 0.5nB

0.1 0.2 0.3 0.4 0.5 0.6 0.1 0.2 0.3 0.4 0.5 0.6 0.01 0.02 0.03 0.04 0.05

  • µQ (GeV)

(b) NEOS BQS

s/nB = 420 s/nB = 144 s/nB = 51 s/nB = 30 µB (GeV) T (GeV)

  • µQ (GeV)

0.005 0.01 0.015 0.02 0.025

0.1 0.2 0.3 0.4 0.5 0.6 0.1 0.2 0.3 0.4 0.5 0.6 1 2 3 4 5

P/T4

(a) NEOS BQS

s/nB = 420 s/nB = 144 s/nB = 51 s/nB = 30 µB (GeV) T (GeV) P/T4

0.5 1 1.5 2 2.5 3 3.5 4 4.5

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Stefan-Boltzmann limit

n Parton gas pressure

The diagonal and off-diagonal susceptibilities are

where , ,

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Stefan-Boltzmann limit

n The chemical potential ratio

NEOS B ( and ) NEOS BS ( and ) NEOS BQS ( and ) , , , , , ,

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Sound velocity cs

n s/nB dependence

Finite ns is relevant to cs

2 in NEOS B

0.1 0.2 0.3

s/nB=420

cs

2 NEOS B NEOS BS NEOS BQS 0.1 0.2 0.3 0.05 0.1 0.15 0.2 0.25 0.3 0.35

s/nB=30

cs

2

T (GeV)

0.1 0.2 0.3 0.05 0.1 0.15 0.2 0.25 0.3 0.35

s/nB=30

cs

2

T (GeV)

0.1 0.2 0.3 0.05 0.1 0.15 0.2 0.25 0.3 0.35

s/nB=30

cs

2

T (GeV)

In dense systems, cs is suppressed at lower T The effect of strangeness neutrality becomes more apparent The “conventional definition” w/o Q and S leads to underestimation

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

μB-μQ-μS space

n Constant pressure plane

The intercepts

0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.1 0.2 0.3

µQ (GeV)

(a) T = 0.14 GeV

P/T4 = 0.8 µB (GeV) µS (GeV) µQ (GeV)

0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.1 0.2 0.3

µQ (GeV)

(a) T = 0.14 GeV

µB (GeV) µS (GeV) µQ (GeV)

in the hadronic phase because the lightest hadron to carry them are ordered in mass as

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

μB-μQ-μS space

n Constant pressure plane

The intercepts

0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.1 0.2 0.3

µQ (GeV)

(a) T = 0.14 GeV

P/T4 = 0.8 µB (GeV) µS (GeV) µQ (GeV)

0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.1 0.2 0.3

µQ (GeV)

(a) T = 0.14 GeV

µB (GeV) µS (GeV) µQ (GeV)

0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.1 0.2 0.3

µQ (GeV)

(b) T = 0.2 GeV

P/T4 = 2 µB (GeV) µS (GeV) µQ (GeV)

0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.1 0.2 0.3

µQ (GeV)

(b) T = 0.2 GeV

µB (GeV) µS (GeV) µQ (GeV)

in the QGP phase as , , in the parton gas limit implies

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

μB-μQ-μS space

n Exploration of the QCD phase diagram

We do not explore the μB-T plane in the BES experiments but a certain slice in the μB-μQ-μS-T hyperplane

0.1 0.2 0.3 0.4 0.5 0.6 0.05 0.1 0.15 0.2 0.25 0.005 0.01 0.015 0.02 0.025 0.03

  • µQ (GeV)

s/nB=420 s/nB=144 s/nB=51 s/nB=30 µB (GeV) µS (GeV)

  • µQ (GeV)

This may well affect the QCD critical point search

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

n with multiple charges

Hydrodynamic model

Relativistic hydrodynamic model Dynamical Glauber model UrQMD Equation of state Information of QCD Transport coefficients

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Hydrodynamic results

n 3+1 D viscous hydro + UrQMD for Pb-Pb 17.3 GeV in SPS

π+ π− K+ K− p ¯ p φ Λ ¯ Λ Ξ− ¯ Ξ+ Ω ¯ Ω 10−2 10−1 100 101 102 dN/dy √sNN = 17.3 GeV esw = 0.26 GeV/fm3 NEOS B NEOS BS NEOS BQS π−/π+K+/K− ¯ p/p

2φ (π++π−)

¯ Λ/Λ Ξ−/Λ ¯ Ξ+/Ξ− ¯ Ω/Ω 10−2 10−1 100 ratio √sNN = 17.3 GeV esw = 0.26 GeV/fm3 NEOS B NEOS BS NEOS BQS

Strange neutrality visibly improves description of strange hadrons Charge-to-baryon ratio fixing has small effects; π-/π+ ratio (> 1) is improved

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Hydrodynamic results

n Switching temperature dependence

The preferred switching to UrQMD is 0.16-0.26 GeV/fm3 Effects of chemical potential becomes larger for lower esw

π+ π− K+ K− p ¯ p φ Λ ¯ Λ Ξ− ¯ Ξ+ Ω ¯ Ω 10−2 10−1 100 101 102 dN/dy √sNN = 17.3 GeV NEOS BQS esw = 0.16 GeV/fm3 esw = 0.26 GeV/fm3 esw = 0.36 GeV/fm3 π−/π+K+/K− ¯ p/p

2φ (π++π−)

¯ Λ/Λ Ξ−/Λ ¯ Ξ+/Ξ− ¯ Ω/Ω 10−2 10−1 100 ratio √sNN = 17.3 GeV NEOS BQS esw = 0.16 GeV/fm3 esw = 0.26 GeV/fm3 esw = 0.36 GeV/fm3

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Akihiko Monnai (KEK), “Phenomenology and experiments at RHIC and the LHC”, 16th February 2019

  • 3. Summary and outlook
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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Summary and outlook

n The QCD matter at finite density poses us challenges:

Interplay of multiple charges (B, Q, S) are important

  • Strangeness neutrality condition leads to finite positive μS, and

realistic charge-to-baryon ratio for Au/Pb to finite negative μQ

  • Particle-to-antiparticle ratios are described better in hydro model

Estimation of baryon, strangeness and charge diffusion including cross-coupling currents pT spectra, flow harmonics and rapidity distribution Realistic EoS for small systems as well as isobar experiments

  • Equation of state is constructed

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Akihiko Monnai (KEK), HIPLQH 2019, 28th March 2019

Summary and outlook

n Our QCD equation of state model NEOS is publicly available:

https://sites.google.com/view/qcdneos/home

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