Hydrodynamic approach to nuclear collisions at beam energy scan energies Akihiko Monnai (KEK) In collaboration with: Björn Schenke (BNL) and Chun Shen (Wayne) AM, B. Schenke, C. Shen, arXiv:1902.05095 [nucl-th] Hadron Interactions and Polarization from Lattice QCD, Quark Model, and Heavy Ion Collisions 28 th March 2019, Yukawa Institute for Theoretical Physics, Kyoto, Japan
Introduction n The quark-gluon plasma (QGP) Transverse momentum spectra A high-temperature phase of QCD (> 2 � 10 12 K) Well-established theoretically by lattice QCD at vanishing μ B and experimentally by nuclear collisions LHC - BNL Relativistic Heavy Ion Collider (RHIC) - CERN Large Hadron Collider (LHC) Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 2 / 37
Introduction n Little is known at finite density (“sign problem” of lattice QCD) Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 3 / 37
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, μ B Verify the existence of a QCD critical point (QCP) Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 3 / 37
Introduction n Modeling nuclear collisions QCD properties Experimental data 60 STAR 7.7 GeV STAR 11.5 GeV 50 STAR 19.6 GeV dN/dp t dy (GeV -1 ) STAR 27 GeV 40 STAR 39 GeV 30 ? 20 10 0 0 0.5 1 1.5 2 2.5 3 p T (GeV) We need a “link” between fundamental QCD properties and experimental data of nuclear collisions We consider the relativistic hydrodynamic model Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 4 / 37
Introduction n Relativistic nuclear collisions Hadronic transport τ > 10 fm Freeze-out Hydrodynamic evolution τ = 1-10 fm Local equilibration Glasma Nuclei τ < 1 fm Collision (saturated gluons) Color glass condensate τ < 0 fm Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 5 / 37
Introduction n Relativistic nuclear collisions Hadronic transport τ > 10 fm Freeze-out Hydrodynamic evolution τ = 1-10 fm Local equilibration Glasma Nuclei τ < 1 fm Collision (saturated gluons) Color glass condensate τ < 0 fm Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 5 / 37
Introduction n Relativistic nuclear collisions Hadronic transport τ > 10 fm Freeze-out Hydrodynamic evolution τ = 1-10 fm Local equilibration Glasma Glasma τ < 1 fm Collision (Longitudinal color magnetic & electric fields) Color glass condensate τ < 0 fm Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 5 / 37
Introduction n Relativistic nuclear collisions Hadronic transport τ > 10 fm Freeze-out Hydrodynamic evolution τ = 1-10 fm Local equilibration Glasma QGP fluid τ < 1 fm Collision (After local thermalization) Color glass condensate τ < 0 fm Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 6 / 37
Introduction n Relativistic nuclear collisions Hadronic transport τ > 10 fm Freeze-out Thermal hadrons Hydrodynamic evolution τ = 1-10 fm Local equilibration Glasma τ < 1 fm Collision Color glass condensate τ < 0 fm Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 6 / 37
Introduction n Relativistic nuclear collisions Hadronic transport τ > 10 fm Decay hadrons Freeze-out Thermal hadrons Hydrodynamic evolution τ = 1-10 fm Local equilibration Glasma τ < 1 fm Collision Color glass condensate τ < 0 fm Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 6 / 37
Introduction n Evidence for the QGP fluid y p y x p x In-medium Interaction Spatial anisotropy Momentum anisotropy Characterized by Fourier harmonics of azimuthal distribution : elliptic flow Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 7 / 37
Introduction n Experimental data Kolb et al., PLB 500, 232 (2001) ✓ Gas Gas Liquid: strong-coupling limit Gas ✗ Gas: weak-coupling limit Consistent with the nearly-perfect liquid picture up to p T ~ 2 [GeV] - The QGP is strongly-coupled near the quark-hadron transition - We may use hydrodynamics for an effective theory of QGP Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 8 / 37
Is it good at BES energies? n A historical point of view LHC √s NN Discovery of a 1000 Hydro nearly-perfect fluid RHIC 100 Not hydro SPS 10 AGS Bevalac 1 2010 2018 1990 2000 1980 Year Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 9 / 37
Is it good at BES energies? n A historical point of view LHC √s NN Discovery of a 1000 Hydro nearly-perfect fluid RHIC 100 RHIC-BES ? Not hydro SPS Hydro 10 AGS Bevalac 1 2010 2018 1990 2000 1980 Year Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 9 / 37
Is it good at BES energies? n A historical point of view (around 2000) √s NN 1000 Ideal hydro RHIC 100 Not hydro SPS 10 AGS Bevalac 1 2010 2018 1990 2000 1980 Year Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 10 / 37
Is it good at BES energies? n A historical point of view (around 2018) √s NN LHC 1000 RHIC Viscous hydro 100 RHIC-BES Shear viscosity: Csernai, Kapusta & SPS McLerran, PRL 97, 152303 (2006) 10 AGS Not hydro Bevalac 1 2010 2018 1990 2000 1980 Year Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 11 / 37
Small systems and beam energy scan n Similar but different physics Small systems Beam energy scan Temperature: small Temperature: large Volume: large Volume: small “Evidence of the QGP” such as jet quenching is more sensitive to volume, thermal photons to temperature Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 12 / 37
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 Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 13 / 37
Overview 1. Introduction 2. Multiple charges 3. Summary and outlook 4. Diffusion and dissipation Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 14 / 37
2. Multiple charges AM, B. Schenke, C. Shen, arXiv:1902.05095 [nucl-th] Akihiko Monnai (KEK), “Phenomenology and experiments at RHIC and the LHC”, 16 th February 2019
Conserved charges n in relativistic nuclear collisions Dunlop et.al., PRC 84 044914 Baryon number (B) p n (> 0 in total) +1 +1 Electric charge (Q) p n (> 0 in total) +1 0 Strangeness (S) p n (= 0 in total) 0 0 Essential in understanding particle-antiparticle ratios Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 15 / 37
Overview of hydro model n with multiple charges Relativistic Initial Hadronic hydrodynamic conditions transport model Equation of state Information of QCD Transport coefficients We start with construction of the QCD equation of state Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 16 / 37
Equation of state n Construction Lattice QCD: expansion up to the 4 th order HotQCD: PRD 86, 034509 (2012); PRD 90, 094503 (2014); PRD 92, 073743 (2015) Wuppertal-Budapest: PLB 730, 99 (2013); JHEP 01, 138 (2012); PRD 92, 114505 (2015) Match to hadron resonance gas (HRG) at lower T 1. Taylor expansion is not reliable when the fugacity is large 2. Agreement between lattice QCD and HRG is good in hadronic phase Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 17 / 37
Equation of state n Construction (Cont’d) 3. EOS of hydrodynamic model should match EOS of kinetic theory for correct energy-momentum/charge conservation Freezeout t Kinetic transport Hydrodynamics Stefan-Boltzmann limits are used as anchors at very high T where lattice QCD data are scarce Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 18 / 37
Equation of state n Construction Connect to HRG at low T where Crossover-type EOS The dependences on sub-leading μ’s are approximated to be small Parameters are chosen to satisfy thermodynamic conditions: , Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 19 / 37
Strangeness and charge densities n Strange neutrality condition (n S = 0) μ S is finite positive at μ B > 0 because of s quarks (or strange baryons) s quark chemical potential: density s d u _ _ _ u d s μ S = 0 leads to n S ≠ 0 The condition can be modified by initial fluctuations and diffusion Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 20 / 37
Strangeness and charge densities n Charge-to-baryon ratio (n Q = c n B ) μ Q is finite negative at μ B > 0 for neutron rich nuclei (Z/A < 1/2) d quark abundance: proton rich/neutral nuclei; μ Q ≥ 0 for μ B > 0 relevant for background of isobars c ≃ 0.4 for Au and Pb nuclei Akihiko Monnai (KEK), HIPLQH 2019, 28 th March 2019 21 / 37
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