Constraining the QCD equation of state in hadron colliders Akihiko Monnai (KEK, Japan) with Jean-Yves Ollitrault (IPhT Saclay, France) AM and J.-Y. Ollitrault, Phys. Rev. C 96, 044902 (2017) New Frontiers in QCD 2018 7th June 2018, Yukawa Institute for Theoretical Physics, Kyoto, Japan
Introduction n The quark-gluon plasma (QGP) Transverse momentum spectra A high-temperature phase of QCD where quarks are deconfined from hadrons (> 2 10 12 K) It can be created in relativistic nuclear collider experiments One can study the properties of the hot matter under strong interaction quantitatively 2 / 24
Introduction n Relativistic nuclear colliders: a gateway to the QGP Transverse Relativistic momentum Heavy Ion Collider spectra (RHIC)@BNL, s NN = 5.5-200 GeV (2000-) Large Hadron Collider (LHC)@CERN, s NN = 2.76-5.44 TeV (2010-) FAIR@GSI, NICA@JINR, SPS@CERN, J-PARC@JAEA/KEK? 3 / 24
Introduction n A standard model of heavy-ion collisions t Graphics by AM Colliding nuclei z Color glass condensate (< 0 fm/c) Gluons are emitted in an accelerated nucleus gluon gluon gluon gluon Gluons eventually overlap and saturate gluon gluon gluon gluon (called color glass condensate) 4 / 24
Introduction n A standard model of heavy-ion collisions n momentum spectra t Graphics by AM Colliding nuclei z Glasma (~0-1 fm/c) Little bangs Color glass condensate (< 0 fm/c) (Color) glass + plasma = glasma Longitudinal color electric and magnetic fields Details of equilibration is not known 5 / 24
Introduction n A standard model of heavy-ion collisions n momentum spectra t Graphics by AM Colliding nuclei Hadronic fluid QGP fluid z Hydrodynamic model (~1-10 fm/c) Local equilibration Glasma (~0-1 fm/c) Little bangs Color glass condensate (< 0 fm/c) Hydrodynamic evolution The hot QCD matter behaves as a relativistic fluid 6 / 24
Introduction n A standard model of heavy-ion collisions n momentum spectra t Hadronic gas Graphics by AM Colliding nuclei QGP fluid Freeze-out Hadronic fluid z Hadronic transport (> 10 fm/c) Freeze-out Hydrodynamic model (~1-10 fm/c) Local equilibration Glasma (~0-1 fm/c) Little bangs Color glass condensate (< 0 fm/c) Hadronic decay and transport Interaction becomes weaker when cold QCD liquid to QCD gas 7 / 24
Motivation and goals Motivation To investigate the QGP dynamics using hydrodynamic models (the first principle calculations are difficult at finite T and μ) 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 Experimental data THIS WORK First principle calculations Hydrodynamic models EoS, transport coefficients 8 / 24
Relativistic hydrodynamics n Energy-momentum tensor (in the local rest frame) Matching condition or AM, 1803.03318 where : energy density : pressure Landau frame : bulk pressure : shear stress tensor In a general frame : flow (four-velocity) 9 / 24
Overview of the model n Constraining the QCD equation of state in hadron colliders Information of QCD Equation of state Transport coefficients, Indirect constraining Experimental data Initial conditions Relativistic hydrodynamics Observables Hadronic transport Comparison 10 / 24
QCD equation of state (EoS) n Static relation among thermodynamic variables; sensitive to degrees of freedom in the system We have lattice QCD calculations at μ B = 0 Wuppertal-Budapest, PLB 730, 99 (2013) HotQCD, PRD 90, 094503 (2014) Is it what we see in heavy-ions collisions? 11 / 24
QCD equation of state (EoS) n We may see something different in HIC for various reasons: Finite size effect Chemical equilibration p zp (1 z)p Strong magnetic field B 12 / 24
QCD equation of state (EoS) n We systematically generate variations of EoS at μ B = 0: 4 P/T 7 6 5 4 3 2 1 EOS A EOS B EOS L EOS C (a) Varying DOF Finite size? Fewer quarks? 4 P/T 6 5 4 3 2 1 EOS D EOS E EOS L EOS F B field? (b) Varying Tc 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 T (GeV) 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 T (GeV) We estimate observables using hydrodynamic models for each EoS and find the correspondence between them and the EoS 13 / 24
Observable sensitive to EoS n Particle spectra PHENIX, PRC 69, 034909 (2004) (I) Integrate p T out particle number at y = 0 (II) Integrate p T out with p T as weight momentum per particle Rapidity : related to momentum in the beam axis direction 14 / 24
Observable sensitive to EoS n Particle spectra PHENIX, PRC 69, 034909 (2004) (I) Integrate p T out particle number at y = 0 (II) Integrate m T out with m T as weight energy per particle Transverse mass : effective mass of a particle where is incorporated *At, except for thermal blurring 15 / 24
Rough picture of hydro expansion n Transverse expansion and τ eff Longitudinal expansion is dominant ( ) Transverse expansion is relevant ( ) Effective radius of the medium: Cf: J.-Y. Ollitrault, PLB 273, 32 (1991) 16 / 24
Imprint of the EoS n Entropy density vs. Particle number Effective entropy per volume Particle number at Total entropy conservation : effective temperature when transverse expansion starts : effective radius of the medium where : freeze-out temperature (constant) : dimensionless constant factor 17 / 24
Imprint of the EoS n Energy density over entropy density vs. Mean m T Effective energy per entropy Energy per number at Once transverse expansion sets in ( ), longitudinal work becomes smaller and total energy is conserved : dimensionless constant factor 18 / 24
Input for hydrodynamic model n Transport coefficients Shear viscosity Bulk viscosity P. Kovtun et al., PRL 94, 111601 (2005) A. Buchel, PLB 663, 286 (2008) *Minimalistic choices from the gauge-string correspondence n Initial conditions Monte-Carlo Glauber model M. L. Miller et al., ARNPS 57, 205 (2007); AM, 1408.1410 Monte-Carlo KLN model H.-J. Drescher and Y. Nara, PRC 75, 034905 (2007) We show the results of the MC Glauber model here The scaling relations not affected; may affect comparison to data 19 / 24
Determination of a and b central n Ideal hydro calculations, Au-Au collisions, 0-5% central events peripheral 0.35 0.3 (a) 0.35 0.3 (b) Hydro calculations for 5 different energies (scaled) 0.25 0.25 /s (GeV) 0.2 0.15 0.1 0.05 a = 4.534, b = 0.202 EOS A EOS B EOS L EOS C ideal (w/o dec.) (EOS A) ideal (w/o dec.) (EOS B) ideal (w/o dec.) (EOS L) ideal (w/o dec.) (EOS C) 0 0 10 20 30 40 50 60 70 80-3 s (fm ) /s (GeV) 0.2 0.15 0.1 0.05 a = 4.534, b = 0.202 EOS D EOS E EOS L EOS F ideal (w/o dec.) (EOS D) ideal (w/o dec.) (EOS E) ideal (w/o dec.) (EOS L) ideal (w/o dec.) (EOS F) 0 0 10 20 30 40 50 60 70 80-3 s (fm ) A single set of fits hydro results on to all the EoS There is correspondence between the EoS and observables 20 / 24
Before comparing to data n Must considered are the effects of hadronic decay and viscosity 1.4 1.2 1 <m T > (GeV) 0.8 0.6 0.4 0.2 ideal (w/o dec) a=4.534, b=0.202 ideal (w/ decay) a=3.310, b=0.292 viscous (w/ decay) a=3.387, b=0.301 viscous+ δf (w/ decay) a=3.460, b=0.313 0 0 2 4 6 8 10 12 14 16 18 20 22 3-3 (1/R )dn/dy (fm ) 0 can be determined so that all the EoS are satisfied Hadronic decay reduces <m T > and increases dn/dy Viscosity increases dn/dy by entropy production 21 / 24
Comparisons to experimental data n Viscous hydro results with hadronic decays, Au-Au, 0-5% events <m T > (GeV) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 ALICE 2.76 TeV PHENIX 200 GeV STAR 200 GeV STAR 130 GeV STAR 62.4 GeV 0 0 2 4 6 8 10 12 14 16 3-3 (1/R )dn/dy (fm ) 0 EOS A EOS B EOS L EOS C 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 T (GeV) Conclusions Compatible with the lattice QCD equation of state within errors Larger effective # of degrees of freedom allowed by the data 4 P/T 7 6 5 4 3 2 1 EOS A EOS B EOS L EOS C (a) 22 / 24
Summary and outlook n We have probed collective properties of the hot QCD matter QCD equation of state is constrained using dn/dy and <m T > 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 AM and J.-Y. Ollitrault, in preparation dn/dp t dy (GeV -1 ) 60 50 40 30 20 10 STAR 7.7 GeV STAR 11.5 GeV STAR 19.6 GeV STAR 27 GeV STAR 39 GeV? 0 0 0.5 1 1.5 2 2.5 3 p T (GeV) 23 / 24
The end Thank you for listening! 24 / 24