Study of QCD Phase Diagram by Heavy Ion Experiments and Lattice QCD - PowerPoint PPT Presentation

Study of QCD Phase Diagram by Heavy Ion Experiments 
 and Lattice QCD Atsushi Nakamura Far Eastern Federal University "Theory of Hadronic Matter under Extreme Conditions”, Lab. of Theor. Phys. , Moscow April 18, 2016

Plan of the Talk FEFU Group, Zn Collaboration Transport Coefficients Motivation Formulation Difficult Points Finite Density Sign Problem Canonical Approach Zn collabartion and FEFU collaboration Experimental Data One summary Slied Lee-Yang Zeros If the time allows Summary

V.Braguta in Collaboration with V . Bornyakov, D. Boyda, M. Chernodub, V . Goy, A. Molochkov, A. Nikolaev and V . I. Zakharov Our GPU machine

Zn Collaboration R.Fukuda (Tokyo), S. Oka(Rikkyo), S.Sakai (Kyoto), A.Suzuki, Y. Taniguchi (Tsukuba) and A.N. JHEP02(2016)054 (arXiv:1504.04471) arXiv:1504.06351

5 /75 Experiments Lattice Neutron Star

/75 Story of Transport Coefficients Fighting against Noise Determine Spectral Functions 6

Transport Coefficients A Step towards Gluon Dynamical Behavior. They are (in principle) calculable by a well established formula (Linear Response Theory). They are important to understand QGP which is realized in Heavy Ion Collisions and early Universe. Hydro-Model Experimental QCD Data

RHIC-data Big Surprise ! Oh, really ? Hydro-dynamical Model describes RHIC data well ! At SPS, the Hydro describes well one-particle distributions, HBT etc., but fails for the elliptic flow.

Hydro describes well v2 Hydrodynamical calculations are based on Ideal Fluid, i.e., zero shear viscosity. 9 /75

Or not so surprise … E. Fermi, Prog. Theor. Phys. 5 (1950) 570 Statistical Model S.Z.Belen’skji and L.D.Landau, 
 Nuovo.Cimento Suppl. 3 (1956) 15 Criticism of Fermi Model 
 “Owing to high density of the particles and to strong interaction between them, one cannot really speak of their number.” Hagedorn, Suppl. Nuovo Cim. 3 (1956) 147. Limiting Temperature

Another Big Surprise ! • The Hydrodynamical Oh, model assumes zero really ? viscosity, 
 i.e., Perfect Fluid. • Phenomenological Analyses suggest also small viscosity.

Liquid or Gas ? Frequent Momentum Exchange Opposite Situation Perfect fluid Ideal Gas 12 /75

If produced matter at RHIC is (perfect) Fluid, not Free Gas, what does it matter ? Is QGP not a A new state free Gas ? of Matter is Fluid.

Lowest Perturbation 
 (Illustration purpose only) Pressure Ideal Free Gas Viscosity Perfect Fluid • At weak coupling, 
 it increases.

20th Century Karsch and Wyld (1987) Masuda, Nakamura and Sakai (Lattice 95) Sakai, Nakamura, Saito(QM97,Lattice 98) (Improved Action) Aarts and Martinez-Resco (2002) 21st Century Sakai, Nakamura (2004) Anisotropic Lattice caliburation for improved gauge actions η /s Nakamura and Sakai (2005) Aarts, Allton, Foley, Hands, Kim (2007) Meyer (2007) Luescher-Weiz 2-level 15 /75

Linear Response Theory Zubarev 
 “Non-Equilibrium Statistical Thermo- dynamics” Kubo, Toda and Saito 
 “Statistical Mechanics” 16 /75

: Shear Viscosity : Bulk Viscosity we do not consider this : Heat Conductivity in Quench simulations.

18 /75 Green Functions in the above formula are Retarded, but on Lattice you measure 
 Temperature Green Functions !

Abrikosov-Gorkov-Dzyalosinski- Fradkin Theorem Kernel Z ∞ d ω Green Function G ( t ) = 2 π K ( τ , ω ) ρ ( ω ) 0 Spectral Function On the lattice, we measure Temperature Green function 
 at We must reconstruct Advance or Retarded Green function.

Transport Coefficients of QGP We measure Correlations of Energy-Momentum tensors Convert them (Matsubara Green Functions) to Retarded ones (real time). Transport Coefficients (Shear Viscosity, Bulk Viscosity and Heat Conductivity) 20 /75

Still difficult to determine Spectral Function from Lattice data Ansatz for the Spectral Functions We measure Matsubara Green Function on Lattice (in coordinate space). x ) T µ, ν (0 , ~ h T µ, ν ( t, ~ 0) i = G β ( t, ~ x ) = F.T.G β ( ! n , ~ p ) d ! ⇢ ( ~ p, ! ) Z G β ( ~ p, i ! n ) = i ! n − ! We assume (Karsch-Wyld) and determine three parameters, A, m, γ .

22 /75 Spectral Functions at Market Breit-Wigner We use this Weak coupling Aarts and Resco, JHEP 053,(2002) (hep-ph/ 0203177) Holography Teaney, Phys. Rev. D74 (2006) 045025 (hep- ph0602044) Myers, Starinetsa and Thomsona, JHEP 0711:091,2007(hep-th0706.0162) )

Aarts B.W. Nt=8 23 /75

Lattice and Statistics Iwasaki Improved Action β = 3.05 : 1.3M sweeps 
 β = 3.05 : 3.0M sweeps 
 β =3.20 : 1.2M sweeps 
 β =3.20 : 2.5M sweeps 
 Crazy ! β =3.30 : 1.3M sweeps β =3.30 : 2.0M sweeps β = 3.05 : 0.6M sweeps 
 β = 3.05 : 6.0M sweeps 
 β =3.30 : 0.8M sweeps β =3.30 : 6.0M sweeps Quench

History 1995 1995 1998 SU(3) Improved Action 2005 U(1) 
 SU(2) Coulomb and Two Definitions: Confinement The first F=log U Phases calculation of eta/s F=U-1 on the lattice, which is consistent 
 with KSS bound.

Fluctuations in MC sweeps Standard Ac*on Improved Ac*on 26 /75

Nakamura and Sakai, 2005

Kovtun, Son and Starinets, hep-th/ 0405231 for N=4 supersymmetric Yang-Mills theory in the large N. Policastro, Son and Starinets, Phys. Rev. Lett. 87 (2001) 081601

29 /75 How to reduce Noise ? Improved Actions Multi-hit (Luescher-Weiss) Source method (Parisi) Gradient Flow (Luescher)

lattice raw data beta=6.40,Nt=8, 2,000 conf. fixed smeared length in lattice unit flow-time t/a^2=0.50 flow-time=0 beta=6.72,Nt=12, 650 conf. beta=6.57,Nt=10, 1,100 conf. E.Itou Talk at FEFU C ( ⌧ ) = h 1 x, ⌧ ) 1 X X U 12 ( ~ U 12 ( ~ y, 0) i N 3 N 3 s s ~ ~ x y 0.01 N � =8,flow-time=0.00 N � =8,flow-time=0.50 N � =10,flow-time=0.00 N � =10,flow-time=0.50 N � =12,flow-time=0.00 N � =12,flow-time=0.50 0.01 C( � ) 0.001 C( � ) 0.0001 0.0001 1e-06 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 � /N � � /N �

Magne*c Degrees of Freedom 
 • G.t’Hoo=, Nucl.Phys. B190 (1981) 455 • H Shiba and T Suzuki. Phys. LeT. B (1994) 461 • A. Di Giacomo and G. Paffu*, Phys.Rev.D56,6816 (1997) • Kei-ichi Kondo, Phys.Rev.D58,105019 (1998) • ….. • J. Liao and E. Shuryak, Phys.Rev.LeT.,101, 162302 (2008) • M.N. Chernodub and V.I. Zakharov, Phys. Rev. LeT.98, 082002 (2007) • M.N. Chernodub, A. Nakamura and V.I. Zakharov 
 Phys.Rev.D78:074021,2008 • M.N. Chernodub and V.I. Zakharov, Phys.Atom.Nucl. 72:2136-2145,2009 (arXiv:0806.2874) 31 /75

Who has seen the Mag. Monopole ? N S Neither I nor you 32 /75

Spin System

Singular Configura*on, or Vortex No Monopole ! But it looks like ,,,

Center Projec*on Del Debbio, Faber, Giedt, Greensite, Olejnik Phys.Rev. D58, 1998, 094501 Landau gauge or Coulomb Gauge Gauge Rota*on. Therefore non-local

PlaqueTe pierced by a Vortex A Vortex pierces the PlaqueTe. 1-d Object Wilson Wilson 2-d Object (Charge) Loop Loop (Vortex Line)

Vortex Removing Remember that By defini*on, now All vor*ces are fading out (by defini*on).

38 /75

Improve Ac*on (Symanzik)

40 /75 Finite Density LatticeQCD Brief History 1984 SU(2) 
 A.Nakamura, Phys. Lett. 149B (1984) 391 2001Taylor Expansion 
 QCD-TARO Collaboration: S. Choe, Ph. de Forcrand, M. Garcia Perez, S. Hioki, Y. Liu,H. Matsufuru, O. Miyamura, A. Nakamura, I. -O. Stamatescu, T. Takaishi, T. Umeda,Phys. Rev. D65, 054501 (2002) 2002 Multi-Parameter Reweighting 
 Z. Fodor, S. D. Katz, JHEP 0203 (2002) 014, (hep-lat/0106002). 2002 Multi-Parameter Reweighting+Taylor Expantion 
 C. R. Allton, S. Ejiri, S. J. Hands, O. Kaczmarek, F. Karsch, E. Laermann, Ch. Schmidt, L. Scorzato (Bielefeld-Swansea), Phys. Rev. D66 074507 (2002), (hep-lat/0204010). 2002 Imaginary Chemical Potential 
 M. D’Elia, M. P. Lombardo, Proceedings of the GISELDA Meeting held in Frascati, Italy,14-18 January 2002, hep-lat/0205022. 2002 Imaginary Chemical Potential 
 Ph. de Forcrand, O. Philipsen, Nucl. Phys. B642 290 (2002), hep-lat/0205016.

41 /75 Sign Problem

QCD at finite density

For Real (in general) For Complex Complex Sign Problem 43

In Monte Carlo simulation, configurations are generated according to the Probability: : Complex Monte Carlo Simulations very difficult !

/75 DUO det ∆ e − S G � O � O � = O � DU det ∆ e − S G det ∆ = | det ∆ | e i θ e i θ DUO | det ∆ | e i θ e − S G e i θ DU | det ∆ | e − S G � � O � O � = � O e i θ � � DU | det ∆ | e − S G DU | det ∆ | e i θ e − S G e i θ = � Oe i θ � | det | O � e i θ � | det | e i θ 45

Pion-Condensation Problem Phase Quench = Finite-Isospin � � | det ∆ ( µ ) | 2 e − S G = det ∆ ( µ ) det ∆ ( µ ) ∗ e − S G � det ∆ ( µ ) det ∆ ( − µ ) e − S G = � det ∆ ( µ u ) det ∆ ( µ d ) e − S G = µ u = µ, µ d = − µ µ > m π π π For π + is created π π π 2 by µ π ¯ d π π π u π π π π π

Origin of the Sign Problem Wilson Fermions KS(Staggered) Fermions 47