Past, Present, and Future of the QGP Physics

Transcription

1 Past, Present, and Future of the QGP Physics Masayuki Asakawa Department of Physics, Osaka University November 8, 2018

2 oward Microscopic Understanding In Condensed Matter Physics 1st Macroscopic Properties bulk quantities: heat capacity, heat conductivity, transport coefficients, phase structure 1

3 oward Microscopic Understanding 2nd effective mass Microscopic Properties band structure, gap structure various correlations spectral function 3rd Microscopic Understanding (Normal) Superconductor: BCS theory Fractal Quantum Hall Effect: Laughlin wave function 2

4 In QGP Physics In Condensed Matter Physics 1st Macroscopic Properties bulk quantities: heat capacity, heat conductivity, transport coefficients, phase structure 2nd Microscopic Properties We are HERE effective mass, band structure gap structure various correlations spectral function We are HERE 3rd Microscopic Understanding (Normal) Superconductor: BCS theory Fractal Quantum Hall Effect: Laughlin wave function 3

5 Past and Now of QGP Past weakly interacting soup of quarks and gluons expected from asymptotic freedom of QCD Collins and Perry (1975) Now strongly interacting system of quarks and gluons from small η/s of QGP RHIC experiments 2004~ Why small η/s strongly interacting system? η = 1 3 nvml his is obtained by dilute gas approximation his approximation is not valid for strongly interacting cases 4

6 Qualitative Understanding of Shear Viscosity strongly interacting case y x σ F x shear stress (F x ) = p x that crosses unit surface (σ) per unit time : small 5

7 Qualitative Understanding of Shear Viscosity weakly interacting case y σ x F x more p x crosses unit surface (σ) per unit time : larger stress = larger shear viscosity 6

8 Landau s Insight 7

9 Landau s Insight Strongly interacting system Mean Free Path : so small Quantum mechanically, concept of the number of particles loses its meaning Mean Free Path makes sense only when it is much larger than de Broglie wave length Hydrodynamics 8

10 Future of Hydrodynamics? Although Mean Free Path argument kills a lot of transport models, hydrodynamics is not the end Hydrodynamics should be compared to Jellium Model in condensed matter physics What is the next step? A possible answer: microscopic structure of jellium (or fluid) For example, structure function: Fourier transform of spatial correlation 9 homa, QM2005

11 How can we see interaction on Lattice? In the following, µ B =0 I e 3p 4 = : Interaction Measure or race Anomaly Naïve questions: Isn t there interaction in hadron phase or in the vacuum? Doesn t there exist trace anomaly in the vacuum (strongly interacting!)? 10

12 What is shown by Lattice Calculation On the lattice, vacuum subtraction is carried out Since QCD vacuum is more stable than perturbative vacuum, e 0 p 0 00 = < QCD vacuum ii = > QCD vacuum 0 0 From Lorentz invariance of the vacuum, = eg µν µν QCD vacuum 0 What is plotted as e or p: vacuum subtracted e= ii ii p= = 0 = 0 11

13 Where is interaction? = eg i: not summed µν µν = ii ii = 00 ii + = 0 = 0 s = e + p = Entropy density s is not affected by this subtraction (From Nernst s theorem: s=0 at =0) s has a direct physical meaning: density of degrees of freedom Suppose a sudden phase transition from free massless pion gas to free quark-gluon plasma takes places at c hen how does interaction measure behave? 12

14 hermodynamics p( ) = s() t dt + p 0 e( ) = s( ) p( ) 0 with p 0 =0 (vacuum subtraction) all needed is entropy density (entropy monism) s 3 free QGP 4 ( e 3p) peak structure: change of d.o.f. does not measure interaction free pions c Furthermore, e-3p is increasing if d() is increasing (s()=d() 3 ) c Hatsuda and M.A. (1997) hen, where is interaction? 13

15 Slow Fall-off of Interaction Measure 4 ( e 3p) Sudden Change of d.o.f. Lattice c Since all needed is s(), this can be explained by the behavior of s() s 3 Slow rise of d()=s()/ 3 14

16 race Anomaly race Anomaly (up to fermion contribution) β ( g) = G G 2g µ a µν, a µ µν identity α ~ (360MeV) β ( g ) < 0 0 s a µν, a 4 Gµν G π = a, a G G µν µν decreases around the phase transition β ( g) = 2g G G µ a µν, a µ µν approaches zero (and eventually becomes positive) 15

17 race Anomaly? Although this quantity is also called race Anomaly, this quantity is not trace anomaly without vacuum subtraction What we are seeing is g 2g µ µ µ µ = 0 β ( ) a µν, a a µν, a = G G G G 4 4 µν µν = 0 decreasing >0 his peak is due to disappearance or decrease of race Anomaly It is not appropriate to interpret this peak as appearance of race Anomaly 16

18 Although QGP is strongly interacting, 1 2 In conclusion, we cannot interpret this figure is showing that QGP around c is strongly interacting or anomalous (in the meaning of field theory) 17

19 oward Microscopic Understanding In Condensed Matter Physics 1st Macroscopic Properties bulk quantities: heat capacity, heat conductivity, transport coefficients, phase structure 18

20 QCD Phase Diagram LHC RHIC QGP (quark-gluon plasma) ~160 MeV crossover CP (critical point) 1st order Hadron Phase chiral symmetry breaking confinement order? CSC (color superconductivity) 5-10ρ 0 µ B 19

21 Conserved Charge Fluctuations he original idea of conserved charge fluctuations M.A, Heinz, Müller, Jeon, Koch (2000) Conserved charge fluctuations change only through diffusion hus, in particular, they are not affected by phase transition Quark-Gluon Plasma Hadronization 20

22 ime Evolution of C.C. fluctuation Quark-Gluon Plasma Hadronization Freezeout In the η dependence of C.C. Fluctuation, history of system is encoded 21

23 Critical Phenomena + ime Evolution Experiments cannot observe critical fluctuation in equilibrium directly. Generation + Growth Critical fluctuations tend to develop. But, relaxation toward equilibration is slow around CP because of the critical slowing down. Disappearance by diffusion Fluctuations developed at CP are diffused by the time evolution in later stage. 22

24 Correlation Length of Non-Conserved Quantity ime evolution of correlation length around CP with critical slowing down usual argument ~ distance from CP Berdnikov, Rajagopal (2000) Nonaka, M.A. (2004) K ~ ξ, K ~ ξ, K ~ ξ higher order cumulants are advantageous his ξ is m σ 1, not a conserved quantity (not diffusive mode) Conserved charge cumulants change more slowly In HI collisions, ξ and conserved charge cumulants are not synchronized Furthermore, conserved charge cumulants are scale dependent 23

25 ime Evolution of C.C. fluctuation Conserved charge cumulants are scale dependent Quark-Gluon Plasma Hadronization Freezeout In the η dependence of C.C. Fluctuation, history of system is encoded 24

26 Similarity with Balance Function Information at Larger y = Earlier Stage Local Charge Conservation Diffusion Information at Smaller y = Later Stage Pratt, QM

27 Critical Fluctuation and η Dependence y CP Later Earlier y 26

28 Critical Phenomena and Diffusive Mode Effective Potential Soft mode of QCD CP σ: fast damping cf. Onsager relation δ F δσ δ F δ n ξ σ + ξn Evolution of baryon number density (slow and small k) DY 2 n = Dη n + 2 δ ( ητ, ) ( τ) δ ( ητ, ) ξητ (, ) τ η y ( τ), χ ( τ) ξ( y, τ ) ξ( y, τ ) = 2 χ ( τ ) D ( τ ) δ( y y ) δ( τ τ ) η η 1 η :parameters characterizing criticality D 2 η( τ ) = DC( τ ) τ, χη( τ ) = τχc( τ ) 27

29 Parametrizing D and χ: critical + regular model-h (3d-Ising) mapping to (,µ) / time evolution 1D Bjorken expansion Berdnikov, Rajagopal (2000) Nonaka, M.A. (2004) Stephanov (2011) Mukherjee, Venugopalan, Yin (2015) 0 crossover (r>0) (reduced temperature) critical slowing down χqgp χ hadron = 0.5 QCD CP at =160MeV kinetic f.o. at =100MeV 28

30 Cumulant and Correlation Function total charge charge density 2 nd order cumulant (fluctuation) correlation function 1-to-1 correspondence 1-dim case 29

31 ime Evolution 1, Fluctuation: No CP D C () [fm] χ() χ H [MeV] 30 Sakaida, Fujii, Kitazawa, M.A. (2017)

32 ime Evolution 1, Correlation: No CP D () [fm] C χ() χ H monotonically decreasing [MeV] Analytic result monotonically increasing monotonically increasing 31

33 ime Evolution 2, Fluctuation: With CP D () [fm] C [fm] χ() χ H [MeV] Non-monotonic η dependence manifests itself Robust experimental evidence of the existence of a peak in χ() 32

34 With Narrower Critical Region D C () [fm] χ() χ H non-monotonic behavior Peak in [MeV] 33

35 ime Evolution 2, Correlation: With CP [fm] D C () [fm] χ() χ H non-monotonic y dep. [MeV] Analytic result non-monotonic non-monotonic 34

36 Comparison: Fluctuation and Correlation Non-monotonicity in K( y) disappears But C(y) is still non-monotonic Analytic result C( y) monotonic no information on is better to see non-monotonicity 35

37 Away from CP (Crossover) Signal of the critical enhancement can be clearer along paths away from the CP Away from the CP: Weaker critical slowing down 36

38 Mapping from 3-d Ising to QCD 3d Ising r = c c Hadrons 0 µ 37

39 Away from CP (Crossover) Signal of the critical enhancement can be clearer along paths away from the CP Away from the CP: Weaker critical slowing down 38

40 Blurring: loss of y-η correspondence y: (momentum space) rapidity, η: space-time rapidity y =η in Bjorken picture is blurred in one particle distribution owing to thermal motion Accordingly, conserved charge fluctuation (two particle correlation) is modified time t hadron phase QGP phase position z Blurring in rapidity space takes place! 39

41 Similarity with Balance Function Information at Larger y = Earlier Stage Local Charge Conservation Diffusion Information at Smaller y = Later Stage Pratt, QM

42 Blurring: loss of y-η correspondence y: (momentum space) rapidity, η: space-time rapidity y =η in Bjorken picture is blurred in one particle distribution owing to thermal motion Accordingly, conserved charge fluctuation (two particle correlation) is modified time t hadron phase QGP phase position z Low energy collision (such as BES) y-η relation: more complex his should be taken into account in interpretation Blurring in rapidity space takes place! 41

43 Future 1: from Lattice to Dileptons Nonperturbative calculation of dilepton production 1. Quark dispersion relation on the Lattice Nonperturbative m = 0.768(0.725) at = 1.5 (3 ) c c Kaczmarek et al. (2012) 2 pole fit with widths (Not HL calculation) 42

44 Future 1: from Lattice to Dileptons 2. Ward Identity and Dilepton production rate Π (, q) R, µ µ ω Ward identity Gauge Symmetry production rate dγ α = 4 2 βω Π dωdq 12π Q e 1 ω q R, µ Im µ (, ) 3. Dilepton Yield he result happened to be close to that by HL Vertex correction: important Kim, Kitazawa, M.A. (2015) 43

45 Future 2: Coupling of Heavy Quarks and Matter Lattice Result (J/ψ) Spectral Function at p=0 Shift of peak position? Dispersion Relation for and L modes E( ) (0) p = E + p also at finite? Residue unchanged up to =1.62 c p i 2 π pˆ sin i = aσ Nσ 44 Ikeda, Kitazawa, M.A. (2017)

46 Future 2: Coupling of Heavy Quarks and Matter Coupling of Heavy (anti)quarks with Matter? Note: Debye Screening assumes small eϕ(r) and static matter Stress ensor Distribution around Quark-Antiquark Pair? On Lattice, ranslational Invariance is lost Energy Momentum ensors: Noether Currents of ranslational Symmetry A lot of difficulty met on Lattice: Definition of Energy Momentum ensor on Lattice? Supersymmetry on Lattice? A way to restore ranslational Invariance: Gradient Flow Lüscher (2010) 45

47 Future 2: Coupling of Heavy Quarks and Matter =0 Heavy quark and antiquark Eigenvectors of ij (i,j=1,2,3) and Signs of Eigenvalues One eigenvector: perpendicular to yz-plane Flux ube is visible (U(1) case) Yanagihara et al. (2018) Finite analysis: in progress 46

48 In QGP Physics In Condensed Matter Physics 1st Macroscopic Properties bulk quantities: heat capacity, heat conductivity, transport coefficients, phase structure 2nd Microscopic Properties effective mass, band structure gap structure various correlations spectral function We are HERE correct understanding of data: needed We are HERE 3rd Microscopic Understanding Next Decade(s) (Normal) Superconductor: BCS theory Fractal Quantum Hall Effect: Laughlin wave function 47