Quark Gluon Plasma. Rajiv V. Gavai T. I. F. R., Mumbai. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V.

Quark Gluon Plasma Rajiv V. Gavai T. I. F. R., Mumbai Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 1

Quark Gluon Plasma Rajiv V. Gavai T. I. F. R., Mumbai Introduction QGP in Bulk J/ψ suppression Jet Quenching QCD Phase Diagram Summary Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 1

Introduction Measurement Fit O meas O fit /σ meas 0 1 2 3 α (5) had (m Z ) 0.02758 ± 0.00035 0.02766 m Z [GeV] 91.1875 ± 0.0021 91.1874 Γ Z [GeV] 2.4952 ± 0.0023 2.4957 σ 0 had [nb] 41.540 ± 0.037 41.477 R l 20.767 ± 0.025 20.744 A 0,l fb 0.01714 ± 0.00095 0.01640 A l (P τ ) 0.1465 ± 0.0032 0.1479 R b 0.21629 ± 0.00066 0.21585 R c 0.1721 ± 0.0030 0.1722 A 0,b fb 0.0992 ± 0.0016 0.1037 A 0,c fb 0.0707 ± 0.0035 0.0741 A b 0.923 ± 0.020 0.935 A c 0.670 ± 0.027 0.668 A l (SLD) 0.1513 ± 0.0021 0.1479 sin 2 θ lept eff (Q fb ) 0.2324 ± 0.0012 0.2314 m W [GeV] 80.392 ± 0.029 80.371 Γ W [GeV] 2.147 ± 0.060 2.091 m t [GeV] 171.4 ± 2.1 171.7 0 1 2 3 Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 2

Measurement Fit O meas O fit /σ meas 0 1 2 3 α (5) had (m Z ) 0.02758 ± 0.00035 0.02766 m Z [GeV] 91.1875 ± 0.0021 91.1874 Γ Z [GeV] 2.4952 ± 0.0023 2.4957 σ 0 had [nb] 41.540 ± 0.037 41.477 R l 20.767 ± 0.025 20.744 A 0,l fb 0.01714 ± 0.00095 0.01640 A l (P τ ) 0.1465 ± 0.0032 0.1479 R b 0.21629 ± 0.00066 0.21585 R c 0.1721 ± 0.0030 0.1722 A 0,b fb 0.0992 ± 0.0016 0.1037 A 0,c fb 0.0707 ± 0.0035 0.0741 A b 0.923 ± 0.020 0.935 A c 0.670 ± 0.027 0.668 A l (SLD) 0.1513 ± 0.0021 0.1479 sin 2 θ lept eff (Q fb ) 0.2324 ± 0.0012 0.2314 m W [GeV] 80.392 ± 0.029 80.371 Γ W [GeV] 2.147 ± 0.060 2.091 m t [GeV] 171.4 ± 2.1 171.7 0 1 2 3 Introduction Precision tests from LEP Standard Model Very Successful! All tests based on perturbation theory Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 2

Measurement Fit O meas O fit /σ meas 0 1 2 3 α (5) had (m Z ) 0.02758 ± 0.00035 0.02766 m Z [GeV] 91.1875 ± 0.0021 91.1874 Γ Z [GeV] 2.4952 ± 0.0023 2.4957 σ 0 had [nb] 41.540 ± 0.037 41.477 R l 20.767 ± 0.025 20.744 A 0,l fb 0.01714 ± 0.00095 0.01640 A l (P τ ) 0.1465 ± 0.0032 0.1479 R b 0.21629 ± 0.00066 0.21585 R c 0.1721 ± 0.0030 0.1722 A 0,b fb 0.0992 ± 0.0016 0.1037 A 0,c fb 0.0707 ± 0.0035 0.0741 A b 0.923 ± 0.020 0.935 A c 0.670 ± 0.027 0.668 A l (SLD) 0.1513 ± 0.0021 0.1479 sin 2 θ lept eff (Q fb ) 0.2324 ± 0.0012 0.2314 m W [GeV] 80.392 ± 0.029 80.371 Γ W [GeV] 2.147 ± 0.060 2.091 m t [GeV] 171.4 ± 2.1 171.7 0 1 2 3 Introduction Precision tests from LEP Standard Model Very Successful! All tests based on perturbation theory Need to understand non-perturbative QCD, e.g., to explain baryonic mass in our Universe, i.e., us. Also, total cross sections, matrix elements, structure functions... Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 2

Measurement Fit O meas O fit /σ meas 0 1 2 3 α (5) had (m Z ) 0.02758 ± 0.00035 0.02766 m Z [GeV] 91.1875 ± 0.0021 91.1874 Γ Z [GeV] 2.4952 ± 0.0023 2.4957 σ 0 had [nb] 41.540 ± 0.037 41.477 R l 20.767 ± 0.025 20.744 A 0,l fb 0.01714 ± 0.00095 0.01640 A l (P τ ) 0.1465 ± 0.0032 0.1479 R b 0.21629 ± 0.00066 0.21585 R c 0.1721 ± 0.0030 0.1722 A 0,b fb 0.0992 ± 0.0016 0.1037 A 0,c fb 0.0707 ± 0.0035 0.0741 A b 0.923 ± 0.020 0.935 A c 0.670 ± 0.027 0.668 A l (SLD) 0.1513 ± 0.0021 0.1479 sin 2 θ lept eff (Q fb ) 0.2324 ± 0.0012 0.2314 m W [GeV] 80.392 ± 0.029 80.371 Γ W [GeV] 2.147 ± 0.060 2.091 m t [GeV] 171.4 ± 2.1 171.7 0 1 2 3 Introduction Precision tests from LEP Standard Model Very Successful! All tests based on perturbation theory Need to understand non-perturbative QCD, e.g., to explain baryonic mass in our Universe, i.e., us. Also, total cross sections, matrix elements, structure functions... Lattice QCD only well-understood, viable tool for this: Iconic Results - Wilczek. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 2

Measurement Fit O meas O fit /σ meas 0 1 2 3 α (5) had (m Z ) 0.02758 ± 0.00035 0.02766 m Z [GeV] 91.1875 ± 0.0021 91.1874 Γ Z [GeV] 2.4952 ± 0.0023 2.4957 σ 0 had [nb] 41.540 ± 0.037 41.477 R l 20.767 ± 0.025 20.744 A 0,l fb 0.01714 ± 0.00095 0.01640 A l (P τ ) 0.1465 ± 0.0032 0.1479 R b 0.21629 ± 0.00066 0.21585 R c 0.1721 ± 0.0030 0.1722 A 0,b fb 0.0992 ± 0.0016 0.1037 A 0,c fb 0.0707 ± 0.0035 0.0741 A b 0.923 ± 0.020 0.935 A c 0.670 ± 0.027 0.668 A l (SLD) 0.1513 ± 0.0021 0.1479 sin 2 θ lept eff (Q fb ) 0.2324 ± 0.0012 0.2314 m W [GeV] 80.392 ± 0.029 80.371 Γ W [GeV] 2.147 ± 0.060 2.091 m t [GeV] 171.4 ± 2.1 171.7 Introduction Precision tests from LEP Standard Model Very Successful! All tests based on perturbation theory Need to understand non-perturbative QCD, e.g., to explain baryonic mass in our Universe, i.e., us. Also, total cross sections, matrix elements, structure functions... Lattice QCD only well-understood, viable tool for this: Iconic Results - Wilczek. 0 1 2 3 It predicts a transition to Quark-Gluon Plasma (QGP), and QGP properties. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 2

Quest for Quark-Gluon Plasma : Heavy Ion Collisions at SPS, RHIC and LHC. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 3

Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 4

Another fundamental aspect Critical Point in T -µ B plane; based on symmetries and models. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 5

Another fundamental aspect Critical Point in T -µ B plane; based on symmetries and models. Expected QCD Phase Diagram Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 5

Another fundamental aspect Critical Point in T -µ B plane; based on symmetries and models. Expected QCD Phase Diagram... but could, however, be... Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 5

Another fundamental aspect Critical Point in T -µ B plane; based on symmetries and models. Expected QCD Phase Diagram... but could, however, be... Τ Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 5

Transition temperature, Critical energy density, Order of Phase Transition? What are the properties of QGP (EoS, Excitations, Screening..)? Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 6

Transition temperature, Critical energy density, Order of Phase Transition? What are the properties of QGP (EoS, Excitations, Screening..)? Need N s N t for thermodynamic limit and large N t for continuum limit. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 6

Transition temperature, Critical energy density, Order of Phase Transition? What are the properties of QGP (EoS, Excitations, Screening..)? Need N s N t for thermodynamic limit and large N t for continuum limit. Completely parameter-free : Λ QCD and quark masses from hadron spectrum. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 6

The Transition Temperature T c 170 MeV (Bielefeld & CP-PACS, Tsukuba 2001) and Equation of State (EOS), have been predicted by lattice QCD. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 7

The Transition Temperature T c 170 MeV (Bielefeld & CP-PACS, Tsukuba 2001) and Equation of State (EOS), have been predicted by lattice QCD. OLD results on order parameters & EoS from Bielefeld 2001 (Coarse N t =4 lattices). Other quantities, notably strangeness enhancement in Heavy Ion Physics, the Wróblewski Parameter λ s (RVG & Sourendu Gupta PR D 2002) have also been predicted by lattice QCD. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 7

Thrust of new results now on continuum limit, lighter quarks, 2+1 flavours transition temperature T c = 192(7)(4)MeV (Bielefeld-RBC hep-lat/0608013). = A gap between freeze-out and transition temperatures? more complex observables, speed of sound, transport coefficients, Fluctuations, J/ψ-dissolution/persistence, dileptons... etc. and T -µ phase diagram. An interesting theoretical issue Conformal Invariance and AdS/CFT predictions. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 8

Thrust of new results now on continuum limit, lighter quarks, 2+1 flavours transition temperature T c = 192(7)(4)MeV (Bielefeld-RBC hep-lat/0608013). = A gap between freeze-out and transition temperatures? more complex observables, speed of sound, transport coefficients, Fluctuations, J/ψ-dissolution/persistence, dileptons... etc. and T -µ phase diagram. An interesting theoretical issue Conformal Invariance and AdS/CFT predictions. Lot of activity in Model Building to explain Lattice QCD results: Quasi-particle models, Hadron Resonance Gas, Quarkonia from Lattice Q Q potential, sqgp and coloured states... Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 8

QGP in Bulk : EoS, Speed of Sound... Recent results for EoS : N t =6, Smaller quark masses. Bernard et al., MILC hep-lat/0509053; Aoki et al., hep-lat/0510084. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 9

Small differences; ɛ(t c ) 6Tc 4 still. Too small volumes = Thermodynamic Limit? Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 10

Small differences; ɛ(t c ) 6Tc 4 still. Too small volumes = Thermodynamic Limit? C s Crucial for elliptic flow, hydrodynamical studies... C v Event-by-event temperature/p T fluctuations. Can be obtained from ln Z by taking appropriate derivatives which relate it to the temperature derivative of anomaly measure /ɛ. (RVG, S. Gupta and S. Mukherjee, PR D71 (2005) ) New method to obtain these differentially without getting negative pressure. Introduced an improved operator than used in earlier Bielefeld studies. (RVG, S. Gupta and S. Mukherjee, hep-lat/0506015) Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 10

Small differences; ɛ(t c ) 6Tc 4 still. Too small volumes = Thermodynamic Limit? C s Crucial for elliptic flow, hydrodynamical studies... C v Event-by-event temperature/p T fluctuations. Can be obtained from ln Z by taking appropriate derivatives which relate it to the temperature derivative of anomaly measure /ɛ. (RVG, S. Gupta and S. Mukherjee, PR D71 (2005) ) New method to obtain these differentially without getting negative pressure. Introduced an improved operator than used in earlier Bielefeld studies. (RVG, S. Gupta and S. Mukherjee, hep-lat/0506015) Using lattices with 8, 10, and 12 temporal sites (38 3 12 and 38 4 lattices) and with statistics of 0.5-1 million iterations, ɛ, P, s, C 2 s and C v obtained in continuum. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 10

30 0.4 25 20 Ideal Gas 0.35 0.3 0.25 Ideal Gas C v /T 3 15 C s 2 0.2 10 5 ( f ) 0.15 0.1 0.05 ( e ) 0 1 1.5 2 2.5 3 3.5 T/T c 0 1 1.5 2 2.5 3 3.5 T/T c (RVG, S. Gupta and S. Mukherjee, hep-lat/0506015) Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 11

30 0.4 25 20 Ideal Gas 0.35 0.3 0.25 Ideal Gas C v /T 3 15 C s 2 0.2 10 5 ( f ) 0.15 0.1 0.05 ( e ) 0 1 1.5 2 2.5 3 3.5 T/T c 0 1 1.5 2 2.5 3 3.5 T/T c (RVG, S. Gupta and S. Mukherjee, hep-lat/0506015) C v 4ɛ for 2T c but No Ideal Gas limit. Specific heat fluctuations in p T? Cs 2 closer to Ideal Gas limit; Any structure near T c?? Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 11

Entropy agrees with strong coupling SYM prediction (Gubser, Klebanov & Tseytlin, NPB 98, 202) for T = 2 3T c but fails at lower T, as do various weak coupling schemes : s s 0 = f(g 2 N c ), where f(x) = 3 4 + 45 32 ζ(3)x 3/2 + and s 0 = 2 3 π2 Nc 2 T 3. 1 3T c 2T c 1.5T c 1.25T c ( b ) AdS/CFT (s/s 0 )-(3/4) 0.1 0.01 0.001 5 6 7 g 2 N 8 9 10 c Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 12

Entropy agrees with strong coupling SYM prediction (Gubser, Klebanov & Tseytlin, NPB 98, 202) for T = 2 3T c but fails at lower T, as do various weak coupling schemes : s s 0 = f(g 2 N c ), where f(x) = 3 4 + 45 32 ζ(3)x 3/2 + and s 0 = 2 3 π2 Nc 2 T 3. 1 ( b ) 3T c 2T c 1.5T c AdS/CFT 1.25T c 2 1.5 Ideal gas (s/s 0 )-(3/4) 0.1 0.01 P/T 4 1 0.5 Conformal 0.001 5 6 7 g 2 N 8 9 10 c 0 0 1 2 3 4 5 6 ε/t 4 Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 12

Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 13

Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 14

QGP - (Almost) Perfect Liquid v 2 (p T ) 0.2 0.18 0.16 0.14 0.12 b 6.8 fm (16-24% Central) STAR Data Γ s /τ o = 0 0.1 0.08 0.06 0.04 0.02 Γ s /τ o = 0.1 Γ s /τ o = 0.2 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 p T (GeV) Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 15

QGP - (Almost) Perfect Liquid v 2 (p T ) 0.2 0.18 b 6.8 fm (16-24% Central) Elliptic flow consistent with Ideal Hydrodynamics bound on Shear viscosity. (D. Teaney, nucl-th/03010099; PRC 2003) 0.16 0.14 0.12 STAR Data Γ s /τ o = 0 0.1 0.08 Γ s /τ o = 0.1 0.06 0.04 Γ s /τ o = 0.2 0.02 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 p T (GeV) Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 15

QGP - (Almost) Perfect Liquid v 2 (p T ) 0.2 0.18 0.16 0.14 0.12 0.1 0.08 b 6.8 fm (16-24% Central) STAR Data Γ s /τ o = 0 Γ s /τ o = 0.1 Elliptic flow consistent with Ideal Hydrodynamics bound on Shear viscosity. (D. Teaney, nucl-th/03010099; PRC 2003) 4 3 Γ s = η st, (1) where η is Shear Viscosity and s is entropy density; τ = t 2 z 2 is the time scale of expansion. 0.06 0.04 Γ s /τ o = 0.2 0.02 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 p T (GeV) Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 15

QGP - (Almost) Perfect Liquid v 2 (p T ) 0.2 0.18 0.16 0.14 0.12 0.1 0.08 b 6.8 fm (16-24% Central) STAR Data Γ s /τ o = 0 Γ s /τ o = 0.1 Elliptic flow consistent with Ideal Hydrodynamics bound on Shear viscosity. (D. Teaney, nucl-th/03010099; PRC 2003) 4 3 Γ s = η st, (1) where η is Shear Viscosity and s is entropy density; τ = t 2 z 2 is the time scale of expansion. 0.06 0.04 0.02 Γ s /τ o = 0.2 Perturbation theory Large η/s Small η/s Strongly Coupled Liquid. 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 p T (GeV) Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 15

2.0 1.5 1.0 0.5 0.0 η s 16 3 8 24 3 8 Perturbative Theory KSS bound -0.5 1 1.5 2 2.5 3 Nakamura and Sakai, PRL 94 (2005). T Tc Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 16

2.0 1.5 η s 16 3 8 24 3 8 Kubo s Linear Response Theory : Transport Coefficients in terms of equilibrium correlation functions. 1.0 Perturbative Theory 0.5 KSS bound 0.0-0.5 1 1.5 2 2.5 3 Nakamura and Sakai, PRL 94 (2005). T Tc Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 16

2.0 1.5 1.0 0.5 η s 16 3 8 24 3 8 Perturbative Theory KSS bound Kubo s Linear Response Theory : Transport Coefficients in terms of equilibrium correlation functions. Obtain Energy-Momentum Correlation functions on Lattice (at discrete Matsubara frequencies). 0.0-0.5 1 1.5 2 2.5 3 T Tc Continue them to get Retarded ones Shear, Bulk Viscosities. Nakamura and Sakai, PRL 94 (2005). Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 16

2.0 1.5 1.0 0.5 η s 16 3 8 24 3 8 Perturbative Theory KSS bound Kubo s Linear Response Theory : Transport Coefficients in terms of equilibrium correlation functions. Obtain Energy-Momentum Correlation functions on Lattice (at discrete Matsubara frequencies). 0.0-0.5 1 1.5 2 2.5 3 Nakamura and Sakai, PRL 94 (2005). T Tc Continue them to get Retarded ones Shear, Bulk Viscosities. Larger lattices and inclusion of dynamical quarks in future. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 16

Wróblewski Parameter Measure of Strangeness produced. Quark number susceptibilities, χ ij ln Z/ µ i µ j, can provide a handle; QNS also useful theoretical check on models. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 17

Wróblewski Parameter Measure of Strangeness produced. Quark number susceptibilities, χ ij ln Z/ µ i µ j, can provide a handle; QNS also useful theoretical check on models. Fluctuation-Dissipation Theorem Production of Strange quark-antiquark pair imaginary part of generalized strange quark susceptibility. Kramers - Krönig relation can be used to relate it to the real part of the susceptibility, which we obtain from lattice QCD simulations. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 17

Wróblewski Parameter Measure of Strangeness produced. Quark number susceptibilities, χ ij ln Z/ µ i µ j, can provide a handle; QNS also useful theoretical check on models. Fluctuation-Dissipation Theorem Production of Strange quark-antiquark pair imaginary part of generalized strange quark susceptibility. Kramers - Krönig relation can be used to relate it to the real part of the susceptibility, which we obtain from lattice QCD simulations. Finally, make a relaxation time approximation (ωτ 1) ratio of real parts is the same as the ratio of imaginary parts. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 17

We use m/t c = 0.03 for u, d and m/t c = 1 for s quark; At each T, ratio of χ s and χ ud λ s (T ). Extrapolate it to T c. (RVG & Sourendu Gupta, PRD 2002, PRD 2003 and PRD 2006) Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 18

We use m/t c = 0.03 for u, d and m/t c = 1 for s quark; At each T, ratio of χ s and χ ud λ s (T ). Extrapolate it to T c. (RVG & Sourendu Gupta, PRD 2002, PRD 2003 and PRD 2006) AGS Si-Au Quenched QCD (T ) c RHIC Au-Au SpS S-S SpS S-Ag SpS Pb-Pb AGS Au-Au 0.2 0.4 0.6 0.8 1 λs Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 18

We use m/t c = 0.03 for u, d and m/t c = 1 for s quark; At each T, ratio of χ s and χ ud λ s (T ). Extrapolate it to T c. (RVG & Sourendu Gupta, PRD 2002, PRD 2003 and PRD 2006) Quenched QCD (T ) c 1 RHIC Au-Au 0.8 SpS S-S SpS S-Ag 0.6 SpS Pb-Pb AGS Au-Au λ s 0.4 Nt = 4 Nf = 2 QCD AGS Si-Au 0.2 0.2 0.4 0.6 0.8 1 λs 0 0 0.5 1 1.5 2 2.5 3 T/Tc Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 18

Baryon-Strangeness Correlation Correlation between quantum numbers K and L can be studied through the ratio C (KL)/L = KL K L. L 2 L 2 These are robust : theoretically & experimentally. Baryon Number(Charge) Strangeness correlation : C (BS)/S (C (QS)/S ) (Koch, Majumdar and Randurp, PRL 95 (2005); RVG & Sourendu Gupta, PR D 2006; S. Mukherjee, hep-lat/0606018); u-d Correlation. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 19

Baryon-Strangeness Correlation Correlation between quantum numbers K and L can be studied through the ratio C (KL)/L = KL K L. L 2 L 2 These are robust : theoretically & experimentally. Baryon Number(Charge) Strangeness correlation : C (BS)/S (C (QS)/S ) (Koch, Majumdar and Randurp, PRL 95 (2005); RVG & Sourendu Gupta, PR D 2006; S. Mukherjee, hep-lat/0606018); u-d Correlation. 1.5 1.25 X=Q 1 XS C 0.75 0.5 0.25 X=B 0 0.5 1 1.5 2 2.5 T/Tc Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 19

Baryon-Strangeness Correlation Correlation between quantum numbers K and L can be studied through the ratio C (KL)/L = KL K L. L 2 L 2 These are robust : theoretically & experimentally. Baryon Number(Charge) Strangeness correlation : C (BS)/S (C (QS)/S ) (Koch, Majumdar and Randurp, PRL 95 (2005); RVG & Sourendu Gupta, PR D 2006; S. Mukherjee, hep-lat/0606018); u-d Correlation. XS C 1.5 1.25 1 0.75 0.5 0.25 X=Q X=B C (ud)/u 1 0.8 0.6 0.4 0.2 0 0.5 1 1.5 2 2.5 T/Tc 0 0.5 1 1.5 2 2.5 T/Tc Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 19

Anomalous J/ψ Suppression : CERN NA50 results Matsui-Satz idea J/ψ suppression as a signal of QGP. Deconfinement Screening of coloured quarks, which cannot bind. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 20

Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 21

J/ψ Suppression Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 22

J/ψ Suppression or Not? Original Matsui-Satz idea Based on Quarkonium potential model calculations and an Ansatz for temperature dependence dissolution of J/ψ and χ c by 1.1T c. Impressive NA50 results from CERN and now PHENIX at RHIC. A critical assessment of the original theoretical argument: Made feasible by the recognition of MEM technique as a tool to extract spectral functions from the temporal correlators computed on the Euclidean lattice. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 22

J/ψ Suppression or Not? Original Matsui-Satz idea Based on Quarkonium potential model calculations and an Ansatz for temperature dependence dissolution of J/ψ and χ c by 1.1T c. Impressive NA50 results from CERN and now PHENIX at RHIC. A critical assessment of the original theoretical argument: Made feasible by the recognition of MEM technique as a tool to extract spectral functions from the temporal correlators computed on the Euclidean lattice. Caution : nonzero temperature obtained by making temporal lattices shorter : 48 3 12 to 64 3 24 Lattices used. (S. Datta et al., Phys. Rev. D 69, 094507 (2004).) Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 22

0.16 η c J/ψ 0.1 0.75T c 1.1T c 1.5T c 0.12 χ c0 χ c1 ρ(ω) 0.08 ρ(ω) 0.05 0.04 0.9T c 1.5T c 2.25T c 3T c 0 0 2 4 6 2 4 6 ω[gev] 0 1 3 5 1 3 5 ω[gev] χ c seems to indeed dissolve by 1.1T c, however, J/ψ and η c persist up to 2.25 T c and are gone at 3T c ; Similar results by Asakawa-Hatsuda and Matsufuru. Since about 30-40 % observed J/ψ come through χ and ψ decays, expect changes of suppression patterns as a function of T or s. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 23

0.16 η c J/ψ 0.1 0.75T c 1.1T c 1.5T c 0.12 χ c0 χ c1 ρ(ω) 0.08 ρ(ω) 0.05 0.04 0.9T c 1.5T c 2.25T c 3T c 0 0 2 4 6 2 4 6 ω[gev] 0 1 3 5 1 3 5 ω[gev] χ c seems to indeed dissolve by 1.1T c, however, J/ψ and η c persist up to 2.25 T c and are gone at 3T c ; Similar results by Asakawa-Hatsuda and Matsufuru. Since about 30-40 % observed J/ψ come through χ and ψ decays, expect changes of suppression patterns as a function of T or s. No Significant Effect of inclusion of dynamical fermions? Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 23

Jet Quenching Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 24

Jet Quenching Rare, Highly Energetic Scatterings produce jets of particles : g + g g + g. Quark-Gluon Plasma, any medium in general, interacts with a jet, causing it to lose energy Jet Quenching. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 24

On-Off test possible Compare Collisions of Heavy-Heavy nuclei with Light-Heavy or Light-Light. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 25

Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 26

QCD Phase Diagram Expected QCD Phase Diagram and Lattice Approaches to unravel it. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 27

QCD Phase Diagram Expected QCD Phase Diagram and Lattice Approaches to unravel it. Lee-Yang Zeroes and Two parameter Re-weighting (Z. Fodor & S. Katz, JHEP 0203 (2002) 014 ). Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 27

QCD Phase Diagram Expected QCD Phase Diagram and Lattice Approaches to unravel it. Lee-Yang Zeroes and Two parameter Re-weighting (Z. Fodor & S. Katz, JHEP 0203 (2002) 014 ). Imaginary Chemical Potential (Ph. Forcrand & O. Philipsen, NP B642 (2002) 290; M.-P. Lombardo & M. D Elia PR D67 (2003) 014505 ). de Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 27

QCD Phase Diagram Expected QCD Phase Diagram and Lattice Approaches to unravel it. Lee-Yang Zeroes and Two parameter Re-weighting (Z. Fodor & S. Katz, JHEP 0203 (2002) 014 ). Imaginary Chemical Potential (Ph. Forcrand & O. Philipsen, NP B642 (2002) 290; M.-P. Lombardo & M. D Elia PR D67 (2003) 014505 ). de Taylor Expansion (C. Allton et al., PR D66 (2002) 074507 & D68 (2003) 014507; R.V. Gavai and S. Gupta, PR D68 (2003) 034506 ). Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 27

Critical Point Estimate 5 4 3 B /T µ 2 1 RVG & S. Gupta, PR D 71 2005. /T B µ 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 n 0 1 2 3 4 5 6 7 n Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 28

Critical Point Estimate 5 4 3 B /T µ 2 1 RVG & S. Gupta, PR D 71 2005. /T B µ 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 n 0 1 2 3 4 5 6 7 n Radii of convergence as a function of the order of expansion at T = 0.95T c on N s = 8 (circles) and 24 (boxes). Left panel for ρ n and right one for r n. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 28

Critical Point Estimate 5 4 3 B /T µ 2 1 RVG & S. Gupta, PR D 71 2005. /T B µ 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 n 0 1 2 3 4 5 6 7 n Radii of convergence as a function of the order of expansion at T = 0.95T c on N s = 8 (circles) and 24 (boxes). Left panel for ρ n and right one for r n. Extrapolation in n µ E /T E = 1.1 ± 0.2 at T E = 0.95T c. Finite volume shift consistent with Ising Universality class. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 28

Summary Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 29

Lattice QCD predicts transition to Quark-Gluon Plasma and several of its properties, T c, EoS, λ s, η... RHIC data exhibits tell-tale signs of QGP : Flow, Jet Quenching, J/ψ... BUT agreement with theory still not very quantitative, e.g., v 2. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 30

Lattice QCD predicts transition to Quark-Gluon Plasma and several of its properties, T c, EoS, λ s, η... RHIC data exhibits tell-tale signs of QGP : Flow, Jet Quenching, J/ψ... BUT agreement with theory still not very quantitative, e.g., v 2. Our results on correlations of quantum numbers suggest quark-like excitations in QGP. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 30

Lattice QCD predicts transition to Quark-Gluon Plasma and several of its properties, T c, EoS, λ s, η... RHIC data exhibits tell-tale signs of QGP : Flow, Jet Quenching, J/ψ... BUT agreement with theory still not very quantitative, e.g., v 2. Our results on correlations of quantum numbers suggest quark-like excitations in QGP. Phase diagram in T µ B plane has begun to emerge: Our estimate for the critical point is µ B /T 1 2. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 30

Lattice QCD predicts transition to Quark-Gluon Plasma and several of its properties, T c, EoS, λ s, η... 1.1 RHIC data exhibits tell-tale signs of QGP : Flow, Jet Quenching, J/ψ... BUT agreement with theory still not very quantitative, e.g., v 2. T/Tc 1 0.9 30 GeV 20 GeV 18 GeV (CERN) 10 GeV Our results on correlations of quantum numbers suggest quark-like excitations in QGP. Phase diagram in T µ B plane has begun to emerge: Our estimate for the critical point is µ B /T 1 2. 0.8 Freezeout curve 0.7 0 1 2 3 4 5 µ B /T Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 30

1.0 NL 0.9 HTL χ 3 /Τ 2 0.8 0.7 0.6 1 2 3 T/T c Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 31

Quarkonia moving in the Heat Bath Should see more energetic gluons. More Dissociation at the same T as momentum of J/ψ increases? Datta et al. SEWM 2004, PANIC 2005. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 32

Quarkonia moving in the Heat Bath Should see more energetic gluons. More Dissociation at the same T as momentum of J/ψ increases? Datta et al. SEWM 2004, PANIC 2005. 0.2 0.15 ρ(ω) η c 0.2 0.15 ρ(ω) J/ψ T 0 0.64 1.28 1.92 p[gev] 0.1 0.05 0 0.75T c 1.1T c 0 0.64 1.28 1.92 p [GeV] 1 3 5 1 3 5 ω[gev] 0.1 0.05 0 0.75T c 1.1T c 1 3 5 1 3 5 ω[gev] Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 32

Quarkonia moving in the Heat Bath Should see more energetic gluons. More Dissociation at the same T as momentum of J/ψ increases? Datta et al. SEWM 2004, PANIC 2005. 0.2 0.15 ρ(ω) η c 0.2 0.15 ρ(ω) J/ψ T 0 0.64 1.28 1.92 p[gev] 0.1 0.05 0 0.75T c 1.1T c 0 0.64 1.28 1.92 p [GeV] 1 3 5 1 3 5 ω[gev] 0.1 0.05 0 0.75T c 1.1T c 1 3 5 1 3 5 ω[gev] Both J/ψ and η c do show this trend. The effect is significant at both 0.75 and 1.1T c. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 32

m ρ /T c m π /m ρ m N /m ρ N s m π flavours T E /T c µ E B /T E 5.372 (5) 0.185 (2) 1.9 3.0 2+1 0.99 (2) 2.2 (2) 5.12 (8) 0.307 (6) 3.1 3.9 2+1 0.93 (3) 4.5 (2) 5.4 (2) 0.31 (1) 1.8 (2) 3.3 10.0 2 0.95 (2) 1.1 (2) 5.4 (2) 0.31 (1) 1.8 (2) 3.3 2 5.5 (1) 0.70 (1) 15.4 2 Table 1: Summary of critical end point estimates the lattice spacing is a = 1/4T. N s is the spatial size of the lattice and N s m π is the size in units of the pion Compton wavelength, evaluated for T = µ = 0. The ratio m π /m K sets the scale of the strange quark mass. Results are sequentially from Fodor-Katz 04, Fodor-Katz 02, Gavai-Gupta, de Forcrand- Philipsen and Bielefeld-Swansea. Workshop on LHC Physics 2006, T. I. F. R., Mumbai, September 7, 2006 R. V. Gavai Top 33