Heavy quark bindings at high temperature

Transcription

1 Universität Bielefeld Olaf Kaczmarek Felix Zantow Matthias Döring Kay Hübner Frithjof Karsch RBC-Bielefeld Sourendu Gupta February 9, 27 apenext workshop, Firenze, February 9, 27 p.1/25

2 Machines for lattice QCD - used by RBC-Bielefeld apenext QCDOC APEmille Installation in Bielefeld 1999/ Gflops APEmille (2 crates) 25/26 5 Tflops apenext (6 racks) apenext workshop, Firenze, February 9, 27 p.2/25

3 Motivation - Heavy quark bound states above deconfinement Quarkonium suppression as a probe for thermal properties of hot and dense matter [Matsui and Satz] - heavy quark potential gets screened - screening radius related to parton density r D 1 g n/t - at high T screening radius smaller than size of a quarkonium state Typical length scales of heavy quark bound states: 1/Λ QCD 1 fm - screening has to be strong enough to modify short distance behaviour - detailed analysis of heavy quark potentials - temperature and r dependence - screening properties above deconfinement - What is the correct effective potential at finite temperature? F 1 (r,t) = U 1 (r,t) T S 1 (r,t) apenext workshop, Firenze, February 9, 27 p.3/25

4 Heavy quark bound states above deconfinement Strong interactions in the deconfined phase T> T c Possibility of heavy quark bound states? Charmonium (χ c,j/ψ) as thermometer above T c Suppression patterns of charmonium/bottomonium = Potential models heavy quark potential (T =) V 1 (r) = 4 3 α(r) r + σ r heavy quark free energies (T > T c ) F 1 (r,t) 4 3 α(r,t) r e m(t)r heavy quark internal energies (T ) F 1 (r,t) = U 1 (r,t) T S 1 (r,t) = Charmonium correlation functions/spectral functions apenext workshop, Firenze, February 9, 27 p.4/25

5 The lattice set-up Polyakov loop correlation function and free energy: L. McLerran, B. Svetitsky (1981) Z Q Q Z (T) 1 Z (T) Z D A... L(x) L (y) exp ( Z 1/T Z dt ) d 3 xl [A,...] F Q Q (r,t) T Q Q = 1, 8, av Lattice data used in our analysis: N f = : ,8,16-lattices ( Symanzik ) HB-OR O. Kaczmarek, F. Karsch, P. Petreczky, F. Zantow (22, 24) N f = 2: lattices ( Symanzik, p4-stagg. ) hybrid-r m π /m ρ.7 (m/t =.4) O. Kaczmarek, F. Zantow (25), O. Kaczmarek et al. (23) N f = 3: lattices ( stagg., Asqtad ) hybrid-r m π /m ρ.4 P. Petreczky, K. Petrov (24) N f = 2+1: lattices ( Symanzik, p4fat3 ) RHMC m π 22 MeV, phys. m s OK, RBC-Bielefeld preliminary apenext workshop, Firenze, February 9, 27 p.5/25

6 The lattice set-up Polyakov loop correlation function and free energy: L. McLerran, B. Svetitsky (1981) Z Q Q Z (T) 1 Z (T) Z D A... L(x) L (y) exp ( Z 1/T Z dt ) d 3 xl [A,...] F Q Q (r,t) T Q Q = 1, 8, av a 1/3 V =N σ a ln 1/T =N τ a O. Philipsen (22) O. Jahn, O. Philipsen (24) ( ln TrL(x) TrL ) (y) ( ln TrL(x)L ) (y) ( 9 8 TrL(x) TrL (y) 1 8 TrL(x)L (y) GF GF ) = F qq(r,t) T = F 1(r,T) T = F 8(r,T) T apenext workshop, Firenze, February 9, 27 p.5/25

7 Heavy quark free energy F 1 [MeV] (a) r [fm].81t c.9t c.96t c 1.2T c 1.7T c 1.23T c 1.5T c 1.98T c 4.1T c Renormalization of F(r, T) by matching with T = potential e F 1(r,T)/T = ( Z r (g 2 ) ) 2N τ Tr (L x L y) apenext workshop, Firenze, February 9, 27 p.6/25

8 Heavy quark free energy F 1 [MeV] (a) r [fm].81t c.9t c.96t c 1.2T c 1.7T c 1.23T c 1.5T c 1.98T c 4.1T c F 1 [MeV] Renormalization of F(r, T) by matching with T = potential e F 1(r,T)/T = ( Z r (g 2 ) ) 2N τ Tr (L x L y) T -independent r 1/ σ F(r,T) g 2 (r)/r -2 r [fm] apenext workshop, Firenze, February 9, 27 p.6/25

9 Heavy quark free energy 1 F 1 [MeV] (a) String breaking T < T c F(r σ 1,T) < 5-5 r [fm].81t c.9t c.96t c 1.2T c 1.7T c 1.23T c 1.5T c 1.98T c 4.1T c F [MeV] N f = N f =2 N f =3 T -independent r 1/ σ F(r,T) g 2 (r)/r T/T c 4 apenext workshop, Firenze, February 9, 27 p.6/25

10 Heavy quark free energy 1 F 1 [MeV] (a) String breaking T < T c F(r σ 1,T) < 5-5 r [fm].81t c.9t c.96t c 1.2T c 1.7T c 1.23T c 1.5T c 1.98T c 4.1T c high-t physics rt 1 ; screening µ(t) g(t)t F(,T) T F [MeV] N f = N f =2 N f =3 T -independent r 1/ σ F(r,T) g 2 (r)/r T/T c 4 apenext workshop, Firenze, February 9, 27 p.6/25

11 Heavy quark free energy 1 F 1 [MeV] (a) String breaking T < T c F(r σ 1,T) < 5-5 N f = 2 r [fm].81t c.9t c.96t c 1.2T c 1.7T c 1.23T c 1.5T c 1.98T 1 c 4.1T c F(r,T) [MeV] high-t physics rt 1 ; screening µ(t) g(t)t F(,T) T T -independent r 1/ σ F(r,T) g 2 (r)/r -5-1 N f = 2+1 T/T c r [fm] apenext workshop, Firenze, February 9, 27 p.6/25

12 Temperature depending running coupling 2.5 α qq (r,t) Free energy in perturbation theory: T/T c F 1 (r,t) V(r) 4 α(r) 3 r F 1 (r,t) 4 α(t) e m D(T)r 3 r for rλ QCD 1 for rt 1 QCD running coupling in the qq-scheme.1.5 r [fm] 1 non-perturbative confining part for r>.4 fm α qq (r,t) = 3 4 r2 df 1(r,T) dr α qq (r) 3/4r 2 σ present below and just above T c remnants of confinement at T> T c temperature effects set in at smaller r with increasing T maximum due to screening = At which distance do T -effects set in? = definition of the screening radius/mass = definition of the T -dependent coupling apenext workshop, Firenze, February 9, 27 p.7/25

13 Temperature depending running coupling ~ define α qq (T) by maximum of α qq (r,t): α qq (T) 2-flavor QCD ւ quenched α qq (T) α qq (r max,t) perturbative behaviour at high T : ( ) µt g 2 2-loop (T) = 2β ln + β ( ( )) 1 µt ln 2ln, Λ MS β Λ MS T/T c 2.5 Using T c /Λ MS =.77(21) we find µ= 1.14(2)π non-perturbative large values near T c not a large Coulombic coupling remnants of confinement at T> T c string breaking and screening difficult to separate = At which distance do T -effects set in? = calculation of the screening mass/radius slope at high T well described by perturbation theory apenext workshop, Firenze, February 9, 27 p.8/25

14 Screening mass - perturbative vs. non-perturbative effects m D /T N f = N f =2 Screening masses obtained from fits to: F 1 (r,t) F 1 (r =,T) = 4α(T) e m D(T)r 3r at large distances rt > 1 leading order perturbation theory: 1 T/T c m D (T) T ( = A 1+ N f 6 ) 1/2 g(t) apenext workshop, Firenze, February 9, 27 p.9/25

15 Screening mass - perturbative vs. non-perturbative effects m D /T A Nf =2+1 = 1.89(2) A Nf =2 = 1.42(2) A Nf = = 1.52(2) N f = N f =2 N f =2+1 T/T c Screening masses obtained from fits to: F 1 (r,t) F 1 (r =,T) = 4α(T) e m D(T)r 3r at large distances rt > 1 leading order perturbation theory: m D (T) T ( = A 1+ N f 6 ) 1/2 g(t) perturbative limit reached very slowly T depencence qualitatively described by perturbation theory 3 m D /T A Nf = = 1.39(2) But A = non-perturbative effects 2 A 1 in the (very) high temperature limit Difference between N f =,2 disappears when converting to physical units T/T c apenext workshop, Firenze, February 9, 27 p.9/25

16 Screening mass - density dependence [M.Döring et al.] leading order perturbation theory: m D (T,µ q ) = g(t) 1+ N f T 6 + N ( f µq 2π 2 T ) 2 Taylor expansion: m D (T) = m (T)+m 2 (T) ( µq T ) 2 +O (µ 4 q ) m 1 /T 2 m 1 2 /T 1/2 m av 2 /T T/T c T/T c m 2 (T) agrees with perturbation theory for T> 1.5T c non-perturbative effects dominated by gluonic sector apenext workshop, Firenze, February 9, 27 p.1/25

17 Heavy quark bound states above T c? 1.5 r [fm] r med bound states above deconfinement? first estimate: 1 ψ mean charge radii of charmonium states compared to screening radius χ c.5 J/ψ thermal modifications on ψ and χ c already at T c J/ψ may survive above deconfinement T/T c 4 r med : V(r med ) F 1 (r,t) 1 r D [fm] <r> r med r entropy 2/m D (a) r (b) 2r cloud (c).1.1 T/T c apenext workshop, Firenze, February 9, 27 p.11/25

18 Heavy quark bound states above T c? 1.5 r [fm] r med bound states above deconfinement? first estimate: 1.5 ψ χ c J/ψ mean charge radii of charmonium states compared to screening radius thermal modifications on ψ and χ c already at T c J/ψ may survive above deconfinement T/T c 4 Better estimates: Better estimates: effective potentials in Schrödinger Equation Potential models, effective potential V e f f (r,t) But: Free energies vs. internal energies F(r,T) = U(r,T) TS(r,T) direct calculation using correlation functions Maximum entropy method spectral function apenext workshop, Firenze, February 9, 27 p.11/25

19 Free energy vs. Entropy at large separations 15 F [MeV] N f = N f =2 N f =3 Free energies not only determined by potential energy 1 F = U T S 5 Entropy contributions play a role at finite T S = F T T/T c 4 apenext workshop, Firenze, February 9, 27 p.12/25

20 Free energy vs. Entropy at large separations 4 U [MeV] High temperatures: U = T 2 F /T T F (T) 4 3 m D(T)α(T) O (g 3 T) TS (T) 4 3 m D(T)α(T) U (T) 4m D (T)α(T) β(g) g O (g 5 T) (a) T/T c 4 r (b) (c) 2r cloud 4 3 TS [MeV] N f = N f =2 N f =3 The large distance behavior of the finite temperature energies is rather related to screening than to t he temperature dependence of masses of corresponding heavylight mesons! 2 1 S = F T T/T c apenext workshop, Firenze, February 9, 27 p.12/25

21 r-dependence of internal energies TS 1 [MeV] 1 (b) 5 F 1 (r,t) = U 1 (r,t) TS 1 (r,t) S 1 (r,t) = F 1(r,T) T U 1 (r,t) = T 2 F 1(r,T)/T T Entropy contributions vanish in the limit r F 1 (r 1,T) = U 1 (r 1,T) V 1 (r) r [fm] important at intermediate/large distances apenext workshop, Firenze, February 9, 27 p.13/25

22 r-dependence of internal energies U 1 [MeV] r [fm].88t c.93t c.98t c U 1 [MeV] 15 F 1 (r,t) = U 1 (r,t) TS 1 (r,t) S 1 (r,t) = F 1(r,T) T U 1 (r,t) = T 2 F 1(r,T)/T T Entropy contributions vanish in the limit r F 1 (r 1,T) = U 1 (r 1,T) V 1 (r) important at intermediate/large distances 1 = Implications on heavy quark bound states? 5 r [fm] 1.9T c 1.13T c 1.19T c 1.29T c 1.43T c 1.57T c 1.89T c = What is the correct V e f f (r,t)? apenext workshop, Firenze, February 9, 27 p.13/25

23 Heavy quark bound states 1 V eff (r,t) [MeV] V( ) E J/ψ (T=) r [fm] steeper slope of V e f f (r,t) = U 1 (r,t) = J/ψ stronger bound using V e f f = U 1 (r,t) = dissociation at higher temperatures compared to V e f f (r,t) = F 1 (r,t) apenext workshop, Firenze, February 9, 27 p.14/25

24 Estimates on bound states from Schrödinger equation Schrödinger equation for heavy quarks: [ 2m f + 1 ] 2 +V e f f (r,t) Φ f i = E f i m (T)Φ f i f, f = charm, bottom T -dependent color singlet heavy quark potential mimics in-medium modifications of q q interaction reduction to 2-particle interaction clearly too simple, in particular close to T c recent analysis: using V e f f = F 1 : S.Digal, P.Petreczky, H.Satz, Phys. Lett. B514 (21)57 using V e f f = V 1 : C.-Y. Wong, hep-ph/482 using V e f f = V 1 : W.M. Alberico, A. Beraudo, A. De Pace, A. Molinari, hep-ph/5784 state J/ψ χ c ψ ϒ χ b ϒ χ b ϒ E i s[gev] T d /T c T d /T c T d /T c apenext workshop, Firenze, February 9, 27 p.15/25

25 Colored bound states - Diquarks [M. Döring, K. Hübner, OK, FK, 27] Coloured bound states speculated just above T c (SQGP) [E.V. Shuryak,I. Zahed (24/5)] - Is the interaction strong enough to support diquarks? - Potential models for coloured bound states - Diquark free and internal energies Colour antitriplet (anti-symmetric) or color sextet (symmetric) state: 3 3 = 3 6. Cqq(R,T) 3 = 3 2 Tr L()Tr L(R) 1 Tr L()L(R) 2 Cqq(R,T) 6 = 3 4 Tr L()Tr L(R) + 1 Tr L()L(R) 4 F 3,6 qq (R,T) = T lnc 3,6 qq (R,T) apenext workshop, Firenze, February 9, 27 p.16/25

26 Diquark free energies - qq vs. q q in the deconfined phase perturbative relation between diquark and quark-antiquark free energies F 1 Q Q (r,t)/σ1/2 2(F 3 QQ (r,t)-f Q (T))/σ 1/2 rσ 1/2 T/T c F 3 qq(r,t) 1 2 F1 q q(r,t) good approximation above T c. apenext workshop, Firenze, February 9, 27 p.17/25

27 Diquark free energies - qq vs. q q in the deconfined phase perturbative relation between diquark and quark-antiquark free energies F 1 Q Q (r,t)/σ1/2 2(F 3 QQ (r,t)-f Q (T))/σ 1/2 rσ 1/2 T/T c F 3 qq(r,t) 1 2 F1 q q(r,t) good approximation above T c. 2 temperature dependence for all separations F av Q Q (r,t)/σ1/2 F av QQ (r,t)/σ1/2 rσ 1/2 T/T c = entropy contributions play a role for all r. same asymptotic value for qq and q q = quarks in both systems are screened independently by the medium apenext workshop, Firenze, February 9, 27 p.17/25

28 Diquark free energies - qq vs. q q in the deconfined phase perturbative relation between diquark and quark-antiquark free energies F 1 Q Q (r,t)/σ1/2 2(F 3 QQ (r,t)-f Q (T))/σ 1/2 rσ 1/2 T/T c F 3 qq(r,t) 1 2 F1 q q(r,t) good approximation above T c. Dissociation temperatures for heavy q q and qq bound states: state cc (J/ψ) cc bb (ϒ) bb Es i [GeV] T dis /T c apenext workshop, Firenze, February 9, 27 p.17/25

29 Diquark free energies - Screening and string breaking.5 N QQ T/T c =.87 T/T c =.9 T/T c =.96 Net quark number induced by a qq-pair: N (c) QQ (r,t) = N q L (c) QQ N q = QQ (r,t), L (c) QQ (r,t) rt N QQ T/T c = 1.2 T/T c = 1.2 T/T c = 1.7 T/T c = 1.16 T/T c = 1.5 where N q is the quark number operator, N q = 1 ( ) ] D( ˆm,µ) [D 2 Tr 1 ( ˆm,). µ µ= Net quark number induced by a single static quark source, N Q (T) = N q Tr P( ) N q Q =. Tr P( ) rt apenext workshop, Firenze, February 9, 27 p.18/25

30 Diquark free energies - Screening and string breaking.5 N QQ T/T c =.87 T/T c =.9 T/T c =.96 Net quark number induced by a qq-pair: N (c) QQ (r,t) = N q L (c) QQ N q = QQ (r,t), L (c) QQ (r,t) rt N QQ (r ).8 N Q N - 3 QQ (r ) T/T c where N q is the quark number operator, N q = 1 ( ) ] D( ˆm,µ) [D 2 Tr 1 ( ˆm,). µ µ= Net quark number induced by a single static quark source, N Q (T) = N q Tr P( ) N q Q =. Tr P( ) Diquark is neutralized by quarks or antiquarks from the vacuum to be color neutral overall lim N QQ(r,T) = T 1, r < r c, 2, r > r c apenext workshop, Firenze, February 9, 27 p.18/25

31 Renormalized Polyakov loop Using short distance behaviour of free energies Renormalization of F(r, T) at short distances e F1(r,T)/T = ( Z r (g 2 ) ) 2N τ Tr (L x L y) Renormalization of the Polyakov loop 1 F 1 [MeV].76T c.81t c 5.9T c.96t c 1.T c 1.2T c 1.7T c 1.23T c 1.5T c 1.98T c r [fm] 4.1T c L ren = ( Z R (g 2 ) ) N t L lattice 15 1 F [MeV] N f = N f =2 N f =3 L ren defined by long distance behaviour of F(r,T) ( L ren = exp ) F(r =,T) 2T T/T c 4 apenext workshop, Firenze, February 9, 27 p.19/25

32 Renormalized Polyakov loop F 1 [MeV] 1.5 L ren 2F-QCD: N τ =4 SU(3): N τ =4 N τ =8 1.76T c.81t c 5.9T c.96t c 1.T c 1.2T c 1.7T c 1.23T c 1.5T c 1.98T c r [fm] 4.1T c F [MeV] N f = N f =2 N f =3 T/T c ( L ren = exp ) F(r =,T) 2T T/T c 4 apenext workshop, Firenze, February 9, 27 p.19/25

33 Renormalized Polyakov loop 1.5 L ren 1.5 N τ =4 N τ =8 High temperature limit, L ren = 1, reached from above as expected from PT Clearly non-perturbative effects below 5T c Renormalized T/T c Polyakov loop well defined 25 in quenched and full QCD - non-zero for finite quark mass - strong increase near T c ( L ren = exp ) F(r =,T) 2T apenext workshop, Firenze, February 9, 27 p.19/25

34 Renormalization constants Renormalization constants obtained from heavy quark free energies 1.4 Z R (g 2 ) g 2 4 =6/β The renormalization constants depend on the bare coupling, i.e. Z R (g 2 ) N τ ( ) Z R (g 2 ) exp g 2 (N 2 1)/NQ (2) + g 4 Q (4) +O (g 6 ) with Q (2) =.597(13) consistent with lattice perturbation theory (Heller + Karsch, 1985) apenext workshop, Firenze, February 9, 27 p.2/25

35 Direct renormalization of the Polyakov loop [S. Gupta,K. Hübner,OK] Instead of renormalizing heavy quark free energies Use Polyakov loops obtained at different N τ Assume no volume dependence (T > T c ) The renormalization constants only depend on coupling, i.e. Z(g 2 ) L R D (T) L D (g 2,N τ ) g fixed N τ,1 N τ,2 T 1 T start apenext workshop, Firenze, February 9, 27 p.21/25

36 Direct renormalization of the Polyakov loop [S. Gupta,K. Hübner,OK] Instead of renormalizing heavy quark free energies Use Polyakov loops obtained at different N τ Assume no volume dependence (T > T c ) The renormalization constants only depend on coupling, i.e. Z(g 2 ) L R D (T) g fixed 1.2 L D (g 2,N τ ) N τ,1 1. N τ,2.8.6 L 3 R N τ =4 N τ =6 N τ =8.4.2 T 1 T start. T/T c apenext workshop, Firenze, February 9, 27 p.21/25

37 Direct renormalization of the Polyakov loop [S. Gupta,K. Hübner,OK] Instead of renormalizing heavy quark free energies Use Polyakov loops obtained at different N τ Assume no volume dependence (T > T c ) The renormalization constants only depend on coupling, i.e. Z(g 2 ) L ren direct renormalization plc renormalization Z R (g 2 ) direct renormalization plc renormalization.2 T/T c Both renormalization procedures are equivalent g 2 solely based on gauge-invariant quantities apenext workshop, Firenze, February 9, 27 p.21/25

38 Polyakov loops in higher representations [S. Gupta,K. Hübner,OK] use character property of direct product rep: χ p q (g) = χ p (g)χ q (g) Z(3) symmetry: L D e itφ L D triality (Z(3) charge): t p q mod 3 adjoint link variable [ U D=8] i j := 1 2 Tr [ U D=3 λ i (U D=3 ) λ j ] D (p,q) t C 2 (r) d D = C D /C F L D (x) 3 (1,) 1 4/3 1 L 3 6 (2,) 2 1/3 5/2 L3 2 L 3 8 (1,1) 3 9/4 L (3,) 6 9/2 L 3 L 6 L 8 15 (2,1) 1 16/3 4 L3 L 6 L 3 15 (4,) 1 28/3 7 L 3 L 1 L (3,1) 2 25/3 25/4 L3 L 1 L 6 27 (2,2) 8 6 L 6 2 L 8 1 apenext workshop, Firenze, February 9, 27 p.22/25

39 Polyakov loops in higher representations [S. Gupta,K. Hübner,OK] perturbation theory: F D (r,t) = C D α s (r) r for rλ QCD 1 renormalization of free energies: e F1 D (r,t)/t = ( Z r (g 2 ) ) 2d D N τ Tr (L D x L D y ) i.e. the renormalization constants are related by Casimir [G.Bali, Phys.Rev.D62 (2) 11453] 3. F 1,R Q Q,8 (r,t)/σ1/ rσ 1/2 T/T c apenext workshop, Firenze, February 9, 27 p.22/25

40 Polyakov loops in higher representations [S. Gupta,K. Hübner,OK] Does Casimir scaling hold beyond leading order? Singlet free energies of static quarks in representation D=3,8: F sing D (r,t) T ( = ln TrL ) D (x)l D (y) GF with L D made up of U D=3 and [ U D=8] i j := 1 2 Tr [ U D=3 λ i (U D=3 ) λ j ] 1. F 1,R Q Q,D (r,t)/c(d)/σ1/ D=8 D=3 rσ 1/2 T/T c apenext workshop, Firenze, February 9, 27 p.22/25

41 Polyakov loops in higher representations [S. Gupta,K. Hübner,OK] Does Casimir scaling, L 1/C F 3 L 1/C D D, hold beyond two-loop order? renormalization of the Polykov loop: L ren D = ( Z D (g 2 ) ) N τ d D L bare D, i.e. the renormalization constants are related by Casimir [G.Bali, Phys.Rev.D62 (2) 11453] Z R D (g2 ) D=3 D=6 D=8 D=1 D=15 D sing =3 D sing = g 2 apenext workshop, Firenze, February 9, 27 p.22/25

42 Polyakov loops in higher representations [S. Gupta,K. Hübner,OK] Does Casimir scaling, L 1/C F 3 L 1/C D D, hold beyond two-loop order? renormalization of the Polykov loop: L ren D = ( Z D (g 2 ) ) N τ d D L bare D, i.e. the renormalization constants are related by Casimir [G.Bali, Phys.Rev.D62 (2) 11453] Casimir scaling equivalent for bare or renormalized Polyakov loops.5 <L D > 1/d D D=3.3 D=6 D=8 D=1.25 D=15 D=15 D=24.2 D=27.15 T/T c apenext workshop, Firenze, February 9, 27 p.22/25

43 Polyakov loops in higher representations [S. Gupta,K. Hübner,OK] Does Casimir scaling, L 1/C F 3 L 1/C D D, hold beyond two-loop order? renormalization of the Polykov loop: L ren D = ( Z D (g 2 ) ) N τ d D L bare D, i.e. the renormalization constants are related by Casimir [G.Bali, Phys.Rev.D62 (2) 11453] Casimir scaling equivalent for bare or renormalized Polyakov loops 1.6 L R D D=3 D=6 D=8 D=1 D=15 D sing =3 D sing = T/T c apenext workshop, Firenze, February 9, 27 p.22/25

44 String breaking for adjoint Polyakov loops [S. Gupta,K. Hübner,OK] string breaking expected for representations with triality t = non-zero for L R 8 even below T c.5.4 L R D D=3 D= T/T c apenext workshop, Firenze, February 9, 27 p.23/25

45 String breaking for adjoint Polyakov loops [S. Gupta,K. Hübner,OK] string breaking expected for representations with triality t = non-zero for L R 8 even below T c finite values of F 8 (r) at large distances [GeV] F R Q Q,8 d 8 F 1,R Q Q,3 F 1,R Q Q,8. r string (F 8 ) r string (V 8 ) r [fm] apenext workshop, Firenze, February 9, 27 p.23/25

46 String breaking for adjoint Polyakov loops [S. Gupta,K. Hübner,OK] string breaking expected for representations with triality t = non-zero for L R 8 even below T c finite values of F 8 (r) at large distances might be related to binding energy of gluelumps 2.8 F [GeV] r string [fm] 1..8 V 8 F 8 T/T c apenext workshop, Firenze, February 9, 27 p.23/25

47 Polyakov loops in higher representations [S. Gupta,K. Hübner,OK] 2-flavour QCD:.3 <L D > 1/d D D=3.1 D=6 D=8 D=1.5 D= T/T c apenext workshop, Firenze, February 9, 27 p.24/25

48 Polyakov loops in higher representations [S. Gupta,K. Hübner,OK] 2-flavour QCD: L R D D=3 D=6 D=8 D=1 D= Freedom to set the scale:. T/T. c V T= (r) V T= (r)+c Be carefull to extract T c by slope of L R Susceptibility not renormalized in this way L R D L R D exp( C/2T) Z R D Z R D exp( Ca(g 2 )/2) apenext workshop, Firenze, February 9, 27 p.24/25

49 Conclusions - Heavy quark free energies, internal energies and entropy Complex r and T dependence Running coupling shows remnants of confinenement above T c Entropy contributions play a role at finite T Non-perturbative effects in m D up to high T Non-perturbative effects dominated by gluonic sector - Bound states in the quark gluon plasma First estimates from potential models Higher dissociation temperature using V 1 (directly produced) J/ψ exist well above T c Diquarks unlikely to exist above T c - Renormalized Polyakov loop Two consistent renormalization procedures Renormalization constant depend on the bare coupling Applicable for higher representations Casimir scaling good approximation at high T apenext workshop, Firenze, February 9, 27 p.25/25