Some selected results of lattice QCD

Transcription

1 Some selected results of lattice QCD Heidelberg, October 12, 27 Kurt Langfeld School of Mathematics and Statistics University of Plymouth p.1/3

2 Glueball spectrum: no quarks (quenched approximation) 12 + r m G * * + * m G (GeV) PC C. J. Morningstar and M. J. Peardon, Phys. Rev. D 6, 3459 (1999) p.2/3

3 Glueball spectrum: no quarks (quenched approximation) and beyond: r m G * * + * PC m G (GeV) (r m π ) 2 C. J. Morningstar and M. J. Peardon, Phys. Rev. D 6, 3459 (1999) r m G ens. e 1 e 2 e 4 e 3 e 5 e 6 Tensor Scalar 2r m π O(a) imp., N f =2 Quenched Quenched, cont. extrap. A. Hart and M. Teper [UKQCD Collaboration], Phys. Rev. D 65, 3452 (22) p.2/3

4 The quark gluon plasma: ε T 4 Stefan Boltzmann limit hadron gas strong non perturbative effects offset? T c T gluon deconfinement - strongly interaction QGP J. Engels, F. Karsch and K. Redlich, Nucl. Phys. B 435, 295 (1995) p.3/3

5 Vortex picture of confinement Too much information in full SU(3) lattice configurations p.4/3

6 Vortex picture of confinement Too much information in full SU(3) lattice configurations remember 3 2 V/sqrt(K) 1 SU(N) -1-2 gauge fixing beta=2.5, Ls=16 beta=2.5, Ls=32 beta=2.635, Ls=48 beta=2.74, Ls= R sqrt(k) projection reducing degrees of freedom red. Theorie * [DelDebbio, Faber, Greensite, Olejnik, PRD55 (1997) 2298.] *? Z N theory of vortices! p.4/3

7 Understanding confinement: SU(2) action density [CSSM, Adelaide] vortex content projection [MCG, LCG,...] p.5/3

8 (pure) SU(2) gauge theory p.6/3

9 Vortex impact on confinement [SU(2)]: SU(2), 12 4 SU(2), full ensemble fit to vortex only 6 4 plot from Langfeld, hep lat/143 full ensemble vortices removed V/sqrt(K) 1 V(r)/σ 1/2 2 V(r)/σ 1/ beta=2.5, Ls=16 beta=2.5, Ls=32 beta=2.635, Ls=48 beta=2.74, Ls= R sqrt(k) r [fm] r [fm] full SU(2) vortices only vortices removed p.7/3

10 (pure) SU(3) gauge theory p.8/3

11 Vortex impact on confinement [SU(3)]: quark antiquark potential: 3 SU(3) improved action: LCG σa 2 =.1186(26), 12 4, β= V(r) /σ 1/ full r σ 1/2 p.9/3

12 Vortex impact on confinement [SU(3)]: quark antiquark potential: 3 2 SU(3) improved action: LCG σa 2 =.1186(26), 12 4, β=6.64 σ vor =1.7(22) σ 1 V(r) /σ 1/ full vortices only r σ 1/2 p.1/3

13 Vortex impact on confinement [SU(3)]: quark antiquark potential: 3 2 SU(3) improved action: LCG σa 2 =.1186(26), 12 4, β=6.64 σ vor =1.7(22) σ 1 V(r) /σ 1/ full vortices removed vortices only r σ 1/2 p.11/3

14 SU(3) + 2 dynamical flavors p.12/3

15 Vortex impact on confinement [SU(3) + 2dyn]: String breaking: heavy light SU(3) + 2 dynamical flavors 16 3 x4, m/t =.4, staggered T= V(r)/σ 1/ r σ 1/2 O. Kaczmarek F. Karsch K. Langfeld (GSI Virtual Institute) p.13/3

16 Vortex impact on confinement [SU(3) + 2dyn]: String breaking: heavy light SU(3) + 2 dynamical flavors 16 3 x4, m/t =.4, staggered T= T/T c =.76, full V(r)/σ 1/ r σ 1/2 O. Kaczmarek F. Karsch K. Langfeld (GSI Virtual Institute) p.14/3

17 Vortex impact on confinement [SU(3) + 2dyn]: String breaking: heavy light SU(3) + 2 dynamical flavors 16 3 x4, m/t =.4, staggered T= T/T c =.76, full T/T c =.76, vortex only V(r)/σ 1/ r σ 1/2 O. Kaczmarek F. Karsch K. Langfeld (GSI Virtual Institute) p.15/3

18 Vortex impact on confinement [SU(3) + 2dyn]: String breaking: heavy light SU(3) + 2 dynamical flavors 16 3 x4, m/t =.4, staggered T= T/T c =.76, full T/T c =.76, vortex only T/T c =.76, vortex removed V(r)/σ 1/ r σ 1/2 O. Kaczmarek F. Karsch K. Langfeld (GSI Virtual Institute) p.16/3

19 Random vortex model Why do vortex ensembles confine quarks? (lattice ) universe Wilson loop { } exp V (r)/t ( 1) V (r) static quark potential A Wilson loop 1/T here: V (r) = 2 ρ r vortex intersection density: ρ p.17/3

20 Random vortex model Why do vortex ensembles confine quarks? (lattice ) universe Wilson loop { } exp V (r)/t ( 1) V (r) static quark potential A Wilson loop 1/T here: V (r) = 2 ρ r vortex intersection density: ρ Vortex density ρ string tension: σ = 2ρ p.17/3

21 Are vortices physical? Vortex density ρ string tension p.18/3

22 Are vortices physical? Vortex density ρ string tension Vortex properties must be indepedent of the lattice spacing a p.18/3

23 Are vortices physical? Vortex density ρ string tension Vortex properties must be indepedent of the lattice spacing a The quest for physical vortices: gauge + projection vortex matter p.18/3

24 Are vortices physical? Vortex density ρ string tension Vortex properties must be indepedent of the lattice spacing a The quest for physical vortices: gauge + projection vortex matter Mandelstam 1975 t Hooft 1978 Mack 198 Tomboulis Debbio, Faber, Greensite, Ojelnik 1997 continuum limit? MCG Langfeld, Reinhardt, Tennert 1998 continuum [Alexandru, Engelhardt, Forcrand, Haymaker, dofs! Kovacs, Stack,...] p.18/3

25 Vortex density: SU(2) σ a 2 ρa 2 (β) 1 1 ρ ~ 3.6/fm β ρ /σ independent of the lattice spacing! [Langfeld, Reinhardt, Tennert, PLB 419 (1998) 317.] p.19/3

26 Brief summary [T=]: [remember SU(2): MCG] Vortices extrapolate to the continuum limit Vortex configurations recover ~1% string tension Vortex removed configurations do not confine quarks p.2/3

27 Brief summary [T=]: [remember SU(2): MCG] Vortices extrapolate to the continuum limit Vortex configurations recover ~1% string tension Vortex removed configurations do not confine quarks [here SU(3): LCG] Vortices extrapolate to the continuum limit: liquid Vortex configurations recover the string tension There is no string tension without vortices Vortices realize string breaking p.2/3

28 What do we learn from the vortex picture about deconfinement at high temperatures? p.21/3

29 A puzzle at high temperatures Spatial Wilson loop: Ws (R, L) exp{ σ s R L} 1/T time Expectations: space R L Dimensional reduction: 3D Yang-Mills theory σ s σ 3 [Appelquist, Pisarski, 1981] Perturbation theory: T Λ QCD asymptotic freedom σ s = p.22/3

30 Lattice calculation: σ s =.136g 4 (T)T 2 T σs 1 g 2 (T) [Bali, Fingberg, Heller, Karsch, Schilling, PRL 71 (1993) 359.] p.23/3

31 Deconfinement at high T [SU(2) so far] Wilson loop W ( 1) W vortex time axis p.24/3

32 Deconfinement at high T [SU(2) so far] Wilson loop W ( 1) W vortex time axis W 2 ( 1) W = W p.24/3

33 Deconfinement at high T [SU(2) so far] Wilson loop W ( 1) W vortex time axis W 2 ( 1) W = W remember = exp{ V(r)/T} static quark potential p.24/3

34 Vortex picture of deconfinement T=: spatial Wilson Loop random vortex model! p.25/3

35 Vortex picture of deconfinement T=: spatial Wilson Loop random vortex model! T > T c : vortex depercolation randomly distributed deconfinement σ s T 2 [Gattnar, KL, Schäfke, Reinhardt, PLB 489 (2) 251.] p.26/3

36 Vortex picture of deconfinement T=: Langfeld, Tennert, Engelhardt, Reinhardt, PLB 452 (1999) 31. Engelhardt, Langfeld, Reinhardt, Tennert, PRD 61 (2) Langfeld, PRD 67 (23) (rapid comm.) spatial Wilson Loop random vortex model! T > T c : vortex depercolation randomly distributed deconfinement σ s T 2 [Gattnar, KL, Schäfke, Reinhardt, PLB 489 (2) 251.] p.26/3

37 Depercolation of vortices:.5 T =.9 T c.8 T = 1.1 T c.4.6 probability.3.2 probability cluster extension cluster extension from Engelhardt, Langfeld, Reinhardt, Tennert, PRD 61 (2) p.27/3

38 Depercolation of vortices:.5 T =.9 T c.8 T = 1.1 T c probability T = 1.4 T c probability T = 1.8 T c.1 probability cluster extension.2 probability cluster extension cluster extension cluster extension from Engelhardt, Langfeld, Reinhardt, Tennert, PRD 61 (2) p.27/3

39 Finite size scaling analysis: Can we realize the order of the phase transition in the vortex picture? P(β) β p.28/3

40 Finite size scaling analysis: Can we realize the order of the phase transition in the vortex picture? x = (β β c ) L 1/ν P(β) β p.29/3

41 Finite size scaling analysis: Can we realize the order of the phase transition in the vortex picture? x = (β β c ) L 1/ν P(β) β L=8 L=12 L=16 L=2 L=24 P(x) (β β c ) L 1/ν ν = (3D Ising critical exponent! ) from Langfeld, PRD 67 (23) (rapid comm.) p.29/3

42 Brief summary [T ]: [SU(2): lattice] deconfinement vortex depercolation transition explains the spatial string tension: σ s (T) universality class correctly anticipated by the vortex structure [SU(3): vortex model] correctly reproduces the 1st order transition [Engelhardt, Quandt, Reinhardt, NPB 685 (24) 227.] p.3/3