From confinement to new states of dense QCD matter

Transcription

1 From confinement to new states of dense QCD matter From Quarks and Gluons to Hadrons and Nuclei, Erice, Sicily, 17 Sept2011 Kurt Langfeld School of Comp. and Mathematics and The HPCC, Univ. of Plymouth, UK Andreas Wipf TPI, University of Jena, Germany From confinement to new states of dense QCD matter p. 1/24

2 Introduction: The empty vacuum of Yang-Mills theory centre sectors From confinement to new states of dense QCD matter p. 2/24

3 Introduction: The empty vacuum of Yang-Mills theory centre sectors Yang-Mills theories with matter: Centre sector transitions in QCD-like theories From confinement to new states of dense QCD matter p. 2/24

4 Introduction: The empty vacuum of Yang-Mills theory centre sectors Yang-Mills theories with matter: Centre sector transitions in QCD-like theories Lessons from the Schwinger model at finite densities What is Fermi Einstein condensation? From confinement to new states of dense QCD matter p. 2/24

5 Introduction: The empty vacuum of Yang-Mills theory centre sectors Yang-Mills theories with matter: Centre sector transitions in QCD-like theories Lessons from the Schwinger model at finite densities What is Fermi Einstein condensation? SU(3) Fermi gas with confinement and FEC From confinement to new states of dense QCD matter p. 2/24

6 Introduction: The empty vacuum of Yang-Mills theory centre sectors Yang-Mills theories with matter: Centre sector transitions in QCD-like theories Lessons from the Schwinger model at finite densities What is Fermi Einstein condensation? SU(3) Fermi gas with confinement and FEC Conclusions From confinement to new states of dense QCD matter p. 2/24

7 Yang-Mills moduli My name is vacuum - the vacuum: (pert.) vacuum all contractible loops are 1 exp{i A µ dx µ } = 1 = 1 = 1 example: A µ (x) = 0 or U µ (x) = 1 more vacua? From confinement to new states of dense QCD matter p. 3/24

8 Yang-Mills moduli My name is vacuum - the vacuum: (pert.) vacuum all contractible loops are 1 exp{i A µ dx µ } = 1 = 1 = 1 example: A µ (x) = 0 or U µ (x) = 1 more vacua? constructing the moduli space need to devide out the gauge transformations [Keurentjes, Rosly, Smilga, PRD 58 (1998) ] [Schaden, PRD 71 (2005) ] [Langfeld, Lages, Reinhardt, PoS LAT2005:201,2006.] From confinement to new states of dense QCD matter p. 3/24

9 Yang-Mills moduli There is a U(1) 4(N c 1) manifold of gauge in-equivalent vacua flat directions tr P =0 standard vac. tr P =1 From confinement to new states of dense QCD matter p. 4/24

10 Yang-Mills moduli There is a U(1) 4(N c 1) manifold of gauge in-equivalent vacua flat directions tr P =0 standard vac. tr P =1 Polyakov line P is sensitive to the vacuum Litmus paper From confinement to new states of dense QCD matter p. 4/24

11 Yang-Mills moduli There is a U(1) 4(N c 1) manifold of gauge in-equivalent vacua flat directions tr P =0 standard vac. tr P =1 Polyakov line P is sensitive to the vacuum Litmus paper none of the vacuum states confines quarks (trivial potential) From confinement to new states of dense QCD matter p. 4/24

12 Yang-Mills moduli: SU(3) quantum fluctuations lift the flat directions standard vac. tr P =1 centre sectors From confinement to new states of dense QCD matter p. 5/24

13 Yang-Mills moduli: SU(3) quantum fluctuations lift the flat directions standard vac. tr P =1 remanent Z 3 symmetry centre sectors centre sectors From confinement to new states of dense QCD matter p. 5/24

14 Yang-Mills moduli: SU(3) quantum fluctuations lift the flat directions standard vac. tr P =1 remanent Z 3 symmetry centre sectors centre sectors confinement phase: centre sector transitions [remarkable entropy!] From confinement to new states of dense QCD matter p. 5/24

15 Yang-Mills moduli: SU(3) quantum fluctuations lift the flat directions standard vac. tr P =1 remanent Z 3 symmetry centre sectors centre sectors confinement phase: centre sector transitions [remarkable entropy!] high temperature phase: frozen centre sector (SSB) deconfinement From confinement to new states of dense QCD matter p. 5/24

16 Yang-Mills moduli: SU(3) including dynamical matter (e.g. quarks, Higgs,...) tunneling? matter bias From confinement to new states of dense QCD matter p. 6/24

17 Yang-Mills moduli: SU(3) including dynamical matter (e.g. quarks, Higgs,...) tunneling? bias towards the trivial centre sector matter bias From confinement to new states of dense QCD matter p. 6/24

18 Yang-Mills moduli: SU(3) including dynamical matter (e.g. quarks, Higgs,...) tunneling? bias towards the trivial centre sector matter bias do centre sector transitions still take place? From confinement to new states of dense QCD matter p. 6/24

19 Yang-Mills moduli: SU(3) including dynamical matter (e.g. quarks, Higgs,...) tunneling? bias towards the trivial centre sector matter bias do centre sector transitions still take place? quarks are sensitive to the centre sector phenomenology of the centre sector transitions? From confinement to new states of dense QCD matter p. 6/24

20 Centre sector transitions: Define: P < = V < tr t U 0(x) Polyakov lines P > = V > tr t U 0(x) 3 space V < V> From confinement to new states of dense QCD matter p. 7/24

21 Centre sector transitions: Define: P < = V < tr t U 0(x) Polyakov lines P > = V > tr t U 0(x) Center map: C(P) C = n : P C z n 3 space V < V> From confinement to new states of dense QCD matter p. 7/24

22 Centre sector transitions: Define: P < = V < tr t U 0(x) P > = V > tr t U 0(x) Polyakov lines Center map: C(P) C = n : P C z n 3 space V < V> Tunneling coefficient: ( ) probability C(P < ) and C(P > ) are different From confinement to new states of dense QCD matter p. 7/24

23 Centre sector transitions: Define: P < = V < tr t U 0(x) P > = V > tr t U 0(x) Polyakov lines Center map: C(P) C = n : P C z n 3 space V < V> Tunneling coefficient: ( ) probability C(P < ) and C(P > ) are different here: SU(2) Yang-Mills in comparison to SU(2) Yang-Mills + Higgs From confinement to new states of dense QCD matter p. 7/24

24 Centre sector transitions: tunneling coefficient for SU(2): C(P < ) C(P > ) tunneling 1/2 SSB 0 From confinement to new states of dense QCD matter p. 8/24

25 Centre sector transitions: tunneling coefficient for SU(2): C(P < ) C(P > ) tunneling 1/2 SSB x 6, pure YM 30 3 x 6, pure YM tunneling coeff KL, HPCC Plymouth β From confinement to new states of dense QCD matter p. 8/24

26 Centre sector transitions: tunneling coefficient for SU(2): C(P < ) C(P > ) tunneling 1/2 SSB x 6, pure YM 30 3 x 6, pure YM 24 3 x 6, YM + qhiggs tunneling coeff KL, HPCC Plymouth β From confinement to new states of dense QCD matter p. 9/24

27 Centre sector transitions: phenomenological impact? From confinement to new states of dense QCD matter p. 10/24

28 The Schwinger model: U(1) gauge theory massless fermion 1+1 dimensions, torus 1/T L From confinement to new states of dense QCD matter p. 11/24

29 The Schwinger model: U(1) gauge theory massless fermion 1+1 dimensions, torus 1/T L Properties: dynamical generated photon mass: m γ U(1) centre symmetry h 0, h 1 [0,1] parameterise the centre sectors From confinement to new states of dense QCD matter p. 11/24

30 The Schwinger model: U(1) gauge theory massless fermion 1+1 dimensions, torus 1/T L Properties: dynamical generated photon mass: m γ U(1) centre symmetry h 0, h 1 [0,1] parameterise the centre sectors physical states: only mesons add quark chemical potential µ partition function is independent of µ silver blaze problem From confinement to new states of dense QCD matter p. 11/24

31 The Schwinger model: partition function factorises: Z(β,L,µ) = (2π) 2 det ( ) det ( +m 2 γ) 1 0 dh 0 dh 1 det(i/ h,µ ), From confinement to new states of dense QCD matter p. 12/24

32 The Schwinger model: partition function factorises: Z(β,L,µ) = (2π) 2 det ( ) det ( +m 2 γ) 1 0 dh 0 dh 1 det(i/ h,µ ), Frozen centre sector: µ/t = 4 overlap problem for MC simulations From confinement to new states of dense QCD matter p. 12/24

33 The Schwinger model: partition function factorises: Z(β,L,µ) = (2π) 2 det ( ) det ( +m 2 γ) 1 0 dh 0 dh 1 det(i/ h,µ ), Frozen centre sector: µ/t = 4 overlap problem for MC simulations ρ B (h 0 ) 0 wrong physics! From confinement to new states of dense QCD matter p. 12/24

34 The Schwinger model: baryon density: [z = exp{ 2πih 0 }] L { ρ B 1 dp π 0 z e β(p µ) +z } z e β(p+µ) +z. From confinement to new states of dense QCD matter p. 13/24

35 The Schwinger model: baryon density: [z = exp{ 2πih 0 }] L { ρ B 1 dp π 0 z e β(p µ) +z } z e β(p+µ) +z. with centre sector transitions: [integrate over h 0,h 1 ] 1 Z(β,L,µ) =. det ( +m 2 γ) V 2 From confinement to new states of dense QCD matter p. 13/24

36 The Schwinger model: baryon density: [z = exp{ 2πih 0 }] L { ρ B 1 dp π 0 z e β(p µ) +z } z e β(p+µ) +z. with centre sector transitions: [integrate over h 0,h 1 ] 1 Z(β,L,µ) =. det ( +m 2 γ) µ independent! V 2 solves the silver blaze problem [K. Langfeld, A. Wipf, arxiv: ] From confinement to new states of dense QCD matter p. 13/24

37 Physics of centre sector transitions: What is Fermi Einstein condensation? From confinement to new states of dense QCD matter p. 14/24

38 Physics of centre sector transitions: What is Fermi Einstein condensation? Schwinger model: h 0 = 1/2 z = exp{ 2πih 0 } = 1 L { ρ B 1 dp. π 0 z e β(p µ) +z quarks acquire Bose statistics! } z e β(p+µ) +z From confinement to new states of dense QCD matter p. 14/24

39 Physics of centre sector transitions: What is Fermi Einstein condensation? Schwinger model: h 0 = 1/2 z = exp{ 2πih 0 } = 1 L { ρ B 1 dp. π 0 z e β(p µ) +z quarks acquire Bose statistics! } z e β(p+µ) +z generic for SU(N c ) (at least for N c even)! [K. Langfeld, A. Wipf, PRD 81 (2010) From confinement to new states of dense QCD matter p. 14/24

40 Physics of centre sector transitions: Consider now SU(3) with matter: q(x+l) = ( 1) q(x) Z Roberge-Weisz transformation From confinement to new states of dense QCD matter p. 15/24

41 Physics of centre sector transitions: Consider now SU(3) with matter: Z Z q(x+l) = ( 1) q(x) Z q(x+l) = ( 1) q(x) Roberge-Weisz transformation From confinement to new states of dense QCD matter p. 15/24

42 Physics of centre sector transitions: SU(N c even): Z = -1 after RW-transformation: quarks obey Bose statistics! From confinement to new states of dense QCD matter p. 16/24

43 Physics of centre sector transitions: SU(N c even): Z = -1 after RW-transformation: quarks obey Bose statistics! centre-dressed quarks can condense: BEC Fermi Einstein condensation does not contradict the Spin-Statistics theorem: since quarks are confined From confinement to new states of dense QCD matter p. 16/24

44 Physics of centre sector transitions: SU(N c even): Z = -1 after RW-transformation: quarks obey Bose statistics! centre-dressed quarks can condense: BEC Fermi Einstein condensation does not contradict the Spin-Statistics theorem: since quarks are confined quark-gluon-plasma phase: spontaneous breaking of centre symmetry Z = 1 sector does not occur Fermi statistics only [K. Langfeld, A. Wipf, PRD 81 (2010) ] From confinement to new states of dense QCD matter p. 16/24

45 SU(3) Fermi gas with confinement FEC in SU(3) QCD-like theories? q(x+l) = [1/2±i 3/2] q(x) From confinement to new states of dense QCD matter p. 17/24

46 SU(3) Fermi gas with confinement FEC in SU(3) QCD-like theories? q(x+l) = [1/2±i 3/2] q(x) minimalistic model: quarks with mass m interacting with the centre background fields From confinement to new states of dense QCD matter p. 17/24

47 SU(3) Fermi gas with confinement FEC in SU(3) QCD-like theories? q(x+l) = [1/2±i 3/2] q(x) minimalistic model: quarks with mass m interacting with the centre background fields no coloured states contributing to the partition function only mesons, baryons,... called confinement in the title, but... no confinement scale from the gluon sector (σ = 0) more realistic vortex background field From confinement to new states of dense QCD matter p. 17/24

48 SU(3) Fermi gas with confinement FEC in SU(3) QCD-like theories? q(x+l) = [1/2±i 3/2] q(x) minimalistic model: quarks with mass m interacting with the centre background fields no coloured states contributing to the partition function only mesons, baryons,... called confinement in the title, but... no confinement scale from the gluon sector (σ = 0) more realistic vortex background field consider extreme conditions: here T and/or µ centre sector freeze out Fermi gas model From confinement to new states of dense QCD matter p. 17/24

49 SU(3) Fermi gas with confinement Model partition function: Z Q = N c n=1 DqD q exp { q ( i /+(A (n) 0 +iµ)γ 0 +im ) } q From confinement to new states of dense QCD matter p. 18/24

50 SU(3) Fermi gas with confinement Model partition function: Z Q = N c n=1 Thermal energy density: DqD q exp { q ( i /+(A (n) 0 +iµ)γ 0 +im ) } q E therm (T) = n ω n [ z n e βe(p) +z n + z n e βe(p) +z n ] ω n : sector weights if ω 1,2 = 0, ω 3 = 1, Fermi-gas model p E(p). ε FEC / ε free ml = 5 ml = 10 ml = T/m From confinement to new states of dense QCD matter p. 18/24

51 SU(3) Fermi gas with confinement Centre-sector weights and deconfinement: ω 1/2 : non-trivial sectors, ω 3 : perturbative sector 1 1 ε FEC / ε free centre sector weights ω 1,2 ml=15 ω 3 ml=15 ω 1,2 ml=5 ω 3 ml=5 0 ml = 5 ml = 10 ml = T/m T/m From confinement to new states of dense QCD matter p. 19/24

52 SU(3) Fermi gas with confinement Baryon density: 2.5 beta=10 Lm=10 beta=10 2 m L = 5 m L = 10 1 ρ FEC / ρ Fermi centre sector weights ω 1, ω 2 ω µ/m µ/m From confinement to new states of dense QCD matter p. 20/24

53 SU(3) Fermi gas with confinement Baryon density: 2.5 beta=10 Lm=10 beta=10 2 m L = 5 m L = 10 1 ρ FEC / ρ Fermi centre sector weights ω 1, ω 2 ω µ/m µ/m transition to Fermi gas at µ c From confinement to new states of dense QCD matter p. 20/24

54 SU(3) Fermi gas with confinement Baryon density: 2.5 beta=10 Lm=10 beta=10 2 m L = 5 m L = 10 1 ρ FEC / ρ Fermi centre sector weights ω 1, ω 2 ω µ/m µ/m transition to Fermi gas at µ c excess of density close to µ c FEC From confinement to new states of dense QCD matter p. 20/24

55 SU(3) Fermi gas with confinement µ T phase diagram: large volumes: ml = 15 [use weight ω 3 ] [ω 3 C for µ 0] From confinement to new states of dense QCD matter p. 21/24

56 SU(3) Fermi gas with confinement µ T phase diagram: small volumes: ml = 5 [use weight ω 3 ] [ω 3 C for µ 0] From confinement to new states of dense QCD matter p. 22/24

57 SU(3) Fermi gas with confinement µ T phase diagram: small volumes: ml = 5 [use weight ω 3 ] [ω 3 C for µ 0] need small volumes (pressure) for FEC! From confinement to new states of dense QCD matter p. 22/24

58 Conclusions: Centre sector transition do take place depsite of the presence of matter unless at extreme conditions From confinement to new states of dense QCD matter p. 23/24

59 Conclusions: Centre sector transition do take place depsite of the presence of matter unless at extreme conditions Schwinger model: centre transitions solve the Silver Blaze Problem From confinement to new states of dense QCD matter p. 23/24

60 Conclusions: Centre sector transition do take place depsite of the presence of matter unless at extreme conditions Schwinger model: centre transitions solve the Silver Blaze Problem Fermi Einstein condensation: centre dressed quarks acquire Bose-type statistics condensation: BEC FEC [confinement phase only] From confinement to new states of dense QCD matter p. 23/24

61 Conclusions: SU(3) Fermi-gas model with confinement: confinement: absence of coloured states does not explain confinement scale From confinement to new states of dense QCD matter p. 24/24

62 Conclusions: SU(3) Fermi-gas model with confinement: confinement: absence of coloured states does not explain confinement scale FEC does take place though small volumes (pressure) are needed [K. Langfeld, A. Wipf, arxiv: ] From confinement to new states of dense QCD matter p. 24/24

63 Conclusions: SU(3) Fermi-gas model with confinement: confinement: absence of coloured states does not explain confinement scale FEC does take place though small volumes (pressure) are needed [K. Langfeld, A. Wipf, arxiv: ] outlook: more realistic QM: including chiral SSB, pions,... centre sectors volumes spanning centre vortices FEC statistical model? From confinement to new states of dense QCD matter p. 24/24