QCD-like theories at finite density

Transcription

1 QCD-like theories at finite density 34 th International School of Nuclear Physics Probing the Extremes of Matter with Heavy Ions Erice, Sicily, 23 September 212 Lorenz von Smekal 23. September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 1

2 Contents Introduction QCD with Isospin Chemical Potential Two-Color QCD N. Strodthoff, B.-J. Schaefer & L.v.S., Phys. Rev. D85 (212) 747 K. Kamikado, N. Strodthoff, L.v.S. & J. Wambach, arxiv:127.4 [hep-ph] G2 Gauge Theory at Finite Baryon Density A. Maas, L.v.S., B. Wellegehausen & A. Wipf, arxiv: [hep-lat] Summary and outlook See also: L.v.S. in Physics at all scales: The Renormalization Group, the 49 th Schladming Winter School on Theoretical Physics, Nucl. Phys. B (PS) 228 (212) pp [arxiv: ] 23. September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 2

3 Phase Diagram critical point QCD triple point Water K. Heckmann, TU Darmstadt, Nov September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 3

4 QCD-like Theories Functional methods and effective models: compare with lattice simulations where there s no sign problem QCD at finite isospin density apply to ultracold fermi gases exploit analogies and polarised fermi gas at unitarity more experimental data graphene strongly correlated fermions in 2+1 dimensions QED 3 (semimetal-insulator transition, N f < 4), electronic properties of Graphene (half-filling, N f =2) SFB September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 4

5 Fermion-Sign Problem Dirac operator: D(µ) =γ µ ( µ + ia µ ) γ µ anti-hermitian Hermitian γ 5 D(µ) γ 5 = D( µ) or Det D(µ) =DetD( µ) in general, fermion-sign problem, except if: (a) anti-unitary symmetry TD(µ)T 1 = D(µ) T 2 = ±1 fermion color representation: Dyson index: (i) pseudo-real T =ΣCγ 5,T 2 =1 color, Σ 2 = 1 charge conjugation, C 2 = 1 two-color QCD B.-J. Schaefer s talk β =1 (ii) real T = Cγ 5,T 2 = 1 β =4 adjoint QCD, or G2-QCD later this talk 23. September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 5

6 Fermion-Sign Problem...except if: Det D(µ) =DetD( µ) Dyson index: (b) two degenerate flavors with isospin chemical potential Det D(µ I )D( µ I ) fermion determinant β =2 QCD at finite isospin density χpt: Silver Blaze: Lattice: NJL: Son & Stephanov, Phys. Rev. Lett. 86 (21) 592 Cohen, Phys. Rev. Lett. 91 (23) 2221 Kogut & Sinclair, Phys. Rev. D 7 (24) 9451; PoS LAT de Forcrand, Stephanov & Wenger, PoS LAT Detmold, Orginos & Shi, arxiv: He, Jin & Zhuang, Phys. Rev. D 71, (25) 1161 Mu, He & Liu, Phys. Rev. D 82 (21) August 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 6

7 Functional RG (Flow) Equations Effective action: Legendre transform Γ[φ j ]=(j, φ j ) ln Z[j] k k S IR k- k k UV k= 1PI vertex functions Γ (n) (x 1,...x n ) grand potential Ω(T,µ), at φ min = φ T,µ 2 k t = 1 k Γ k [φ] extended mean field (emf) bosons fermions Wetterich, Phys. Lett. B 31 (1993) September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 7

8 QM Model with Isospin Chemical Potential Nf = 2 quarks & mesons with Yukawa coupling: chemical potentials: µ µ I : µ I imbalance between up and down µ I µ : µ imbalance between up and anti-down µ =, map to QMD model for QC 2 D: N c : 3 2 (ψ u,ψ d ) (ψ r,τ 2 C ψ g ) µ I µ π +,π, π π 23. September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 8

9 Two-Color QCD QMD model phase diagram with collective baryonic fluctuations purely mesonic CEP diquark condensation 1 st order chiral transition and CEP at µ 2.5 m π no low-t 1 st order transition, no CEP at µ 2.5 m π! N. Strodthoff, B.-J. Schaefer & L.v.S., Phys. Rev. D85 (212) September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 9

10 Two-Color QCD QMD model phase diagram qq normalised quark and diquark condensates qq TCP µ/m π M q >µ: BEC-like M q µ: BCS-like T [MeV] Tricritical point predicted in: Splittorff, Toublan & Verbaarschot, Nucl. Phys. B 62 (22) 29 N. Strodthoff, B.-J. Schaefer & L.v.S., Phys. Rev. D85 (212) September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 1

11 QCD with Isospin Chemical Potential QM Model with fluctuating chiral & pion condensates χsb pion condensation need 2 fields in effective potential U = U(ρ 2,d 2 ),butreplaceρ 2 = σ 2 + π 2 and d 2 = 2 by ρ 2 = σ 2 + π 2 and d 2 = π π 2 2 = π + π K. Kamikado, N. Strodthoff, L.v.S. & J. Wambach, arxiv: September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 11

12 QCD with Isospin Chemical Potential T = isospin density - lattice QCD: Detmold, Orginos & Shi, arxiv: [hep-lat] 23. September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 12

13 QCD with Isospin Chemical Potential T = isospin density - lattice QCD: Detmold, Orginos & Shi, arxiv: [hep-lat] 23. September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 13

14 Baryon & Isospin Chemical Potential Fermionic flow (extended mean-field): µ[mev] Lee-Wick Chandrasekhar-Clogston 1 pion cond T = 1st order sigma 5 SB region TCP CEP µ I [m ] T[MeV] µ[mev] st pion cond 2nd pion cond TCP 1st order sigma SB region µ I [m ] Kamikado, Strodthoff, LvS & Wambach, arxiv: September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 14

15 Baryon & Isospin Chemical Potential Full mesonic flow (2 dimensional): T =: 4 T[MeV] st order sigma SB region second 1st order CEP pion cond. µ[mev] SB region pion cond. 1st order sigma second 1st order CEP µ I [m ] µ[mev] µ I [m ] Kamikado, Strodthoff, LvS & Wambach, arxiv: September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 15

16 Baryon & Isospin Chemical Potential Full mesonic flow (2 dimensional): T[MeV] st order sigma SB region second 1st order CEP pion cond. T [MeV] µ [MeV] µ I [m ] µ[mev] µ I [m ] Kamikado, Strodthoff, LvS & Wambach, arxiv: September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 16

17 Baryon & Isospin Chemical Potential Full mesonic flow (2 dimensional): T[MeV] µ= MeV 5 µ=15 MeV µ=2 MeV µ=25 MeV µ=3 MeV µ I [m ] T[MeV] µ[mev] st order sigma SB region second 1st order CEP pion cond µ I [m ] fixed µ I = m π µ for (up/anti-down) imbalance September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 17

18 Up-Antidown Population Imbalance Fermionic flow (extended mean-field): +µ q 25 2 µ I = m π Sarma crossover 2nd order 1st order µ q µ µ I I +µ q T [MeV] 15 1 µ q = pion condensation Sarma TCP µ q µ q [MeV] Chandrasekhar-Clogston 23. September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 18

19 Up-Antidown Population Imbalance Fermionic flow (extended mean-field): +µ q 25 2 µ I = m π Sarma crossover 2nd order 1st order µ q µ µ I I +µ q T [MeV] 15 1 µ q = pion condensation Sarma TCP compare: µ q Imbalanced Fermi Gases µ q [MeV] Chandrasekhar-Clogston Gubbels, Stoof, arxiv: September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 19

20 Up-Antidown Population Imbalance Full flow with mesonic fluctuations: 4 35 T [MeV] µ I = m π µ q = pion condensation Sarma crossover 1st order 2nd order Sarma CEP µ q [MeV] stable Sarma phase down to T = normal µ[mev] T [MeV] SB region pion cond. T = 5 1st order sigma second 1st order CEP µ I [m ] extended mean field superfluid Sarma crossover 2nd order 1st order Sarma normal µ q [MeV] 23. September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 2

21 Up-Antidown Population Imbalance Full flow with mesonic fluctuations: compare: Chiral Transition polarised fermi gas at unitarity µ I = m π Sarma crossover 1st order 2nd order Gubbels, Stoof, arxiv: Shin et al., Nature 451 (28) 689 T [MeV] µ q = normal pion condensation 4 2 CEP µ q [MeV] stable Sarma phase down to T = part. pol. superfluid near interface in fermi gases? Strodthoff & LvS, in preparation Sarma T [MeV] extended mean field superfluid Sarma crossover 2nd order 1st order Sarma normal µ q [MeV] 23. September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 21

22 G2 Gauge Theory at Finite Density G2 is real: Dirac operator D has antiunitary symmetry S, with S 2 = 1 (symplectic, β =4). Holland, Minkowski, Pepe & Wiese, Nucl. Phys. B 668 (23) 27 Wellegehausen, Wipf & Wozar, Phys. Rev. D 83 (211) Maas, LvS, Wellegehausen & Wipf, arxiv: no sign problem real and positive for single flavor: SU(2) U B (1) 2 Goldstone bosons: scalar (anti)diquarks breaks down to QCD O(3) symmetric effective potential U = U(φ 2 ) where φ =(σ, Re, Im ) diquark condensation as in QC2D but have fermionic baryons also as QCD with adjoint quarks coset: heavy gauge Higgs G 2 SU(3) G 2 /SU(3) SO(7)/SO(6) S 6 (7) (3) ( 3) (1) (14) (3) ( 3) (8) massive Higgs gluons 23. September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 22

23 G2 Gauge Theory at Finite Density phase diagram with 1 flavor dynamcial Wilson fermion Polyakov loop < >(T,µ)/< >(,) sat n B /n B P 2 1 Chiral condensate 1 Baryon number density 1 T [GeV].1 µ Quark [GeV] 2 T [GeV].1 µ Quark [GeV] 2 T [GeV].1 µ Quark Polyakov loop < >(T,µ)/< >(,) sat n B /n B T [GeV] T [GeV] T [GeV] [GeV] µ [GeV] Quark 2 µ [GeV] Quark 2 µ [GeV] Quark Maas, LvS, Wellegehausen & Wipf, arxiv: September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 23

24 G2 Gauge Theory at Finite Density finite baryon density (bosonic and fermionic) P 3 2 Finite-µ/T dependence µ µ Finite-µ/T dependence < >(T,µ)/< >(,) 1 T= sat n B /n B 1.5 Finite-µ/T dependence µ 1 T=98 MeV T=131 MeV µ [GeV] µ [GeV] µ [GeV] Maas, LvS, Wellegehausen & Wipf, arxiv: September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 24

25 G2 Gauge Theory at Finite Density onset of diquark condensation: µ phys in GeV n q Σ.5 µ m π /2 µ m π /2 n q vacuum BEC nuclear matter.998 Σ µ µ β Bjoern Wellegehausen, PhD thesis, Jena September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 25

26 Summary & Outlook Finite Isospin Density in QCD and Baryon Density in Two-Color QCD - detailed understanding of phase diagram - functional methods and models vs. lattice MC - analogies with ultracold fermi gases BEC-BCS crossover, population imbalance with universal phase diagram... Phase Diagram of G2 Gauge Theory - no sign problem fermionic baryons Fermions in 2+1 Dimensions - quantum phase transitions, transport properties, topological aspects... QCD Phase Diagram - refined functional methods & models, baryonic dofs, finite volume... Thank You for Your Attention! European Commission 23. September 212 Fachbereich 5 Institut für Kernphysik Lorenz von Smekal 26