Functional renormalization group approach of QCD and its application in RHIC physics

Transcription

1 Functional renormalization group approach of QCD and its application in RHIC physics Wei-jie Fu Dalian University of Technology The Third Symposium on Theoretical Physics at Peking U. Dec. 2-3, 26 fqcd collaboration: J. Braun, L. Corell, A. Cyrol, WF, M. Leonhardt, M. Mitter, J.M. Pawlowski, M. Pospiech, F. Rennecke, N. Strodthoff, N. Wink Heidelberg, Dalian, Darmstadt Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec. 26 / 3

2 Outline Introduction 2 Functional renormalization group approach 3 QCD from FRG at vacuum 4 Spectral functions and transport properties 5 QCD phase structure and thermodynamics 6 Baryon number fluctuations 7 Summary and outlook 8 Backup Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

3 Heavy-ion collision Little Bang: High Energy Heavy Ion Collision Ions about to collide Ion collision Plasma formation Freeze out What we see Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

4 Heavy-ion collision Little Bang: High Energy Heavy Ion Collision Ions about to collide Ion collision Plasma formation Freeze out What we see Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

5 QCD phase structure A sketch of QCD phase diagram, taken from The Hot QCD White Paper, (25), arxiv: [nucl-ex] Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

6 QCD phase structure σ 2 κ Au+Au Collisions Net proton.4<p < 2 (GeV/c), y <.5 T 5% 5 % 3 4% 7 8% S σ A sketch of QCD phase diagram, taken Colliding Energy STAR Preliminary s NN (GeV) from The Hot QCD White Paper, (25), arxiv: [nucl-ex] Kurtosis and skewness of net-proton distributions measured at RHIC, taken from X. Luo (STAR), PoS CPOD24, 9 (24) Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

7 QCD phase structure σ 2 κ Au+Au Collisions Net proton.4<p < 2 (GeV/c), y <.5 T 5% 5 % 3 4% 7 8% S σ A sketch of QCD phase diagram, taken Colliding Energy STAR Preliminary s NN (GeV) from The Hot QCD White Paper, (25), arxiv: [nucl-ex] Kurtosis and skewness of net-proton distributions measured at RHIC, taken from X. Luo (STAR), PoS CPOD24, 9 (24) The experimental programme should be accompanied by reliable theoretical predictions for the above observables and their relation to the CEP are highly demanded. Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

8 Viscosity of QGP y z x,b Reaction Plane Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

9 Viscosity of QGP z y x,b Reaction Plane /s QCD, Functional Methods SU(3) YM, lattice SU(3) YM, lattice 2 HRG Meson Gas He H2O N2 AdS/CFT bound T-Tc Tc Courtesy by J.M. Pawlowski dn dyp dp dφ = 2π dn dyp dp ( + 2v 2 (p ) cos 2(φ ψ RP ) + ) Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

10 Functional renormalization group k k S IR k- k k UV k= Effective action at RG-scale k Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

11 Functional renormalization group k k S IR k- k k UV k= Effective action at RG-scale k Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

12 Functional renormalization group k k S IR k- k k UV k= Effective action at RG-scale k Dynamical hadronization Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

13 Flow equations for QCD Courtesy of M. Mitter Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

14 QCD at vacuum (hard QCD) gluon dressing /Z A Bowman et al., 4 Sternbeck et al., 6 FRG. p [GeV] quark propagator dressings Bowman et al., 5 /Z q M q. p [GeV] Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

15 QCD at vacuum (hard QCD) gluon dressing /Z A Bowman et al., 4 Sternbeck et al., 6 FRG. p [GeV] quark propagator dressings Bowman et al., 5 /Z q M q. p [GeV] running couplings α s p [GeV] α crit α c - Ac α q - Aq α A 3 (bosonized) 4-fermi-interactions RG-scale k [GeV] M. Mitter, J.M. Pawlowski, N. Strodthoff, PRD 9, 5435 (25) h 2 π /(2 m2 π ) λ η λ (S+P)- adj λ V-A λ V+A λ (V-A) adj λ (S-P)- λ(s-p)- adj λ (S+P)+ λ(s+p)+ adj Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

16 QCD at vacuum (easy QCD) quark mass pion mass sigma mass mass > k Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

17 QCD at vacuum (easy QCD) quark mass pion mass sigma mass mass > k êz A,k=p êz A,k=p J. Braun, L. Fister, J. M. Pawlowski, F. Rennecke, PRD 94,346 (26) F. Rennecke, PRD 92 (25) 762 Courtesy of F. Rennecke êz A,k=p Nf =, Sternbeck et al (25) Nf = 2, Sternbeck (25) Nf =, input Nf =2 Nf = 2, (vacuum polarization only) Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

18 Gluonic spectral functions 5 4 Transversal Propagator GT FRG: T = FRG: T =.36 Tc 3 FRG: T =.93 Tc FRG: T =.8 Tc Lattice: T = Lattice: T =.36 Tc 2 Lattice: T =.93 Tc Lattice: T =.8 Tc p[gev] chromo-magnetic T = MeV GeV Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec. 26 / 3

19 Gluonic spectral functions 5 4 Transversal Propagator GT FRG: T = FRG: T =.36 Tc 3 FRG: T =.93 Tc FRG: T =.8 Tc Lattice: T = Lattice: T =.36 Tc 2 Lattice: T =.93 Tc Lattice: T =.8 Tc p[gev] chromo-magnetic T = MeV GeV Fister, J.M. Pawlowski, arxiv:2.544 T =.44T c Haas, Fister, J.M. Pawlowski, PRD 9 (24) 9, 95 Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec. 26 / 3

20 Quark spectral functions (perturbative) A/p p = 5MeV T = 3MeV g = ReA/p ImA/p p = 5MeV p = MeV p [MeV] 3, p [MeV] p [MeV] 2 2, 2 C[MeV], Rec2 Imc , , p [MeV] p [MeV] p [MeV] ρa ρc..5 ρ [MeV ] p [MeV] p [MeV] p [MeV] WF, J.M. Pawlowski, N. Strodthof in preparation Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec. 26 / 3

21 Quark spectral functions (nonperturbative) ρ [MeV ] g =.5 T = 2MeV p = 5 MeV ρa ρc p = 5 MeV p = MeV p [MeV] p [MeV] p [MeV].2.2 g = ρa ρc.5.5 ρ [MeV ].5..5 T = 3MeV p = 5 MeV..5 p = 5 MeV..5 p = MeV p [MeV] p [MeV] p [MeV] WF, J.M. Pawlowski, N. Strodthof in preparation Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

22 Transport coefficients A B C D E F Kubo relation: ρ ππ(ω, p = ) η = lim ω 2 ω Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

23 Transport coefficients A B C D E F Kubo relation: ρ ππ(ω, p = ) η = lim ω 2 ω η/s result fit GRG/HTL lattice KSS T/T c Haas, Fister, J.M. Pawlowski, PRD 9 (24) 9, 95 Christiansen, Haas, J.M. Pawlowski, Strodthoff, PRL 5 (25), 22 Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

24 Low energy effective models and the truncations êz A,k=p êz A,k=p Nf =, Sternbeck et al (25) Nf = 2, Sternbeck (25) Nf =, input Nf =2 Nf = 2, (vacuum polarization only) Courtesy of F. Rennecke Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

25 Low energy effective models and the truncations 4 4 Nf =, Sternbeck et al (25) Nf = 2, Sternbeck (25) êz A,k=p êz A,k=p Nf =, input Nf =2 Nf = 2, (vacuum polarization t V q k = Z q q ZZ p,q p+q p q Courtesy of F. Rennecke WF, J. M. Pawlowski, F. Rennecke, B.-J. Schaefer, arxiv: For the matter part, we use the following truncations: { Γ k = Z q,k q(γ µ µ γ µ)q + x 2 Z φ,k( µφ) 2 ) } + h k q (T σ + iγ 5T π q + V k (ρ) cσ +, Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

26 Glue potential the glue part is approximated as a QCD-enhanced glue potential with V glue (L, L; t glue ) = V YM (L, L;.57 t glue ) a simple linear rescaling between Yang-Mills theory and QCD [L.M. Haas, R. Stiele, J. Braun, J.M. Pawlowski, J. Schaffner-Bielich, 23]: t YM (t glue ).57 t glue T 3 χ L this work 48 3 x x x8 Roessner et al. T 3 χ T this work 48 3 x x x8 Roessner et al.... T/T c T/T c P.M. Lo et al, PRD 88, 7452 (23) Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

27 Thermodynamics.8 Wuppertal-Budapest, 2 PQM FRG PQM emf PQM MF l,s reduced chiral condensate t Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

28 Thermodynamics l,s Wuppertal-Budapest, 2 PQM FRG PQM emf PQM MF (ε - 3P)/T Wuppertal-Budapest, 2 HotQCD N t =8, 22 HotQCD N t =2, 22 PQM FRG PQM emf+π PQM MF+π PQM emf reduced chiral condensate t Interaction measure t T.K. Herbst et al, PLB 73 (24) 248 Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

29 Thermodynamics l,s Wuppertal-Budapest, 2 PQM FRG PQM emf PQM MF (ε - 3P)/T Wuppertal-Budapest, 2 HotQCD N t =8, 22 HotQCD N t =2, 22 PQM FRG PQM emf+π PQM MF+π PQM emf reduced chiral condensate t Interaction measure t T.K. Herbst et al, PLB 73 (24) 248 (ε 3p)/T Nf = 2 full LPA (ε 3p)/T flavour LPA after rescale 2+ flavour LPA WB continuum limit T [MeV] WF, J.M. Pawlowski, Phys.Rev.D 92,66, T/T c Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

30 Phase structure T [MeV] µ B /T=2 Lattice: curvature range κ= DSE: chiral crossover DSE: critical end point DSE: deconfinement crossover µ B /T= µ q [MeV] 2+ flavor QCD T [MeV] 2 5 χ crossover σ(t=)/2 Φ crossover 5 Φ crossover χ st order CEP µ [MeV] m π =38 MeV QCD-enhanced 2-flavor PQM-model Fischer, Fister, Luecker, Pawlowski, PLB 732,273, 24 Qin, Chang, Chen, Liu, Roberts, PRL 6, 723, 2 Herbst, Pawlowski, Schaefer, PLB , 2; PRD 88 47, 23 Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

31 Baryon number fluctuations The baryon number fluctuations are given by χ B n = n p (µ B /T ) n T 4, they are related with the cumulants of baryon multiplicity distributions by, such as M = VT 3 χ B, σ 2 = VT 3 χ B 2, S = χ B 3 /(χ B 2 σ), κ = χ B 4 /(χ B 2 σ 2 ), mean value variance skewness kurtosis Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

32 Baryon number fluctuations.2.8 LPA full.2.8 LPA full WB continuum limit χ B 4 /χ B PQM χ B 4 /χ B T [MeV] T/Tc.5 χ B 4 /χ B present work results from [2] WB continuum limit T/Tc WF, J. M. Pawlowski, F. Rennecke, B.-J. Schaefer, arxiv: WF, J. M. Pawlowski, Phys.Rev.D 92,66,25 Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

33 Freeze-out line T (MeV) µ b (MeV) new fits (yields) dn/dy 4π parametrization 25 fits, dn/dy data ratios yields 2 s NN (GeV) µ B [MeV] from B from Q SHM model 2 s [GeV] Freeze-out chemical potential obtained from lattice simulations, taken from [S. Borsanyi et al. (24)] Freeze-out temperature and chemical potential obtained from the Statistical Hadronization Model, taken from [A. Andronic, P. Braun- Munzinger, J. Stachel, (29)] Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

34 Rescaling the chemical potential For the chemical potential, we use the following linear rescale: µ B,Nf =2 = T c,n f =2(µ B = ) T c,nf =2+(µ B = ) µ B,N f =2+, Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

35 Rescaling the chemical potential For the chemical potential, we use the following linear rescale: with µ B,Nf =2 = T c,n f =2(µ B = ) T c,nf =2+(µ B = ) µ B,N f =2+, T c,nf =2+(µ B = ) = 55 MeV being the pseudo-critical temperature at µ B = for flavour N f = 2 + from lattice simulations [S. Borsanyi et al. (2)]. This temperature also agrees with the freeze-out temperature [S. Borsanyi et al. (24)]. T c,nf =2(µ B = ) = 8 MeV is the pseudo-critical temperature at µ B = in our calculation. Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

36 Rescaling the chemical potential For the chemical potential, we use the following linear rescale: with µ B,Nf =2 = T c,n f =2(µ B = ) T c,nf =2+(µ B = ) µ B,N f =2+, T c,nf =2+(µ B = ) = 55 MeV being the pseudo-critical temperature at µ B = for flavour N f = 2 + from lattice simulations [S. Borsanyi et al. (2)]. This temperature also agrees with the freeze-out temperature [S. Borsanyi et al. (24)]. T c,nf =2(µ B = ) = 8 MeV is the pseudo-critical temperature at µ B = in our calculation. s [GeV] µ B,Nf =2 [MeV] µ B,Nf =2 corresponding to different collision energy. Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

37 Correlating the skewness and kurtosis of baryon number distributions We employ the skewness Sσ obtained in experiments to determine the freeze-out temperature in our calculations, then use this temperature to obtain the kurtosis κσ 2 of the baryon number distributions. Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

38 Correlating the skewness and kurtosis of baryon number distributions We employ the skewness Sσ obtained in experiments to determine the freeze-out temperature in our calculations, then use this temperature to obtain the kurtosis κσ 2 of the baryon number distributions. This approach is equivalent to inputing Sσ in our theoretical calculations, and then outputing κσ 2, that can be compared with experimental results. Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

39 Correlating the skewness and kurtosis of baryon number distributions We employ the skewness Sσ obtained in experiments to determine the freeze-out temperature in our calculations, then use this temperature to obtain the kurtosis κσ 2 of the baryon number distributions. This approach is equivalent to inputing Sσ in our theoretical calculations, and then outputing κσ 2, that can be compared with experimental results. In the same time, this approach correlates two important quantities of non-gaussian distributions, and emphasise the relation between them. Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

40 Correlating the skewness and kurtosis of baryon number distributions s = 2 [GeV] s = 62.4 [GeV] s = 39 [GeV] Sσ, κσ Sσ κσ T [MeV] T [MeV] T [MeV] s = 27 [GeV].2 s = 9.6 [GeV] 2 s =.5 [GeV].5 Sσ, κσ T [MeV] T [MeV] T [MeV] 5 4 Sσ, κσ 2 s = 7.7 [GeV] T [MeV] WF, J. M. Pawlowski, Phys.Rev.D 93,95(R),26 Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

41 Effects of the full frequency dependence of the quark dispersion.2.2 µb = MeV µb = 222 MeV.8.8 χ B 4 /χb χ B 4 /χb with frequency dependence without µb = 343 MeV T [MeV].2 2 µb = 459 MeV T [MeV] WF, J. M. Pawlowski, F. Rennecke, B.-J. Schaefer, arxiv: Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

42 Comparison with experimental measurements.5 5% centrality at STAR 5 % FRG based on Tf(χ B 2 /χ B ) 3 2 FRG based on Tf(χ B 3 /χ B 2 ) FRG based on Tf(χ B 2 /χ B ) Sσ κσ s [GeV] -3 s [GeV] κσ 2 5% centrality at STAR 5 % present work results from [2] without frequency dependence s [GeV] WF, J. M. Pawlowski, F. Rennecke, B.-J. Schaefer, arxiv: WF, J. M. Pawlowski, Phys.Rev.D 92,66,25 Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

43 Summary and outlook In this talk, I introduce the FRG approach and its development and application in vacuum QCD and RHIC physics. Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

44 Summary and outlook In this talk, I introduce the FRG approach and its development and application in vacuum QCD and RHIC physics. First-principle FRG QCD calculations have been done, which agree very well with lattice QCD. Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

45 Summary and outlook In this talk, I introduce the FRG approach and its development and application in vacuum QCD and RHIC physics. First-principle FRG QCD calculations have been done, which agree very well with lattice QCD. QCD thermodynamics, phase diagram, QGP transport properties, baryon number fluctuations are investigated within the FRG approaches, interesting results are obtained. Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

46 Summary and outlook First-principle FRG QCD calculations at finite temperature, and in particular at large chemical potential are highly demanded. Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

47 Summary and outlook First-principle FRG QCD calculations at finite temperature, and in particular at large chemical potential are highly demanded. Comparisons with experiments are important, e.g., for the baryon number fluctuations, an obvious discrepancy, between the theory and experiment, develops when the colliding energy is less than 9.6 GeV. Glue fluctuations play an important role in this regime. Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

48 Summary and outlook First-principle FRG QCD calculations at finite temperature, and in particular at large chemical potential are highly demanded. Comparisons with experiments are important, e.g., for the baryon number fluctuations, an obvious discrepancy, between the theory and experiment, develops when the colliding energy is less than 9.6 GeV. Glue fluctuations play an important role in this regime. We are working in these directions. Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

49 Summary and outlook First-principle FRG QCD calculations at finite temperature, and in particular at large chemical potential are highly demanded. Comparisons with experiments are important, e.g., for the baryon number fluctuations, an obvious discrepancy, between the theory and experiment, develops when the colliding energy is less than 9.6 GeV. Glue fluctuations play an important role in this regime. We are working in these directions. Thank you for your attentions! Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

50 hard QCD truncations - FRG Yang-Mills results - mom. dep. classical tensor structure mom. dep. classical tensor structure - full mom. dep. all tensor structures mom. dep. full mom. dep. STI-consistent dressing Fierz-complete basis at p = and mom. dep. - mom. dep. full effective... potential mom. dep. Courtesy of M. Mitter Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

51 Thermodynamics: quark-meson model.2 fπ [MeV] LPA LPA LPA + hk full ρ,k=/ T [fm ] T [MeV] T [MeV] p/psb LPA LPA LPA + hk full s/ssb T [MeV] T [MeV] Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

52 Baryon number fluctuations: quark-meson model χ B LPA LPA LPA + hk full χ B T [MeV] T [MeV] Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

53 Baryon number fluctuations: quark-meson model χ B LPA LPA LPA + hk full χ B T [MeV] T [MeV].2 χ B 4 /χb LPA LPA LPA + hk full T [MeV] Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

54 Baryon number fluctuations: QCD-enhanced Polyakov quark-meson model.2. χ B 2.5. LPA full χ B PQM T [MeV] T [MeV] Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3

55 Baryon number fluctuations: QCD-enhanced Polyakov quark-meson model.2. χ B 2.5. LPA full χ B PQM T [MeV] T [MeV].2.8 LPA full.2.8 LPA full WB continuum limit χ B 4 /χ B 2.6 χ B 4 /χ B PQM T [MeV] T/Tc Wei-jie Fu (DUT) FRG and its application in RHIC Beijing, Dec / 3