Baryon number fluctuations within the functional renormalization group approach

Transcription

1 Baryon number fluctuations within the functional renormalization group approach Wei-jie Fu Dalian University of Technology The Third Symposium on Chiral Effective Field Theory, Oct. 28-Nov. 2, 26 talk based on: WF, J. M. Pawlowski, F. Rennecke, B.-J. Schaefer, arxiv: [hep-ph] WF, J. M. Pawlowski, Phys.Rev.D 93,95(R),26 WF, J. M. Pawlowski, Phys.Rev.D 92,66,25 fqcd collaboration: J. Braun, A. Cyrol, L. Fister, WF, T.K. Herbst, M. Mitter, N. Mueller, J.M. Pawlowski, S. Rechenberger, F. Rennecke, N. Strodthoff Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct. 26 / 2

2 Outline Introduction 2 Functional renormalization group approach 3 Low energy effective models and our truncations 4 Thermodynamics 5 Baryon number fluctuations 6 Comparison with experiments 7 Summary and outlook 8 Backup Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2

3 Introduction A sketch of QCD phase diagram, taken from The Hot QCD White Paper, (25), arxiv: [nucl-ex] Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2

4 Introduction 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), arxiv: [nucl-ex] Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2

5 Introduction 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), arxiv: [nucl-ex] 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) Baryon number fluctuations within FRG Guilin, Oct / 2

6 Introduction 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), arxiv: [nucl-ex] The experimental programme should be accompanied by reliable theoretical predictions for the above observables and their relation to the CEP are highly demanded. In this talk, I will present our theoretical results, based on a QCD-improved low energy effective model. Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2

7 Functional renormalization group Effective action at RG-scale k Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2

8 Functional renormalization group Effective action at RG-scale k Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2

9 Functional renormalization group Effective action at RG-scale k Dynamical hadronization Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2

10 FRG to QCD (two representative results) J. Braun, L. Fister, J. M. Pawlowski, F. Rennecke, PRD 94,346 (26), arxiv:42.45 [hep-ph] Γ q - q (p) Bowman et al., 5 /Z q M q gluon dressing /Z A Bowman et al., 4 Sternbeck et al., 6 FRG. p [GeV]. p [GeV] M. Mitter, J.M. Pawlowski, N. Strodthoff, PRD 9, 5435 (25), arxiv: [hep-ph] Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2

11 Low energy effective models and our truncations J. Braun, L. Fister, J. M. Pawlowski, F. Rennecke, PRD 94,346 (26), arxiv:42.45 [hep-ph] Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2

12 Low energy effective models and our truncations J. Braun, L. Fister, J. M. Pawlowski, F. t V q k = Z q q ZZ p,q p+q p q PRD 94,346 (26), arxiv:42.45 [hep-ph] 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) Baryon number fluctuations within FRG Guilin, Oct / 2

13 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, B. Friman, O. Kaczmarek, K. Redlich, C. Sasaki, PRD 88, 7452 (23), arxiv: [hep-lat] Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2

14 Thermodynamics p/t full LPA s/t T/Tc T/Tc (ε 3p)/T Nf = 2 full LPA (ε 3p)/T flavour LPA after rescale 2+ flavour LPA WB continuum limit T/T c Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2

15 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) Baryon number fluctuations within FRG Guilin, Oct / 2

16 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/Tc χ B 4 /χ B present work results from [2] WB continuum limit T/Tc Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct. 26 / 2

17 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) Baryon number fluctuations within FRG Guilin, Oct. 26 / 2

18 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) Baryon number fluctuations within FRG Guilin, Oct / 2

19 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) Baryon number fluctuations within FRG Guilin, Oct / 2

20 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) Baryon number fluctuations within FRG Guilin, Oct / 2

21 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) Baryon number fluctuations within FRG Guilin, Oct / 2

22 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) Baryon number fluctuations within FRG Guilin, Oct / 2

23 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) Baryon number fluctuations within FRG Guilin, Oct / 2

24 Correlating the skewness and kurtosis of baryon number distributions s = 2 [GeV] s = 62.4 [GeV] s = 39 [GeV] Sσ, κσ Sσ κσ s = 27 [GeV].2 s = 9.6 [GeV] 2 s =.5 [GeV].5 Sσ, κσ Sσ, κσ s = 7.7 [GeV] Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2

25 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 µb = 459 MeV Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2

26 Comparison with experimental measurements.5 3 5% centrality at STAR 5 % FRG based on Tf(χ B 2 /χ B ) 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] Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2

27 Summary and outlook The improved truncations also leads to a better agreement with lattice simulations at vanishing chemical potential. Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2

28 Summary and outlook The improved truncations also leads to a better agreement with lattice simulations at vanishing chemical potential. Our calculated results agree with the experimental measurements up to errors, for the colliding energy s 9.6 GeV. Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2

29 Summary and outlook The improved truncations also leads to a better agreement with lattice simulations at vanishing chemical potential. Our calculated results agree with the experimental measurements up to errors, for the colliding energy s 9.6 GeV. An obvious discrepancy, between the theory and experiment, develops when the colliding energy is less than 9.6 GeV. Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2

30 Summary and outlook Dynamical hadronization and glue fluctuations are indispensable to push up the initial scale of flows. Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2

31 Summary and outlook Dynamical hadronization and glue fluctuations are indispensable to push up the initial scale of flows. We are working in this direction. Thank you for your attentions! Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2

32 Thermodynamics: quark-meson model.2 fπ [MeV] LPA LPA LPA + hk full ρ,k=/ T [fm ] p/psb LPA LPA LPA + hk full s/ssb Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2

33 Baryon number fluctuations: quark-meson model χ B LPA LPA LPA + hk full χ B Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2

34 Baryon number fluctuations: quark-meson model χ B LPA LPA LPA + hk full χ B χ B 4 /χb LPA LPA LPA + hk full Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2

35 Baryon number fluctuations: QCD-enhanced Polyakov quark-meson model.2. χ B 2.5. LPA full χ B PQM Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2

36 Baryon number fluctuations: QCD-enhanced Polyakov quark-meson model.2. χ B 2.5. LPA full χ B PQM LPA full.2.8 LPA full WB continuum limit χ B 4 /χ B 2.6 χ B 4 /χ B PQM T/Tc Wei-jie Fu (DUT) Baryon number fluctuations within FRG Guilin, Oct / 2