The Phase Structure of the Polyakov Quark-Meson Model beyond Mean Field

Transcription

1 The Phase Structure of the Polyakov Quark-Meson Model beyond Mean Field Tina Katharina Herbst In Collaboration with B.-J. Schaefer and J.M. Pawlowski arxiv: [hep-ph] (to appear in Phys. Lett. B) Talk at the PhD Seminar WS21/11 Oktober 2, 21 Recipient of a DOC-fFORTE-fellowship of the Austrian Academy of Sciences at the Institute of Physics.

2 Outline: What we are interested in QCD Chiral Symmetry Confinement Fluctuations Effective Description Phase Structure

3 QCD Phase Structure Temperature early universe LHC quark gluon plasma RHIC SPS <ψψ> crossover FAIR/NICA <ψψ> = / vacuum hadronic fluid n B= n B> AGS SIS nuclear matter µ quark matter crossover superfluid/superconducting phases? 2SC <ψψ> = / CFL neutron star cores (approx.) Order Parameters chiral condensate ψψ { ψψ = symmetric broken Chiral Symmetry 1 Polyakov Loop Φ e βfq { = symmetric Φ broken σ/σ Φ Confinement

4 Additional Phases: Quarkyonic Matter [L. McLerran and R.D. Pisarski, Nucl.Phys. A796, 83-1 (27)] Large N c N c, g 2 N c fixed, N f fixed & small mesons: one quark anti-quark pair glueballs: pure glue states (no quarks or anti-quarks) baryons: N c quarks quark loops suppressed by 1/N c compared to gluon contributions

5 Additional Phases: Quarkyonic Matter [L. McLerran and R.D. Pisarski, Nucl.Phys. A796, 83-1 (27)] Large N c order parameter: pressure hadronic phase: O(Nc ) no baryons deconfined phase: O(Nc 2 ) T d (µ) = T d () quarkyonic phase: O(N c ) still confined

6 Additional Phases: Quarkyonic Matter [L. McLerran and R.D. Pisarski, Nucl.Phys. A796, 83-1 (27)] QCD N c = N f = 3: does this fulfill the requirement N c large, N f small? does the quarkyonic phase persist? our definition: confined (Φ ), chirally symmetric ( ψψ )

7 How we Approach these Issues

8 Hierarchy of Scales consider scalar and pseudoscalar mesons (rest integrated out) scale k 2 GeV : q, q, g ~ 2 GeV perturbative QCD k = k φ : compositeness scale k = k χ : ψψ = k = Λ QCD : quark confinement ~ 1 GeV ~.5 GeV ~.2 GeV bound states chiral symmetry breaking confinement k χ k k φ : around Λ QCD : quarks and mesons are most relevant dynamics dominated by Yukawa coupling gluonic interactions

9 Quark-Meson Model Lagrangian L QM = q [ i / h(σ + iγ 5 τ π) ] q ( µφ) 2 U(σ, π) U(Φ, Φ) φ = (σ, π)... O(4)-representation of the meson field (N f = 2) D/ (Φ) = γ µ µ i gγ A (Φ) g... gauge coupling h... Yukawa coupling Meson Potential U(σ, π) = λ 4 (σ2 + π 2 v 2 ) 2 cσ

10 Polyakov-Quark-Meson Model Lagrangian L PQM = q [ i /D h(σ + iγ 5 τ π) ] q ( µφ) 2 U(σ, π) U(Φ, Φ) φ = (σ, π)... O(4)-representation of the meson field (N f = 2) D/ (Φ) = γ µ µ i gγ A (Φ) g... gauge coupling h... Yukawa coupling Meson Potential U(σ, π) = λ 4 (σ2 + π 2 v 2 ) 2 cσ

11 Polyakov Loop Potential Polynomial Ansatz [C. Ratti, M.A. Thaler, W. Weise, Phys.Rev. D73, 1419 (26)] U(Φ, Φ) T 4 = b 2(T ) Φ Φ b (Φ3 + Φ 3 ) + b 4 4 (Φ Φ) 2 coefficients fitted to lattice data (pure glue): b 2 (T ) = a + a 1 T T «+ a 2 T T «2 «3 T + a 3 a a 1 a 2 a 3 b 3 b MeV (pure glue)? T = lower? not even constant? T

12 T (µ) - One Motivation: Experiment experimental information on the QCD phase diagram: chemical freezeout points not raw data, but interpretation using Statistical Model increase of entropy (red band) and density suggests position of phase transition PNJL computation with T = 2 MeV inconsistent (green band) polynomial ansatz for T (µ) greater overlap (blue band) [in these plots: N c = N f = 3] [K. Fukushima, arxiv: ]

13 T (µ) - Another Motivation: Theory FRG flow for QCD: [B.-J. Schaefer, J.M. Pawlowski, J. Wambach, Phys.Rev. D76, 7423 (27)] t Γ k [φ] = dynamical quarks modify the gluon contribution: gluons ghosts quarks mesons Polyakov Loop potential: from pure YM contribution t Γ k [φ] = 1 2 T T (N f, µ)

14 T (µ) - How To [B.-J. Schaefer, J.M. Pawlowski, J. Wambach, Phys.Rev. D76, 7423 (27)] [TKH, J.M. Pawlowski, B.-J. Schaefer, arxiv:18.81] T Λ QCD perturbative 1-loop estimate: β(α) = b(n f ) α 2 + O(α 3 ) µ HDL/HTL: b(n f ) b(n f, µ) T (N f, µ) = T τ e 1/(αb(N f,µ)) µ = : N f T [ MeV] [cf. work by J. Braun and H. Gies]

15 Why Functional Renormalization Group? describes physics on different scales phase transitions: fluctuations important FRG: include fluctuations systematically Flow Equation [C. Wetterich, 1993] t Γ k [ϕ] = 1 { ( ) } 1 2 Tr t R k Γ (2) k [ϕ] + R k R k... regulator Γ k scale dependent effective action

16 Functional Renormalization Group (FRG) Polyakov Quark-Meson Truncation Z Γ k = j d 4 x q (D/ + µγ + ih(σ + iγ 5 τ π)) q + 1 ff 2 ( µφ)2 + Ω k [σ, π, Φ, Φ] at initial scale Λ: Ω Λ [σ, π, Φ, Φ] = U(Φ, Φ) + U(σ, π) + Ω Λ [σ, π, Φ, Φ] t Γ k [φ] =

17 Functional Renormalization Group (FRG) Polyakov Quark-Meson Truncation Z Γ k = j d 4 x q (D/ + µγ + ih(σ + iγ 5 τ π)) q + 1 ff 2 ( µφ)2 + Ω k [σ, π, Φ, Φ] at initial scale Λ: Ω Λ [σ, π, Φ, Φ] = U(Φ, Φ) + U(σ, π) + Ω Λ [σ, π, Φ, Φ] tγ k[φ] = k Ω k Λ = N cn f k 4 3π 2 E q [ 1 Nq (Φ, Φ) N q (Φ, Φ) ] [J. Braun, K. Schwenzer, H.J. Pirner, Phys.Rev. D7, 8516 (24)] [V. Skokov, B. Stokic, B. Friman, Phys.Rev. C82, 1526 (21)]

18 PQM Flow Equation k Ω k (T, µ) = [TKH, J.M. Pawlowski, B.-J. Schaefer, arxiv:18.81] [V. Skokov, B. Stokic, B. Friman, Phys.Rev. C82, 1526 (21)] k 4 [ ( ) 3 Eπ 12π 2 coth + 1 ( ) Eσ coth E π 2T E σ 2T 2ν q E q { 1 Nq (T, µ; Φ, Φ) N q (T, µ; Φ, Φ) } ] N q(t, µ; Φ, Φ) = Φe (Eq µ)/t 2(Eq µ)/t + Φe Φe (Eq µ)/t + 3Φe 2(Eq µ)/t 3(Eq µ)/t + e N q(t, µ; Φ, Φ) N q(t, µ; Φ, Φ) q E π = qk 2 + 2Ω k, Eσ = k 2 + 2Ω k + 4σ2 Ω k, νq = 2Nc N f

19 What we Learned

20 Phase Structure T = 28 MeV const χ crossover CEP χ first order [TKH, J.M. Pawlowski, B.-J. Schaefer, arxiv:18.81]

21 Phase Structure T (µ), T () = 28 MeV χ crossover CEP χ first order [TKH, J.M. Pawlowski, B.-J. Schaefer, arxiv:18.81] [cf. work by Lisa Haas and Jan Pawlowski (phase diagram from QCD)]

22 Normalized Pressure [TKH, J.M. Pawlowski, B.-J. Schaefer, arxiv:18.81] χ crossover 5 CEP χ first order χ crossover 5 CEP χ first order µ = MeV µ = 15 MeV µ = 29 MeV µ = MeV µ = 15 MeV µ = 29 MeV p/p SB p/p SB

23 Normalized Pressure [TKH, J.M. Pawlowski, B.-J. Schaefer, arxiv:18.81] [B.-J. Schaefer, J.M. Pawlowski, J. Wambach, Phys.Rev. D76, 7423 (27)] 2 CEP 15 1 χ crossover 5 CEP χ first order CEP 1.8 µ = MeV µ = 15 MeV µ = 29 MeV p/p SB

24 Vicinity of the CEP [TKH, J.M. Pawlowski, B.-J. Schaefer, arxiv:18.81] χ crossover 5 CEP χ first order χ crossover 5 CEP χ first order T<T CEP T=T CEP T>T CEP T<T CEP T=T CEP T>T CEP.5.5 n q /µ n q /µ

25 Vicinity of the CEP [TKH, J.M. Pawlowski, B.-J. Schaefer, arxiv:18.81] χ crossover 5 CEP χ first order χ crossover 5 CEP χ first order T<T CEP T=T CEP T>T CEP T<T CEP T=T CEP T>T CEP χ q /µ χ q /µ

26 Summary PQM model beyond Mean Field quark-meson fluctuations included within FRG approach Important feature: back-reaction to gluonic sector T T (N f, µ) Modifications of the Phase Structure fluctuations push CEP downwards T (µ): chiral and deconfinement transitions coincide quarkyonic phase suppressed Thermodynamics agree well with lattice studies at µ = χ crossover 5 CEP χ first order