Towards thermodynamics from lattice QCD with dynamical charm Project A4

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1 Towards thermodynamics from lattice QCD with dynamical charm Project A4 Florian Burger Humboldt University Berlin for the tmft Collaboration: E.-M. Ilgenfritz (JINR Dubna), M. Müller-Preussker (HU Berlin), M. P. Lombardo (INFN Frascati), C. Urbach (Uni Bonn), O. Philipsen, C. Pinke, L. Zeidlewicz (Uni Frankfurt) SFB Final Meeting Durbach Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, 2 22 / 26

2 Motivation 2 Location of Crossover 3 Chiral Scenarios 4 Gauge variant T > propagators 5 Thermodynamic Equation of State Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / 26

3 Outline Motivation 2 Location of Crossover 3 Chiral Scenarios 4 Gauge variant T > propagators 5 Thermodynamic Equation of State Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / 26

4 QCD Phase Diagram in the µ B -T plane QGP description includes relativistic hydrodynamics ɛ = (ɛ + p)( u), ṅ B = n B ( u), u µ = µ p ɛ + p plus : EoS EoS accessible on the lattice (at n B ) Aims of tmft Collaboration: - Investigation of the crossover regime: T c vs. m π - Investigation of temperature dependence of gauge-variant propagators and vertices, screening lengthes, topology,... - Determination of EoS with N f = 2 (since 29) and N f = (since 23) Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / 26

5 EoS: Current Status N f = 2 + : Most results based on staggered quarks (physical point) Until recently: differences in EoS by Budapest-Wuppertal and hotqcd resolved Wilson fermions: WHOT-QCD with fixed scale approach N f = 2: Only results at large quark masses and coarse discretizations available. N f = : Efforts started recently with staggered quarks (MILC, Budapest-Wuppertal) Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / 26

6 Twisted Mass Lattice Regularization N f = 2 light sector: S l [U, χ, χ] = x χ(x) ( D W [U] + iaµγ 5 τ 3 + am ) χ(x) N f = + heavy sector: S h [U, χ h, χ h ] = x χ h (x) ( D W [U] + iaµ σ γ 5 τ + aµ δ τ 3 + am ) χh (x) Advantages: at maximal twist κ (2am + 8) = κ c : - Automatic O(a) improvement - Simplified renormalization Disadvantage: explicit flavor symmetry breaking Improved gauge sector: S g [U] = β (c [ 3 ReTr (U P)] + c [ ) 3 ReTr (U R)] P Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / 26 R

7 Simulation Setup N f = 2: Phase space in (β, κ, µ) explored in [PRD8:9452, 29] Simulations: β-scans parallel to κ c (β), µ adapted for m π = const rely on κ c (β), a(β) and m π ± from ETM Collaboration Four pion masses (3 MeV m PS 65 MeV), several N τ N f = : Fixed scale approach: Change N τ for varying temperature T = N τ a(β) Three pion masses (22 MeV m π 4 MeV), µ m π, up to three lattice spacings a strange and charm approximately physical, (µ σ, µ δ ) (m K, m D ) Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / 26

8 Outline Motivation 2 Location of Crossover 3 Chiral Scenarios 4 Gauge variant T > propagators 5 Thermodynamic Equation of State Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / 26

9 Observables Polyakov-Loop L: Order Parameter for m q : ( Re (L) = Nτ 3 ReTr τ= ) { T = U (τ) = > T > T c Chiral Condensate ψψ : Order Parameter for m q : ψψ = Tr ( D ) { > T = = T > T c Intermediate m q : look at fluctuations (susceptibilities), expect maximum around T c Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / 26

10 Results Renormalization Renormalized Polyakov-Loop via: Re(L) R = Re(L) exp (V (r )/2T ) Static potential V (r) from interpolations at T = 2.5 Re(L) R Nσ = 24, Nτ = 2 Re(L) R N f = 2 Nσ = 32, Nτ = 2 Nτ = Nτ = 8 Nτ = 6 Nτ = Nf =2++, a.86 Nf =2++, a.78 Nf =2++, a.6 Nf = 2, Nτ = N f = Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, 2 22 / 26

11 Results: Renormalization ψψ in tmlqcd: ψψ ren = Z P ( χiγ5 τ 3 χ bare + µ c P(β) a 2 ) +... N f = 2 renormalized via: R ψψ = ψψ (T,µ) ψψ (,µ) ψψ (,) + R ψψ.5 Nf =2++, a.86 Nf =2++, a.78 Nf =2++, a.6 Nf = 2, Nτ = Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, 2 22 / 26

12 Results: Renormalization ψψ in tmlqcd: ψψ ren = Z P ( χiγ5 τ 3 χ bare + µ c P(β) a 2 ) +... N f = renormalized via: l,s = ψψ l µ l µs ψψ s ψψ T = l µ l ψψ T = µs s.2.8 Nf =2++, a.86 Nf =2++, a.78 Nf =2++, a.6 l,s Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / 26

13 Results: Suszeptibility of ψψ σ ψψ = V /T ( ψψ 2 ψψ 2) σ 2 ψψ /T N f = 2 Nσ = 24, Nτ = 2 Nσ = 32, Nτ = 2 Nτ = Nτ = 8 Nτ = σ 2 ψψ Nf =2++, a.86 Nf =2++, a.78 Nf = 2, Nτ = N f = Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / 26

14 Outline Motivation 2 Location of Crossover 3 Chiral Scenarios 4 Gauge variant T > propagators 5 Thermodynamic Equation of State Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / 26

15 QCD Phase Diagram at µ B = m tric s ms O(4)? phys. pt. st Nf = 2 Nf = 2 + Nf = 3 Z(2) Z(2) Crossover mud st Nf = pure gauge Symmetries suggest continuum QCD with m s to be in universality class of 3d O(4) magnetic spin model - but other scenarios still possible If 2 nd order O(4) Order parameter should show universal behaviour Previous results compatible with O(4) (or O(2)) universality class for N f = 2 and N f = 2 + (e. g. S. Ejiri et al. [arxiv:99.522]) Other discretizations of QCD help checking systematics and universality! Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / 26

16 Comparison of Chiral Scenarios [tmft, 23] T c (MeV) 2 8 st order Z(2) m π,c = 2 MeV 6 m π,c = MeV O(4) m π (MeV) 2/( βδ) In the chiral limit expect: T c (m π ) = T χ (m π = ) + A mπ Scenarios: 2 nd order O(4), st order (possibly ending in Z(2) endpoint) All do reasonably well can not discriminate with present masses For O(4) scenario: T χ (m π = ) = 52(26) MeV Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / 26

17 Outline Motivation 2 Location of Crossover 3 Chiral Scenarios 4 Gauge variant T > propagators 5 Thermodynamic Equation of State Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / 26

18 Landau Gauge Gluon- and Ghost propagator Non-perturbative gauge-variant Greens-Functions are valuable input for continuum approaches to QCD such as DS and FRG equations Landau gauge Gluon and Ghost studied in the crossover region for N f = 2 (here for 4 coupling or T -values) [Aouane et al., 23] unren. dressing functions: ZT ZL J(q) q[gev] Check for lattice artefacts for selected temperatures for longit. gluon dressing function q[gev] Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / 26 q[gev] transverse gluon longitudinal gluon ghost Z L ren q [GeV] T 24 MeV Nτ = 8 Nτ = Nτ =

19 Outline Motivation 2 Location of Crossover 3 Chiral Scenarios 4 Gauge variant T > propagators 5 Thermodynamic Equation of State Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / 26

20 Standard Integral Method Interaction Measure (Trace Anomaly): I = ɛ 3p = T d ln Z... V d ln a sub... T >... T = sub Starting point for p(t ) and ɛ(t ) via I T 4 = T ( p ) T T 4 on lines of constant physics (LCP) Signal /N 4 τ! p T 4 p T 4 = T T dτ ɛ 3p τ 5 LCP Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / 26

21 Trace Anomaly, Evaluation for N f = 2 tmlqcd ɛ 3p T 4 = T d ln Z VT 4 d ln a ( = a dβ ) Nτ 4 da sub ( c 3 ReTrU P sub + c 3 ReTrU R sub ( ) ( ) (am ) (aµ) χχ β sub χiγ5 τ 3 χ ) β sub }{{} O(a 2 ) β-function: ( a dβ da ) = ( r χ a ) ( ) d( rχ a ) dβ subtracted expectation values need interpolations for T = data rχ/a Interpolation β Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / 26

22 Trace Anomaly Results N f = 2, preliminary m π 37 MeV 22: ǫ 3p T 4 N τ = 2 N τ = N τ = 8 N τ = : ǫ 3p T 4 N τ = 2 N τ = N τ = 8 N τ = 6 N τ = Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / 26

23 EoS Results N f = 2, preliminary m π 37 MeV m π 44 MeV m π 65 MeV ǫ 3p T 4 Interpolation Nτ = 2 Nτ = Nτ = 8 Nτ = 6 Nτ = ǫ 3p T 4 Interpolation Nτ = 2 Nτ = Nτ = 8 Nτ = 6 Nτ = ǫ 3p T 4 Interpolation Nτ = Nτ = 8 Nτ = T Tc.5 2 T Tc.5 T Tc 2 (ǫ 3p)/T 4 ǫ/t 4 3p/T 4 3pSB/T 4 2 (ǫ 3p)/T 4 ǫ/t 4 3p/T 4 3pSB/T 4 2 (ǫ 3p)/T 4 ǫ/t 4 3p/T 4 3pSB/T B mass C mass D mass Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / 26

24 Trace Anomaly (gauge part) N f = 2 + +, preliminary m π 4 MeV 5 5 I/T 4, gauge part N f = 2++ : a.86 Ns = 32, a.78 Ns = 24, a.78 a.6 N f = 2 : Nτ = β-functions obtained from global fits to ETMC hadron mass data: β Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / a d(aµδ) da a d(aµσ) da a d(aµ) da a dβ da A6.24 B55.32 D45.32

25 Summary With present pion masses not able to distinguish chiral scenarios Landau gauge gluon- and ghost propagators as input for DSE/FRG gauge-variant vertices, screening lengthes, topology under investigation EoS for N f = 2 close to finished N f = yet progressing Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / 26

26 Thank you Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / 26

27 χχ in tmlqcd a 3 Z χχ χχ sub = a3 χχ + r Z r + ar Z r S 5 ( + ra 2 Z r S 6 + ) S O(a 3 ). ǫ 3p T 4 (m derivative) 2 - Nτ 8 T = 362 MeV uncorrected /Nτ 2 T = 245 MeV Florian Burger (HU Berlin) Thermodynamics with Wilson tm fermions March, / 26