Chiral restoration and deconfinement in two-color QCD with two flavors of staggered quarks

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1 Chiral restoration and deconfinement in two-color QCD with two flavors of staggered quarks David Scheffler, Christian Schmidt, Dominik Smith, Lorenz von Smekal Motivation Effective Polyakov loop potential Chiral properties Summary and outlook 23/8/2 Lattice 23 D. Scheffler

Motivation effective Polyakov loop potential influence of quarks on Polyakov loop potential compare to effective model descriptions two-color QCD as QCD-like theory where finite density is accessible

2 Motivation effective Polyakov loop potential influence of quarks on Polyakov loop potential compare to effective model descriptions two-color QCD as QCD-like theory where finite density is accessible chiral properties scale setting scaling behavior T (MeV) T [MeV] µa Hadronic BEC? QGP Quarkyonic <qq> <L> BCS? µ q (MeV) Boz, Cotter, Fister, Mehta, Skullerud [ ] Nτ µ [m π ] Φ infl. pt. Φ susc. σ half value Φ half value diquark cond. Strodthoff, von Smekal [ ] /8/2 Lattice 23 D. Scheffler 2

3 Effective Polyakov loop potential per-site probability distribution P(l) via histogram per-site constraint effective potential: V (l) = log P(l) obtain the actual per-site effective potential via Legendre transform W (h) = log dl exp V (l) + hl V eff (ˆl) = sup ˆlh W (h) h 23/8/2 Lattice 23 D. Scheffler 3

4 Polyakov Loop distributions and effective potentials at β = Nt=2 T/Tc=.83 Nt= T/Tc=. Nt=8 T/Tc=.25 Nt=6 T/Tc= Nt=2 T/Tc=.83 Nt= T/Tc=. Nt=8 T/Tc=.25 Nt=6 T/Tc= P(L).5.4 V_(L) L L pure gauge results by Smith, Dumitru, Pisarski, von Smekal [ ] fixed scale 23/8/2 Lattice 23 D. Scheffler 4

5 Polyakov Loop distributions and effective potentials at β = Nt=2 T/Tc=.83 Nt= T/Tc=. Nt=8 T/Tc=.25 Nt=6 T/Tc= Nt=2 T/Tc=.83 Nt= T/Tc=. Nt=8 T/Tc=.25 Nt=6 T/Tc= Veff(L) 3 V_(L) L L pure gauge results by Smith, Dumitru, Pisarski, von Smekal [ ] fixed scale 23/8/2 Lattice 23 D. Scheffler 4

6 Polyakov Loop distributions at β = Nt=2 T/Tc=.83 Nt= T/Tc=. Nt=8 T/Tc=.25 Nt=6 T/Tc=.67.6 P(L) dotted: am=. dashed: am=.5 solid: pure gauge L add N f = 2 staggered quarks β = neglect scale change through quark masses 23/8/2 Lattice 23 D. Scheffler 5

7 Polyakov Loop effective potential at β = Nt=2 T/Tc=.83 Nt= T/Tc=. Nt=8 T/Tc=.25 Nt=6 T/Tc=.67 2 V_(L).5 dotted: am=. dashed: am=.5 solid: pure gauge L β = /8/2 Lattice 23 D. Scheffler 6

8 Polyakov Loop effective potential at β = Nt=2 T/Tc=.83 Nt= T/Tc=. Nt=8 T/Tc=.25 Nt=6 T/Tc=.67 4 Veff(L) 3 2 dotted: am=. dashed: am=.5 solid: pure gauge L 23/8/2 Lattice 23 D. Scheffler 7

9 Modeling the distributions and potentials Fit coefficients at β = pure gauge: for T T c : Vandermonde potential: V (T c) (l) = 2 log( l2 ) C P (Tc) (l) = 2 l 2 π ansatz for T > T c : V (l) = V (T c) (l) + a(t) b(t)l + c(t)l 2 Nt=6, Ns=24, ma=., = Nt=2, Ns=48, ma=.5, = data fit data fit.8.8 distribution P(l).6.4 distribution P(l) Polyakov loop l 23/8/2 Lattice 23 D. Scheffler Polyakov loop l

10 Modeling the distributions and potentials Fit coefficients at β = pure gauge: for T T c : Vandermonde potential: V (T c) (l) = 2 log( l2 ) C P (Tc) (l) = 2 l 2 π ansatz for T > T c : V (l) = V (T c) (l) + a(t) b(t)l + c(t)l 2..8 pure gauge ma=.5 ma= fit coefficient a.6.4 fit coefficient b fit coefficient c T/Tc T/Tc T/Tc β = /8/2 Lattice 23 D. Scheffler 8

11 Chiral properties Simulation setup N f = 2 staggered quarks via RHMC N t = 4, 6, 8 with aspect ratio N s /N t = 4 several masses am =.5,.,.2,.,... finite temperature: vary β symmetry breaking continuum: SU(2N f ) Sp(N f ) staggered: SU(2N f ) O(2N f ), here: SU(4) O(6) O(4) 23/8/2 Lattice 23 D. Scheffler 9

12 Order parameters Nt=4 Ns=6 Nt=4 Ns= m/t=.2 m/t=.4 m/t=.8 m/t= m/t=.2 m/t=.4 m/t=.8 m/t=.4 chiral condensate Polyakov loop /8/2 Lattice 23 D. Scheffler

13 Order parameters Nt=6 Ns=24 Nt=6 Ns= m/t=.3 m/t=.6 m/t=.2 m/t= m/t=.3 m/t=.6 m/t=.2 m/t=.6 chiral condensate Polyakov loop /8/2 Lattice 23 D. Scheffler

14 Order parameters Nt=8 Ns=32 Nt=8 Ns=32 chiral condensate m/t=.4 m/t=.6 m/t=.6 m/t=.8 Polyakov loop m/t=.4 m/t=.6 m/t=.6 m/t= /8/2 Lattice 23 D. Scheffler 2

15 Chiral susceptibilities Nt=4 Ns=6 Nt=6 Ns=24 Nt=8 Ns=32 chiral susceptibility m/t=.2 m/t=.4 m/t=.8 m/t=.4 chiral susceptibility m/t=.3 m/t=.6 m/t=.2 m/t=.6 chiral susceptibility m/t=.4 m/t=.6 m/t=.6 m/t= /8/2 Lattice 23 D. Scheffler 3

16 Chiral susceptibilities 6 Nt=4 Ns=6, am=.5 chiral susceptibility data from F-S reweighting /8/2 Lattice 23 D. Scheffler 3

17 Temperature scale Nt=4 Nt=6.85 Nt=8 fits chiral extrapolation m/t β pc (m, N t ) = β c (N t ) + b am c 23/8/2 Lattice 23 D. Scheffler 4

18 Temperature scale Nt=4 Nt=6.85 Nt=8 fits chiral extrapolation m/t Nt β pc (m, N t ) = β c (N t ) + b am c 23/8/2 Lattice 23 D. Scheffler 4

19 Temperature scale leading scaling behavior: T = exp {b(β β c )} T c data fit 2. Nt= Nt=6 From linear fit: b = Nt= log(nt/4) 23/8/2 Lattice 23 D. Scheffler 5

20 magnetic scaling χ max m /δ chiral susceptibility / T^2 Nt=4 Nt=6 Nt=8 fits delta = (7) 5.(4).. m/t 23/8/2 Lattice 23 D. Scheffler 6

21 Summary and outlook Summary unquenched effective Polyakov loop potentials began scale setting and determine critical exponents Outlook continue: chiral properties need more work, especially at N t = 8 main goal: effective Polyakov loop potentials at finite density possible direction: adjoint representation 23/8/2 Lattice 23 D. Scheffler 7

22 Backup Slides 23/8/2 Lattice 23 D. Scheffler 8

23 Fixed scale parameters pure gauge analysis: Smith, Dumitru, Pisarski, von Smekal [hep-lat/ ] β a σ N t T/T c T(N t ) = N t a β am /8/2 Lattice 23 D. Scheffler 9

24 Polyakov Loop distributions at β = Nt=2 T/Tc=. Nt= T/Tc=.2 Nt=8 T/Tc=.5 Nt=6 T/Tc=2..6 P(L) dotted: am=.83 dashed: am=.44 solid: pure gauge L β = /8/2 Lattice 23 D. Scheffler 2

25 Polyakov Loop effective potential at β = Nt=2 T/Tc=. Nt= T/Tc=.2 Nt=8 T/Tc=.5 Nt=6 T/Tc=2. 2 V_(L).5 dotted: am=.83 dashed: am=.44 solid: pure gauge L β = /8/2 Lattice 23 D. Scheffler 2

26 Fit coefficients at β = pure gauge ma=.44 ma= fit coefficient a.6.4 fit coefficient b fit coefficient c T/Tc T/Tc T/Tc V (l) = V (T c) (l) + a(t) b(t)l + c(t)l 2 β = /8/2 Lattice 23 D. Scheffler 22

27 Finite volume test N t = 8, am =.5 finite size comparison for Nt=8, ma=.5 finite size comparison for Nt=8, am= P.loop Ns=6 P.loop Ns=24 P.loop Ns=32 Ch.cond. Ns=6 Ch.cond. Ns=24 Ch.cond. Ns=32 distribution Ns=6 Ns=24 Ns=32 = Polyakov loop value 23/8/2 Lattice 23 D. Scheffler 23

28 Finite volume test N t = 8, am =.5 finite size comparison for Nt=8, ma=.5 finite size comparison for Nt=8, ma= P.loop Ns=8 P.loop Ns=6 P.loop Ns=24 P.loop Ns=32 Ch.cond. Ns=8 Ch.cond. Ns=6 Ch.cond. Ns=24 Ch.cond. Ns= Ch. susc. Ns=8 Ch. susc. Ns=6 Ch. susc. Ns=24 Ch. susc. Ns= /8/2 Lattice 23 D. Scheffler 24

29 Finite volume test N t = 8, am =.5 finite size comparison for Nt=8, ma=.5 finite size comparison for Nt=8, ma= Ns=8 Ns=6 Ns=24 Ns=32 = Ns=8 Ns=6 Ns=24 Ns=32 =2.2 distribution.4.3 distribution Polyakov loop value Polyakov loop value 23/8/2 Lattice 23 D. Scheffler 24

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