Dynamical Locking of the Chiral and the Deconfinement Phase Transition

Transcription

1 Dynamical Locking of the Chiral and the Deconfinement Phase Transition Jens Braun Friedrich-Schiller-University Jena Quarks, Gluons, and Hadronic Matter under Extreme Conditions St. Goar 17/03/2011 J. Braun, A. Janot, arxiv:

2 QCD phase diagram FAIR,

3 QCD phase diagram FAIR, Relation of chiral symmetry breaking and confinement?

4 Many ways to learn something about QCD... Lattice QCD D. FAIR, finite volume, finite quark masses Many-color QCD Many-flavor QCD L = 1 4 F µνf µν + ψ (i / + iga/) ψ symmetries: SU(N c ) SU L (N f ) SU R (N f ) (cf. H. Gies talk) weak-coupling limit

5 Yet another deformation of QCD... λ ψ -deformed QCD (here two massless flavors and N c colors) L = 1 4 F µνf µν + ψ (i / + iga/) ψ + λ ψ ( ψoψ) 2 two parameters: λ ψ (m τ ) and α s (m τ ) ( Λ QCD )

6 Yet another deformation of QCD... λ ψ -deformed QCD (here two massless flavors and N c colors) L = 1 4 F µνf µν + ψ (i / + iga/) ψ + λ ψ ( ψoψ) 2 two parameters: λ ψ (m τ ) and α s (m τ ) ( Λ QCD ) real QCD: only one parameter, namely α s (m τ ) ( Λ QCD ) L = 1 4 F µνf µν + ψ (i / + iga/) ψ integrate out fluctuations (cf. Gies&Jaeckel 05; JB & Gies, 05, 06, 09; JB, Fischer, Gies 11) L = 1 4 F µνf µν + ψ (i / + iga/) ψ + λ ψ ( ψoψ) quark self-interactions are induced by the gauge degrees of freedom: onset of chiral symmetry breaking is signaled by strong four-fermion interaction ( s become IR-relevant)

7 Yet another deformation of QCD... λ ψ -deformed QCD (here two massless flavors and N c colors) L = 1 4 F µνf µν + ψ (i / + iga/) ψ + λ ψ ( ψoψ) 2 two parameters: λ ψ (m τ ) and α s (m τ ) ( Λ QCD ) real QCD: only one parameter, namely α s (m τ ) ( Λ QCD ) L = 1 4 F µνf µν + ψ (i / + iga/) ψ integrate out fluctuations (cf. Gies&Jaeckel 05; JB & Gies, 05, 06, 09; JB, Fischer, Gies 11) L = 1 4 F µνf µν + ψ (i / + iga/) ψ + λ ψ ( ψoψ) quark self-interactions are induced by the gauge degrees of freedom: onset of chiral symmetry breaking is signaled by strong quark-self interactions ( s become IR-relevant) λ ψ

8 Yet another deformation of QCD... λ ψ -deformed QCD (here two massless flavors and N c colors) scales? L = 1 4 F µνf µν + ψ (i / + iga/) ψ + λ ψ ( ψoψ) 2 two parameters: λ ψ (m τ ) and α s (m τ ) ( Λ QCD )

9 Yet another deformation of QCD... λ ψ -deformed QCD (here two massless flavors and N c colors) L = 1 4 F µνf µν + ψ (i / + iga/) ψ + λ ψ ( ψoψ) 2 two parameters: λ ψ (m τ ) and α s (m τ ) ( Λ QCD ) scale dependence of chiral observables in the chiral limit in real QCD: T χsb, f π, ψψ 1 3, ΛQCD (α s ) scale dependence of chiral observables in the chiral limit in -deformed QCD: λ ψ T χsb (α s, λ ψ ), f π (α s, λ ψ ), ψψ 1 3 (αs, λ ψ ),... α s λ ψ directly related to gluodynamics directly related to chiral observables

10 Yet another deformation of QCD... λ ψ -deformed QCD (here two massless flavors and N c colors) L = 1 4 F µνf µν + ψ (i / + iga/) ψ + λ ψ ( ψoψ) 2 two parameters: λ ψ (m τ ) and α s (m τ ) ( Λ QCD ) phase diagrams... T fixed λ? ψ T fixed α? s α s f π λ ψ f π

11 Yet another deformation of QCD... λ ψ -deformed QCD (here two massless flavors and N c colors) L = 1 4 F µνf µν + ψ (i / + iga/) ψ + λ ψ ( ψoψ) 2 two parameters: λ ψ (m τ ) and α s (m τ ) ( Λ QCD ) phase diagrams... T fixed λ? ψ T fixed α? s this talk α s f π allows to gain insight into the relation of chiral symmetry breaking and confinement λ ψ f π

12 λ ψ -deformed QCD: our model λ ψ -deformed QCD (model) with two massless flavors and N c colors: L = ψ (i / + iγ 0 ḡ A 0 ) ψ + λ ψ [ ( ψψ) 2 ( ψγ 5 τψ) 2] (cf. matter part of QCD in Landau- DeWitt gauge, e. g. JB, Haas, Marhauser, Pawlowski 09) here, the two parameters are λ ψ (Λ) and A 0 ( α s ) order parameter for deconfinement: (JB, Gies, Pawlowski 07; Pawlowski, Marhauser 08) L[ A 0 ] = tr F e iβḡ A 0 tr F e i R β 0 ḡa 0 confer underlying assumption in PNJL/PQM-type models: L[ A 0 ] = tr F e iβḡ A 0! = tr F e i R β 0 ḡa 0 (e. g. Meisinger, Ogilvie 96; Fukushima 03; Ratti, Thaler, Weise 05; Schaefer, Pawlowski, Wambach 08;...)

13 λ ψ -deformed QCD: our model (JB, A. Janot 11) λ ψ -deformed QCD (model) with two massless flavors and N c colors: L = ψ (i / + iγ 0 ḡ A 0 ) ψ + λ ψ [ ( ψψ) 2 ( ψγ 5 τψ) 2] two parameters: λ ψ (Λ) and A 0 ( Λ QCD ) data for L[ A 0 ] L[A 0 ] is available from non-perturbative RG studies: (JB, Gies, Pawlowski 07; JB, Eichhorn, Gies, Pawlowski 10) L[! <A 0 >] SU(2) SU(3) T/T c! 4 V(! <" 0 >) N c = ! <A 0 >/(2#) for our numerical study we employ the RG data: the confinement temperature is fixed, the chiral transition temperature T χ (λ ψ, A 0 ) is a prediction from our model T d

14 λ ψ -deformed QCD: RG fixed-point analysis I (JB, A. Janot 11) λ ψ -deformed QCD (model) with two massless flavors and N c colors: L = ψ (i / ) ψ + λ ψ [ ( ψψ) 2 ( ψγ 5 τψ) 2] k kt λ ψ β-function (RG flow equation): β λψ k k λ ψ = 2λ ψ λ ψ Cλ ψ RG scale k momentum scale λ ψ λ ψ (cf. also H. Gies talk) critical coupling λ ψ : choose λ ψ (Λ) > λ ψ λ ψ increases rapidly 1 m 2 λ ψ χsb

15 λ ψ -deformed QCD: RG fixed-point analysis II (JB, A. Janot 11) λ ψ -deformed QCD (model) with two massless flavors and N c colors: L = ψ (i / ) ψ + λ ψ [ ( ψψ) 2 ( ψγ 5 τψ) 2] k kt λ ψ T>0& A 0 =0 β -function (RG flow equation): β λψ k k λ ψ = 2λ ψ λ ψ C( T k )λ ψ λ ψ λ ψ fixed point coupling λ ψ( T k ) ( T k )3 λ ψ (Λ) > λ ψ(t = 0) for a fixed choice, a critical temperature exists: T χ T > T χ λ ψ decreases no χsb

16 λ ψ -deformed QCD: RG fixed-point analysis III (JB, A. Janot 11) λ ψ -deformed QCD (model) with two massless flavors and N c colors: L = ψ (i /+iγ 0 ḡ A 0 ) ψ + λ ψ [ ( ψψ) 2 ( ψγ 5 τψ) 2] k kt λ ψ T>0& A 0 =0 β -function (RG flow equation): k k λ ψ = 2λ ψ λ ψ C( T k, A 0 )λ ψ for increasing A 0, the fixed point moves to the left: λ ψ A 0 > 0 λ ψ λ ψ( T k, A 0 ) λ ψ(t = 0) + ( T k )3 L[ A 0 ] + O(1/N c )

17 λ ψ -deformed QCD: RG fixed-point analysis III (JB, A. Janot 11) λ ψ -deformed QCD (model) with two massless flavors and N c colors: L = ψ (i /+iγ 0 ḡ A 0 ) ψ + λ ψ [ ( ψψ) 2 ( ψγ 5 τψ) 2] k kt λ ψ T>0& A 0 =0 β -function (RG flow equation): k k λ ψ = 2λ ψ λ ψ C( T k, A 0 )λ ψ for increasing A 0, the fixed point moves to the left: λ ψ A 0 > 0 λ ψ λ ψ( T k, A 0 ) λ ψ(t = 0) + ( T k )3 L[ A 0 ] + O(1/N c ) fixed choice λ ψ (Λ) > λ ψ(t = 0) : confinement order parameter L[ A 0 ] 0 χsb T χ T d (exact in the limit N c )

18 λ ψ -deformed QCD: phase diagram (JB, A. Janot 11) N c = 2 N c = N c = Tχ/Td Tχ/Td real QCD λ UV ψ /λ ψ λ ψ (Λ)/λ ψ f π [MeV] window in which the chiral phase transition is locked to the deconfinement phase transition increases with increasing N c for finite N c, we have three regimes: T χ < T d, T χ T d and T χ > T d below the locking window, we have T χ (λ ψ (Λ) λ ψ) 1/2 f π

19 -deformed QCD: phase diagram λ ψ (JB, A. Janot 11) N c = 2 N c = N c = 3 Tχ/Td Tχ/Td nd order χpt real QCD 1st order χpt(?) λ UV ψ /λ ψ λ ψ (Λ)/λ ψ f π [MeV] window in which the chiral phase transition is locked to the deconfinement phase transition increases with increasing N c for finite, we have three regimes: T χ < T d, T χ T d and below the locking window, we have T χ (λ ψ (Λ) λ ψ) 1/2 f π window with a chiral phase transition of first order may open up due to a rapidly rising deconfinement order parameter N c T χ > T d

20 Conclusions locking mechanism for the phase boundary from a study of the (non-perturbative) fixed-point structure chiral phase transition is locked to the deconfinement phase transition for N c : T χ T conf. locking mechanism works also beyond the large -limit testable prediction; does not suffer from problems present at finite quark chemical potential Outlook more deformations: finite (current) quark masses, finite quark chemical potential,... N c