The Chiral and Deconfinement Phase Transitions in Strongly-Interacting Matter

Transcription

1 The Chiral and Deconfinement Phase Transitions in Strongly-Interacting Matter in collaboration with: B-J. Schaefer & J. Wambach Schaefer, MW: PRD 79 (1418) arxiv: [hep-ph] Mathias Wagner Institut für Kernphysik TU Darmstadt

2 Outline QCD phase diagram chiral phase transition deconfinement phase transition Taylor expansion to finite density! Wambach lectures Mathias Wagner Institut für Kernphysik TU Darmstadt

3 Expectations Mathias Wagner Institut für Kernphysik TU Darmstadt

4 Critical endpoint 2 T, MeV LTE4 HB2 LTE3 17 LR4 9 LR1 1 CO94 5 RM98 INJL98 LSM1 CJT2 PNJL NJL5 NJL1 NJL89a NJL89b Stephanov (27) µ B, MeV Mathias Wagner Institut für Kernphysik TU Darmstadt

5 Quark mass dependence µ =! m tric s 2nd order O(4)? N f = 2 m s X phys. point 1st order crossover Pure 2nd order Z(2) N f = 3 1st order Gauge m, m u d N f = 1! Mathias Wagner Institut für Kernphysik TU Darmstadt

6 Quark mass dependence µ =! m tric s 2nd order O(4)? N f = 2 m s! Real world Heavy quarks X phys. point 1st order 2nd order Z(2) * QCD critical point crossover 1st order Pure N f = 3 Gauge X crossover 1rst! m u,d m s m u, m d N f = 1 Philipsen (27)! Mathias Wagner Institut für Kernphysik TU Darmstadt

7 Quark mass dependence µ =! m tric s 2nd order O(4)? N f = 2 m s! Real world Heavy quarks X phys. point 1st order 2nd order Z(2) QCD critical point DISAPPEARED crossover 1st order Pure N f = 3 Gauge X crossover 1rst! m u,d m s m u, m d N f = 1 Philipsen (27)! Mathias Wagner Institut für Kernphysik TU Darmstadt

8 Chiral phase transition relevant degrees of freedom: quarks and mesons!! quark-meson (QM) model: L qm = L q + L m mesonic fields φ = T a (σ a + iπ a ) L m = Tr ( µ φ µ φ ) m 2 Tr(φ φ) λ 1 [ Tr(φ φ) ] 2 λ2 Tr ( φ φ ) 2 +c ( det(φ) + det(φ ) ) + Tr [ H(φ + φ ) ] L q = q (i / gt a (σ a + iγ 5 π a )) q quarks / antiquarks fit to experimental masses and decay constants explicit symmetry breaking parameters H : m u m d <m s U(1) A - anomaly controlled by parameter c Mathias Wagner Institut für Kernphysik TU Darmstadt

9 Grand potential mean-field approximation neglect mesonic fluctuation, integrate fermionic fluctuations thermodynamic potential Ω(T, µ; σ x, σ y )=U (σ x, σ y )+Ω qq (T, µ; σ x, σ y ) meson contribution U(σ x, σ y )= m2 2 ( σ 2 x + σ 2 y) hx σ x h y σ y c 2 2 σ2 xσ y + λ 1 2 σ2 xσ 2 y (2λ 1 + λ 2 ) σ 4 x (2λ 1 +2λ 2 ) σ 4 y quark contribution Ω qq (T, µ) =ν c T f=u,d,s d 3 k (2π) 3 {ln(1 n q,f (T, µ f )) + ln(1 n q,f (T, µ f ))} 2. Februar 29 Mathias Wagner Institut für Kernphysik

10 Chiral critical surface physical point! [MeV] m K [MeV] 2 1 m σ = 8 MeV m! [MeV] with axial anomaly B.-J. Schaefer, MW (29) Mathias Wagner Institut für Kernphysik TU Darmstadt

11 Chiral critical surface physical point! [MeV] m K [MeV] 2 1 m σ = 8 MeV with axial anomaly B.-J. Schaefer, MW (29) f (6) [i] or σ Mass m = (4 12) MeV Full width Γ = (6 1) MeV 25 5 I G (J PC )= + ( ++ ) Page 3 Created: 9/2/27 16: m! [MeV] Mathias Wagner Institut für Kernphysik TU Darmstadt

12 Chiral critical surface! [MeV] physical point m K [MeV] m! [MeV] ! [MeV] m " = 5MeV m " = 6MeV m " = 7MeV m " = 8MeV m " = 9MeV m! /m! * m σ = 8 MeV with axial anomaly B.-J. Schaefer, MW (29) Mathias Wagner Institut für Kernphysik TU Darmstadt

13 Chiral critical surface! [MeV] 4 physical point 25 2 crossover 1st order m K [MeV] 2 1 m σ = 8 MeV m! [MeV] T [MeV] µ [MeV] with axial anomaly m σ = 6, 8, 9 MeV B.-J. Schaefer, MW (29) Mathias Wagner Institut für Kernphysik TU Darmstadt

14 Confinement Polyakov loop variable P ( x) =P exp ( i β ) dτa ( x, τ) Φ ( x) = 1 N c tr C P ( x) β Polyakov-loop potentials fitted to lattice data for pure gauge first order phase transition at T = 27 MeV various Polyakov loop potentials U ( Φ, Φ ) blue: logarithmic Roessner (27) red: polynomial Ratti (26) brown: Fukushima Fukushima (28)) T T Mathias Wagner Institut für Kernphysik TU Darmstadt

15 Polyakov-Quark-Meson model couple Polyakov loop to quark fields Ω qq (T, µ) = 2T Ω(T, µ; σ x, σ y, Φ, Φ) =U (σ x, σ y )+Ω qq (T, µ; σ x, σ y, Φ, Φ)+U ( Φ, Φ ) f=u,d,s d 3 { [ ( p (2π) 3 tr c ln 1+P exp E q,f µ f T effective confinement in the hadronic phase [( ( ln 1 + exp E ) )] Nc q,f µ f = ln T )] ln (Φ ) [( 1 + exp [ ( 1+P exp E q,f + µ f T ( N c E q,f µ f T ))] )]} approaches QM model in the deconfined phase (Φ 1) [ ( ( ln 1 + exp E )) ] Nc [( ( q,f µ f = N c ln 1 + exp E q,f µ f T T ))] Mathias Wagner Institut für Kernphysik TU Darmstadt

16 Phase transitions consider order parameters for chiral and deconfinement transitions! x QM PQM log PQM pol PQM Fuku ! PQM log PQM pol PQM Fuku Lattice Cheng et al. (26) T = 27 MeV,m σ = 6 MeV T/T " T/T " B.-J. Schaefer, MW (29) Mathias Wagner Institut für Kernphysik TU Darmstadt

17 PQM with log.-pot Influence on the phase structure QM PQM with Fuku.-Pot T [MeV] chiral crossover chiral first order µ [MeV] T [MeV] chiral crossover chiral first order deconfinement µ [MeV] PQM with poly.-pot T [MeV] chiral crossover chiral first order deconfinement µ [MeV] T [MeV] chiral crossover chiral first order deconfinement µ [MeV] Mathias Wagner Institut für Kernphysik TU Darmstadt

18 PQM with log.-pot Influence on the phase structure QM PQM with Fuku.-Pot T [MeV] quarkyonic matter?! McLerran lectures chiral crossover chiral first order µ [MeV] T [MeV] chiral crossover chiral first order deconfinement µ [MeV] PQM with poly.-pot T [MeV] chiral crossover chiral first order deconfinement µ [MeV] T [MeV] chiral crossover chiral first order deconfinement µ [MeV] Mathias Wagner Institut für Kernphysik TU Darmstadt

19 Quark number density n q (T, µ) = Ω(T, µ) µ QM PQM log Mathias Wagner Institut für Kernphysik TU Darmstadt

20 Critical region ( χ q (T, µ) = 2 Ω(T, µ) µ R(T, µ) = χ q(t, µ) χ free 2 µ 2 q = N c N f π 2 + T 2 ) 3 χ free q (T, µ) (T-T c )/T c R=2 R=3 R= (µ-µ c )/µ c PQM log Mathias Wagner Institut für Kernphysik TU Darmstadt

21 Comparison to lattice data normalized pressure p/p SB Lattice QM PQM pol PQM log PQM Fuku T/T! T = 27 MeV,m σ = 6 MeV Cheng et al. (28) Mathias Wagner Institut für Kernphysik TU Darmstadt

22 Extrapolation to finite µ Lattice struggles at finite! extrapolations required imaginary! Taylor expansion p(t, µ) T 4 = c n (T ) n= ( µ T ) n reweighting coefficients from lattice c 2 u SB n f =2+1, m " =22 MeV n f =2, m " =77 MeV filled: N! = 4 open: N! = 6 T[MeV] c 4 u.3 n f =2+1, m " =22 MeV n f =2, m " =77 MeV.2 filled: N! = 4 open: N! = SB.4 SB T[MeV] -.2 T[MeV] c 6 u n f =2+1, m " =22 MeV n f =2, m " =77 MeV Miao (28) Mathias Wagner Institut für Kernphysik TU Darmstadt

23 Coefficients in models pressure is directly connected to thermodynamic potential equations of motion introduce implicit!-dependence comparison of calculation at! with extrapolation to! possible c n (T )= 1 ( n p(t, µ)/t 4) n! (µ/t ) n µ= c c T/T! T/T! Mathias Wagner Institut für Kernphysik TU Darmstadt

24 Higher orders c 8 MW, A. Walther, B.-J. Schaefer (to be published) c 6-15 c e+7 1e+6-5 c 12 c 14-1e+6 c 16-5e+7 3e+9 2e+9 1e+9-1e+9-2e+9-3e+9-4e+9 c 18,98 1 1,2 c 2 5e+1-5e+1,98 1 1,2 T/T c 22,98 1 1,2 2e+12-2e+12-4e Mathias Wagner Institut für Kernphysik TU Darmstadt

25 Extrapolation to pressure difference 25 p(t, µ) T 4 = p(t, µ) p(, ) = n=2,4,... T 4 ( µ ) n c n (T ) T T [MeV] chiral crossover chiral first order deconfinement µ [MeV] µ/t < µ c /T c µ/t = µ c /T c µ/t > µ c /T c th 8th 4th PQM th 8th 4th PQM th 8th 4th PQM!p/T 4 1!p/T 4 1!p/T T/T " T/T " T/T " Mathias Wagner Institut für Kernphysik TU Darmstadt

26 Extrapolation to II quark number susceptibility 25 χ q (T, µ) T 2 = 2 Ω(T, µ) µ 2 = n(n 1)c n (T ) n=2,4,... diverges at ( µ T ) n 2 T [MeV] chiral crossover chiral first order deconfinement µ [MeV] µ/t < µ c /T c µ/t = µ c /T c µ/t > µ c /T c th 8th 4th PQM th 8th 4th PQM th 8th 4th PQM!/T 2 1!/T 2 1!/T T/T! T/T! T/T! Mathias Wagner Institut für Kernphysik TU Darmstadt

27 Convergence radii should be limited by first-order phase transition different definitions r = lim n r 2n = lim n ρ = lim n ρ 2n = lim n c 2n c 2n+2 c 2 c 2n 1/2 1/(2n 2) e diagram: T generic picture ρ 2 ρ 4 ρ 6 root of c B 6 root of c B 8 µ B Schmidt (28) should be equal for n signatures of? Mathias Wagner Institut für Kernphysik TU Darmstadt

28 PQM Convergence radii 1 1 T/T! n=2 n=4 n= T/T! n=8 n=1 n= !/T!!/T! 1 1 T/T! n=14 n=16 n=18 T/T! n=2 n=22 n= !/T!!/T! Mathias Wagner Institut für Kernphysik TU Darmstadt

29 Summary & Outlook parameter dependence of deconfinement transition in the PQM model coincidence of phase transitions realistic description of EOS higher order Taylor expansion include fluctuations:! renormalization group modifications of Polyakov loop potentials at finite! extrapolation methods and the critical end point Mathias Wagner Institut für Kernphysik TU Darmstadt