Chiral phase transition of (2 + 1)-flavor QCD QCD phase diagram - PowerPoint PPT Presentation

Chiral phase transition of (2 + 1)-flavor QCD Chiral phase transition of (2 + 1)-flavor QCD QCD phase diagram Sheng-Tai Li for HotQCD collaboration MEOS Lattice Setup NO evidence Institute of Particle Physics for the 1st order phase Central China Normal University transition Extract T 0 c July 26, 2018 Summary and outlook Backup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 / 18

Chiral crossover transition of QCD in the real world Chiral phase 16 transition of 166 T c (µ B =0) [MeV] non-int. limit � disc (2 + 1)-flavor 164 � sub QCD 162 12 160 � sub HRG 2 � sub 158 � µ B T c 8 � 156 2 � disc 3p/T 4 � µ B QCD phase 154 HotQCD preliminary � /T 4 156.5 ± 1.5 MeV diagram 152 3s/4T 3 4 2 1/N � 150 MEOS c N N N N � o T [MeV] n � = � = � = � = t 1 1 8 6 i n 6 2 Lattice Setup u 0 u m 130 170 210 250 290 330 370 NO evidence for the 1st PRD 90, 094503 (2014) P. Steinbrecher, 1807.05607 order phase transition • The transition from Hadronic phase to Quark Gluon Plasma Extract T 0 c phase at µ B = 0 is a crossover but NOT a PHASE transition Summary and (Y. Aoki .et al, Nature 443 (2006) 675-678 and A. Bazavov et al., Phys.Rev.D85(2012) 054503 and outlook the ref therein) Backup • Latest results T pc ( µ B = 0) = 156 . 5 ± 1 . 5 MeV (“QCD crossover at zero and non-zero baryon densities” by P. Steinbrecher, Wed. 16:10-16:30) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 / 18

QCD chiral phase transition Chiral phase ∞ N f = 2 PURE transition of m s GAUGE 2 nd order Z 2 1 st (2 + 1)-flavor QCD 2 nd order O (4) order m l H = m phy s m phy QCD phase s physical point N f = 3 diagram cross over N f = 1 MEOS Lattice Setup NO evidence m c 2 nd order Z 2 for the 1st 1 st order phase order transition ∞ m u,d = m l Extract T 0 c • The real PHASE transition in the chiral limit ? Summary and outlook • The order and universality class of the phase transition ? Backup • Influence of the criticality in the chiral limit to the thermodynamics at the physical point ? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 / 18

Two different scenarios at µ B ̸ = 0 Chiral phase ∞ PURE ∞ PURE N f = 2 N f = 2 transition of m s m s GAUGE GAUGE 2 nd order Z 2 1 st 1 st 2 nd order Z 2 (2 + 1)-flavor 2 nd order O (4) order 2 nd order O (4) order QCD m l m c m l H = H = m phy − m phy m phy s s s m phy m phy s s physical point physical point N f = 3 N f = 3 QCD phase cross over N f = 1 cross over N f = 1 diagram MEOS m c Lattice Setup m c 2 nd order Z 2 2 nd order Z 2 1 st 1 st NO evidence order order ∞ ∞ m u,d = m l for the 1st m u,d = m l T T order phase m phy < m tri m phy > m tri m l = 0 m l = 0 transition s s s s 1 st 2 nd critical tri-critical Extract T 0 order order point point c Summary and outlook 1 st cross over Backup order µ µ B B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 / 18

Magnetic Equation of State (MEOS) Behaviour of QCD continuous phase transition can be described by Chiral phase transition of the MEOS (2 + 1)-flavor QCD [⟨ ¯ ⟨ ¯ M ( t, h ) = h 1 /δ f G ( z ) + f reg = m s l − 2 m l ] ⟩ ⟩ ψψ ψψ f 4 s m s K QCD phase = m 2 χ M ( t, h ) = ∂M ∂H = H − 1 h 1 /δ f χ ( z ) + ∂f reg (1) diagram s χ subtot ∂H f 4 MEOS K where , f reg = a 1 ( T ) H + a 3 ( T ) H 3 + ... Lattice Setup NO evidence for the 1st order phase Scaling variables transition Extract T 0 T − T 0 t = 1 h = H = 1 m l c z = t/h 1 /βδ , c , (2) Summary and t 0 T 0 h 0 h 0 m s outlook c Backup I. scaling variables, h: external field, t: reduced temperature, II. β and δ are universal critical exponents. III. t 0 , h 0 , T 0 c are unique parameters from QCD, T 0 c is the chiral phase transition tempearture and it is a fundamental quantity of QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 / 18

Scaling functions & universal critical exponents Chiral phase 0.5 2 Z(2) Z(2) transition of 0.45 f χ O(2) 1.8 O(2) O(4) O(4) (2 + 1)-flavor 0.4 1.6 QCD 0.35 1.4 f G 0.3 1.2 0.25 1 0.2 0.8 QCD phase 0.15 0.6 diagram 0.1 0.4 MEOS z=t/h 1/ βδ 0.05 0.2 z=t/h 1/ βδ 0 0 Lattice Setup -4 -2 0 2 4 -4 -2 0 2 4 NO evidence for the 1st s > m phy • m tri → Z(2) at m l = m c order phase s Model β δ transition s < m phy • m tri → O(4) at m l = 0 Z(2) 0.3258 4.805 Extract T 0 s c O(4) 0.380 4.824 • Staggered → O(2) Summary and O(2) 0.349 4.780 outlook Backup Difficulities: I. Critical exponents of O(2), Z(2), O(4) are similar II. Regular contribution from free energy maybe complicated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 / 18

A novel way to determine T 0 c Chiral phase ⎧ 0 z → −∞ � � z − transition of ⎪ H χ M = f χ ( z ) 60% ( H ) = T 0 60% H 1 / βδ ⎨ T − 1 + 1 / δ z = 0 f G ( z ) = c (2 + 1)-flavor z 0 M ⎪ QCD 1 z → + ∞ ⎩ ⎪ ⎩ → ∞ 1 1 0.40 0.40 z p z p Z(2) f χ (z) 0.35 f χ (z) 0.35 f χ /f G O(2) QCD phase O(2) 0.8 0.30 0.30 diagram O(2) O (2) 0.25 0.25 0.6 MEOS 1/ δ z 0 =0 1/ δ z 0 = 1 60% of peak O(4) O(4) 60% of peak 0.20 0.20 z=0 Lattice Setup 0.4 0.15 0.15 z=0 NO evidence 0.10 0.10 0.2 H=1/20 for the 1st H=1/40 0.05 0.05 z=t/h 1/ βδ z=t/h 1/ βδ H=1/80 order phase 0 )/T c 0 (T-T c 1/ δ 0.00 0.00 transition 0 -2 -1 0 1 2 3 -2 -1 0 1 2 3 -0.4 -0.2 0 0.2 0.4 Extract T 0 c Summary and outlook Model z p z − Backup 60% • The crossing point gives T 0 c at H → 0 Z(2) 2.0 0.1 • At z − 60% ≈ T 0 O(4) 1.37 -0.01 60% , T − c O(2) 1.56 -0.009 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 / 18

Lattice Setup Chiral phase ∞ N f = 2 PURE transition of • The strange quark mass is m s GAUGE (2 + 1)-flavor 2 nd order Z 2 1 st QCD 2 nd order O (4) fixed at its physical value order • 4-5 values of quark masses m l H = m phy s QCD phase m phy s physical point are chosen for N τ = 6, 8 ,12 diagram N f = 3 cross over N f = 1 MEOS to approach the chiral limit Lattice Setup • 55 MeV ⩽ m π ⩽ 160MeV NO evidence • m phy = m phy m c for the 1st 2 nd order Z 2 / 27 s l order phase 1 st transition order ∞ m u,d = m l Extract T 0 c (HISQ/tree) action Summary and outlook m phy N τ /m l window m π window N σ /N τ window s Backup 6 [20, 80] [80, 160] MeV [4, 6.7] 8 [20, 160] [55, 160] MeV [4, 7] 12 [20, 80] [80, 160] MeV [4, 5] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 / 18

The volume dependence of the chiral susceptibility Chiral phase transition of (2 + 1)-flavor QCD 450 450 450 450 450 450 550 550 550 550 2 χ subtot /fk 4 2 χ subtot /fk 4 2 χ subtot /fk 4 2 χ subtot /fk 4 2 χ subtot /fk 4 2 χ subtot /fk 4 2 χ subtot /fk 4 2 χ subtot /fk 4 2 χ subtot /fk 4 2 χ subtot /fk 4 χ M =m s χ M =m s χ M =m s χ M =m s χ M =m s χ M =m s χ M =m s χ M =m s χ M =m s χ M =m s N σ =32 500 500 500 500 m π =80MeV,N σ =60 N σ =40 400 400 400 400 400 400 N σ =56 450 450 450 450 m π =80MeV,N σ =48 QCD phase 400 400 400 400 diagram 350 350 350 350 350 350 350 350 350 350 N τ =12 N τ =12 N τ =12 N τ =12 MEOS 300 300 300 300 300 300 300 300 300 300 m π =80 MeV m π =80 MeV m π =80 MeV m π =80 MeV 250 250 250 250 Lattice Setup N τ =8 N τ =8 N τ =8 N τ =8 N τ =8 N τ =8 200 200 200 200 m π =80 MeV m π =80 MeV m π =80 MeV m π =80 MeV m π =80 MeV m π =80 MeV 250 250 250 250 250 250 NO evidence 150 150 150 150 for the 1st T[MeV] T[MeV] T[MeV] T[MeV] T[MeV] T[MeV] T[MeV] T[MeV] T[MeV] T[MeV] 100 100 100 100 order phase 200 200 200 200 200 200 140 140 140 140 140 140 145 145 145 145 145 145 150 150 150 150 150 150 155 155 155 155 155 155 160 160 160 160 160 160 165 165 165 165 165 165 130 130 130 130 135 135 135 135 140 140 140 140 145 145 145 145 150 150 150 150 155 155 155 155 160 160 160 160 165 165 165 165 170 170 170 170 transition Extract T 0 c Summary and • χ M does not grow linearly in the volume outlook Backup • NO evidence for first order phase transition was found in the current pion mass window m π ⩾ 80 MeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 / 18