Lattice QCD @ nonzero temperature and finite density Heng-Tong Ding - PowerPoint PPT Presentation

Lattice QCD @ nonzero temperature and finite density Heng-Tong Ding ( 丁亨通 ) Central China Normal University 34th International Symposium on Lattice Field Theory, 24-30 July 2016, University of Southampton, UK

Outline T>0 & µ =0 • QCD phase structure • Properties of QCD medium T>0 & µ > 0 • Equation of State • QCD phase structure

Milestone: transition temperature from hadronic phase to QGP phase Domain wall fermions Calculations with Domain wall, HISQ, stout fermions consistently give T pc ~155 MeV Not a true phase transition but a crossover HotQCD: PRL 113 (2014) 082001 See also the continuum extrapolated results of HISQ, stout & overlap in: Wuppertal-Budapest: Nature 443(2006)675, JHEP 1009 (2010) 073 , HotQCD: PRD 85 (2012)054503 Borsanyi et al., [WB collaboration], arXiv: 1510.03376, Phys.Lett. B713 (2012) 342

Milestone: QCD Equation of State HotQCD, PRD 90 (2014) 094503, Wuppertal-Budapest, Phys. Lett. B730 (2014) 99

QCD phase structure in the quark mass plane columbia plot, PRL 65(1990)2491 ∞ ∞ ∞ ∞ N f =2 N f =2 N f =2 N f =2 PURE PURE PURE PURE RG arguments: m s m s m s m s GAUGE GAUGE GAUGE GAUGE 2 nd order 2 nd order 2 nd order 2 nd order 1 st 1 st 1 st 1 st 2 nd order 2 nd order 2 nd order 2 nd order Z(2) Z(2) Z(2) Z(2) order order order order O(4) O(4) O(4) O(4) m q =0 or ∞ with N f =3: a first order phase Pisarski & Wilczek, PRD29 (1984) 338 transition physical point physical point physical point physical point N f =3 N f =3 N f =3 N f =3 Critical lines of second order transition m tri m tri m tri m tri cross over cross over cross over cross over N f =1 N f =1 N f =1 N f =1 s s s s N f =2: O(4) universality class N f =3: Z(2) universality class m c 2 nd order 2 nd order 2 nd order 2 nd order 1 st 1 st 1 st 1 st K. Rajagopal & F. Wilczek, NPB 399 (1993) 395 Z(2) Z(2) Z(2) Z(2) order order order order ∞ ∞ ∞ ∞ m u,d m u,d m u,d m u,d F. Wilczek, Int. J. Mod. Phys. A 7(1992) 3911,6951 Gavin, Gocksch & Pisarski, PRD 49 (1994) 3079 HTD, F. Karsch, S. Mukherjee, arXiv:1504.0527 Lattice QCD calculations: tri The value of tri-critical point (m s ) ? The location of 2 nd order Z(2) lines ? The influence of criticalities to the physical point ?

scenarios of QCD phase transition at m l =0 m phy > m tri ∞ ∞ ∞ ∞ N f =2 N f =2 N f =2 N f =2 PURE PURE PURE PURE s s m s m s m s m s GAUGE GAUGE GAUGE GAUGE T 2 nd order 2 nd order 2 nd order 2 nd order 1 st 1 st 1 st 1 st 2 nd order 2 nd order 2 nd order 2 nd order 2 nd Z(2) Z(2) Z(2) Z(2) order order order order O(4) O(4) O(4) O(4) tri-critical order point physical point physical point physical point physical point N f =3 N f =3 N f =3 N f =3 m tri m tri m tri m tri cross over cross over cross over cross over N f =1 N f =1 N f =1 N f =1 s s s s 1 st order m c 2 nd order 2 nd order 2 nd order 2 nd order 1 st 1 st 1 st 1 st μ Z(2) Z(2) Z(2) Z(2) order order order order ∞ ∞ ∞ ∞ m u,d m u,d m u,d m u,d m phy = m tri m phy < m tri s s s s T T tri-critical 1 st critical point order point cross over 1 st order μ μ

QCD phase transition at the physical point ∞ ∞ ∞ ∞ N f =2 N f =2 N f =2 N f =2 PURE PURE PURE PURE m s m s m s m s GAUGE GAUGE GAUGE GAUGE m=m phy 2 nd order 2 nd order 2 nd order 2 nd order 1 st 1 st 1 st 1 st 2 nd order 2 nd order 2 nd order 2 nd order Z(2) Z(2) Z(2) Z(2) order order order order O(4) O(4) O(4) O(4) quark matter cross over physical point physical point physical point physical point N f =3 N f =3 N f =3 N f =3 critical point m tri m tri m tri m tri cross over cross over cross over cross over N f =1 N f =1 N f =1 N f =1 s s s s hadronic matter 1st order m c 2 nd order 2 nd order 2 nd order 2 nd order 1 st 1 st 1 st 1 st Z(2) Z(2) Z(2) Z(2) order order order order ∞ ∞ ∞ ∞ m u,d m u,d m u,d m u,d µ FIRST ORDER N = 2 o o f phys. line CROSSOVER m s N = 3 f 0 m 0 o o u,d Karsch et al., ’03, Nakamura et al., 15’ de Forcrand & Philipsen, ’07

1st order chiral phase transition region π [MeV] m c ∞ ∞ ∞ ∞ N f =2 N f =2 N f =2 N f =2 PURE PURE PURE PURE 350 m s m s m s m s GAUGE GAUGE GAUGE GAUGE 2 nd order 2 nd order 2 nd order 2 nd order 1 st 1 st 1 st 1 st Nt=4, naive stag.[1,2,3] 2 nd order 2 nd order 2 nd order 2 nd order Z(2) Z(2) Z(2) Z(2) order order order order 300 O(4) O(4) O(4) O(4) Nt=6, 8& 10, 250 Wilson clover[6] physical point physical point physical point physical point N f =3 N f =3 N f =3 N f =3 200 m tri m tri m tri m tri cross over cross over cross over cross over N f =1 N f =1 N f =1 N f =1 s s s s Nt=6, naive stag. [2] 150 m c 100 Nt=4, p4fat3[1] 2 nd order 2 nd order 2 nd order 2 nd order Nt=6, HISQ[5] 1 st 1 st 1 st 1 st Z(2) Z(2) Z(2) Z(2) order order order order 50 ∞ ∞ ∞ ∞ m u,d m u,d m u,d m u,d Nt=6, stout[4] 0 [1]F. Karsch et al., Nucl.Phys.Proc.Suppl. 129 (2004) 614 [2] P. de Forcrand et al, PoS LATTICE2007 (2007) 178 [3]D. Smith & C. Schmidt, Lattice 2011 [4]G. Endrodi et al., PoS LAT2007 (2007) 228 [5] HTD et al., Lattice 15’, arXiv: 1511.00553 [6]Y. Nakamura, Lattice 15’,PRD92 (2015) no.11, 114511

Rooting issue? Nf=4 staggered QCD [Philippe De Forcrand, Monday] Unimproved staggered fermions, Nt=4, Nf=4 preliminary Nt ↑ m c ↓

��� � ��� � ��� � � ��� ��� ��� �������� ����� ��� ��� � � � � � � ��� � � � � � ����� � � �� � 1st order chiral phase transition region Nt=6, Wilson-Clover Nt=4, Naive staggered fermions 0.35 ��� �� � � � � Nf=2+1 ��� �� � � � � ��� �� � � � �� ������������� 0.3 � � � � physical point 0.25 tric - C m ud 2/5 m s 0.2 am s 0.15 0.1 750 MeV 0.05 0 0 0.01 0.02 0.03 0.04 am u,d Philippe de Forcrand and Owe Philipsen, [Yoshifumi Nakamura, Monday] JHEP 0701 (2007) 077 Location of the physical point: Inconsistency between results from Wilson-clover and Naive staggered fermions on coarse lattices

Proper order parameter of chiral phase transition in Nf=3 QCD [Shinji Takeda, Tuesday] Karsch, Laermann & Schmidt Phys.Lett. B520 (2001) 41 Cross point moves to the Z(2) critical line with:

Estimate of critical end point at mu=0: analytical continuation from imaginary mu [Alessandro Sciarra, Monday] unimproved Wilson fermions, Nt=6 ⇣ µ ⌘ 2 T Bonati et al.,PRD90 7(2014) 074030 O. Philipsen and C. Pinke, PRD93 11(2016)114507 unimproved Wilson fermions: m c π ( µ = 0 , N τ = 4) ≈ 560 MeV estimate: m c π ( µ = 0 , N τ = 6) ∼ 400 MeV

Chiral phase transition region in Nf=3 QCD ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ N f =2 N f =2 N f =2 N f =2 N f =2 N f =2 N f =2 N f =2 PURE PURE PURE PURE PURE PURE PURE PURE m s m s m s m s m s m s m s m s GAUGE GAUGE GAUGE GAUGE GAUGE GAUGE GAUGE GAUGE 2 nd order 2 nd order 2 nd order 2 nd order 1 st 1 st 1 st 1 st 2 nd order 2 nd order 2 nd order 2 nd order 1 st 1 st 1 st 1 st 2 nd order 2 nd order 2 nd order 2 nd order 2 nd order 2 nd order 2 nd order 2 nd order Z(2) Z(2) Z(2) Z(2) order order order order Z(2) Z(2) Z(2) Z(2) order order order order O(4) O(4) O(4) O(4) O(4) O(4) O(4) O(4) ?? physical point physical point physical point physical point physical point physical point physical point physical point N f =3 N f =3 N f =3 N f =3 N f =3 N f =3 N f =3 N f =3 m tri m tri m tri m tri cross over cross over cross over cross over cross over cross over cross over cross over N f =1 N f =1 N f =1 N f =1 N f =1 N f =1 N f =1 N f =1 s s s s m c 2 nd order 2 nd order 2 nd order 2 nd order 1 st 1 st 1 st 1 st Z(2) Z(2) Z(2) Z(2) order order order order ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ m u,d m u,d m u,d m u,d m u,d m u,d m u,d m u,d Whether the 1st order chiral phase transition is relevant for the physical point at all?

Universal behavior of chiral phase transition in Nf=2+1 QCD [Sheng-Tai Li, Wednesday] Nt=4, p4fat3 Nt=6, HISQ χ /dof is: 14.4133 2.2 m π =160MeV m l /m s =1/20 2 m π =140MeV 1/27 1/40 m π =110MeV M/h 1/ δ 1.8 1/60 m π =90MeV 1.6 m π =80MeV 1/80 O(2) 1.4 1.2 1 Ejiri et al., 0.8 PRD 09’ 0.6 0.4 0.2 z=t/h 1/ βδ 0 -2 -1 0 1 2 3 ∞ ∞ ∞ ∞ N f =2 N f =2 N f =2 N f =2 PURE PURE PURE PURE m s m s m s m s GAUGE GAUGE GAUGE GAUGE 2 nd order 2 nd order 2 nd order 2 nd order 1 st 1 st 1 st 1 st 2 nd order 2 nd order 2 nd order 2 nd order Z(2) Z(2) Z(2) Z(2) order order order order O(4) O(4) O(4) O(4) physical point physical point physical point physical point Scaling window becomes smaller N f =3 N f =3 N f =3 N f =3 cross over cross over cross over cross over N f =1 N f =1 N f =1 N f =1 from Nt=4 p4fat3 to Nt=6 HISQ results ? ∞ ∞ ∞ ∞ m u,d m u,d m u,d m u,d