Deconfinement and Equation of State in QCD Pter Petreczky What is - PowerPoint PPT Presentation

Deconfinement and Equation of State in QCD Péter Petreczky What is deconfinement in QCD ? What is the nature of the deconfined matter ? Tools: screening of color charges, EoS, fluctuation of conserved quantum numbers QGP: state of strongly interacting matter for T � Λ QCD , g ⌧ 1 weakly interacting gas of quark and gluons ? EFT approach: EQCD 2 π T � m D ⇠ gT � g 2 T Magnetic screening scale: Perturbative series is an expansion is in g and not α s non-perturnative Loop expansion breaks down at some order p g ( µ = 10 2 GeV) = 4 πα s ( µ = 10 2 GeV) ' 1 Problem : Lattice QCD g ( µ = 10 16 GeV) ' 1 / 2 ISMD, October 4-9, 2015

Lattice QCD at T>0 now and then Lattice QCD calculations at T>0 around 2002: T c ' 173MeV for both chiral transition and deconfinement transition ( in terms of Polyakov loop) Problems: N τ = 4 : a ≡ 1 / ( N τ a ) = 1 / (4 T ) m π = (500 − 800)MeV costs ∼ N 11 N τ → ∞ Continuum limit and τ ∼ 1 /m 3 physical masses are needed m π = 140MeV π This task can be accomplished using improved staggered fermions actions: Highly Improved Staggered Quark (HISQ) Stout action Fluctuations of conserved charges: new look into deconfinement and QGP properties

The temperature dependence of chiral condensate Renormalized chiral condensate introduced by Budapest-Wuppertal collaboration Bazavov Phys. Rev. D85 (2012) 054503; PRR D 87(2013)094505, With choice : Borsanyi et al, JHEP 1009 (2010) 073 R R � l � s 0.025 0.025 HISQ, m l =m s /20 HISQ, m l =m s /20 HISQ, m l =m s /27 0.02 0.02 stout, m l =m s /27 0.015 0.015 0.01 0.01 0.005 0.005 0 0 -0.005 -0.005 T [MeV] T [MeV] 120 130 140 150 160 170 180 190 200 210 120 130 140 150 160 170 180 190 200 210 • after extrapolation to the continuum limit and physical quark mass HISQ/tree calculation agree with stout results • strange quark condensate does not show a rapid change at the chiral crossover => strange quark do not play a role in the chiral transition

Deconfinement and color screening Onset of color screening is described by Polyakov loop (order parameter in SU(N) gauge theory) Q ( r, T ) /T ) = 1 9 h tr L ( r )tr L † (0) i exp( � F Q ¯ Q ( r → ∞ , T ) = 2 F Q ( T ) F Q ¯ 2+1 flavor QCD, continuum extrapolated (work in progress with Bazavov, Weber … ) L ren (T) 0.9 0.8 0.7 0.6 stout, cont. 0.5 HISQ, cont. 0.4 SU(3) T QCD SU(2) 0.3 T P G c c 0.2 0.1 T [MeV] 0 150 200 250 300 350 400 450 500 free energy of static quark anti-quark SU(N) gauge theory ≠ QCD ! pair shows Debye screening at high temperatures Similar results with stout action Borsanyi et al, JHEP04(2015) 138

Polyakov and gas of static-light hadrons Energies of static-light mesons: Free energy of an isolated static quark: Megias, Arriola, Salcedo, PRL 109 (12) 151601 600 HISQ F Q (T) [MeV] stout Bazavov, PP, PRD 87 (2013) 094505 500 Ground state and first excited states 400 are from lattice QCD Michael, Shindler, Wagner, arXiv1004.4235 300 Wagner, Wiese, JHEP 1107 016,2011 200 Higher excited state energies are estimated from potential model Gas of static-light mesons T [MeV] 100 only works for T < 145 MeV 120 140 160 180 200

The entropy of static quark S Q = − ∂ F Q ∂ T 5 N � =8 10 N � =8 S Q (T) HRG 4.5 S Q (T) 9 HRG N f =0 8 4 N f =2, m � =800 MeV 7 3.5 6 3 5 2.5 4 T c 3 2 2 1.5 1 T [MeV] T/T c 1 0 120 140 160 180 200 220 0.7 0.8 0.9 1 1.1 1.2 1.3 At low T the entropy S Q increases reflecting the increase of states the heavy quark can be coupled to At high temperature the static quark only “sees” the medium within a Debye radius, as T increases the Debye radius decreases and S Q also decreases The onset of screening corresponds to peak is S Q and its position coincides with T c

Casimir scaling of the Polyakov loop Instead of fundamental representations consider Polyakov loop P n in arbitrary representation n P 3 = L ren PP, Schadler, arXiv:1509.07874 Casimir scaling: free energy is proportional to qudratic Casimir operator C n of rep n R n = C n /C 3 P 1 / R n n 1.2 1.0 0.8 32 3 ⇥ 8 0.6 0.4 P 3 P 15 P 6 P 15 0 0.2 P 8 P 24 P 10 P 27 0.0 500 T [MeV] 100 200 300 400 Expected in weak coupling expansion: e.g. at LO F n Q = − C n α s m D

Casimir scaling of the Polyakov loop (con’t) δ n = 1 − P 1 /R n /P 3 n δ n δ 8 0.00 0.00 -0.10 -0.10 24 3 ⇥ 6 -0.20 -0.20 -0.30 -0.30 δ 6 δ 15 0 N τ = 6 -0.40 δ 8 δ 24 -0.40 N τ = 8 δ 10 δ 27 N τ = 10 δ 15 N τ = 12 -0.50 -0.50 T [MeV] 100 200 300 400 500 600 700 T [MeV] 150 200 250 300 Casimir scaling holds for T>300 MeV color screening like in weakly coupled QGP ?

Equation of state in the continuum limit Equation of state has be calculated in the continuum limit up to T=400 MeV using two different quark actions and the results agree well Bazavov et al, PRD 90 (2014) 094503 0.34 16 c 2 0.32 non-int. limit s 0.3 0.28 12 0.26 HRG 0.24 HISQ/tree T c 0.22 8 stout 3p/T 4 0.2 HRG � /T 4 0.18 3s/4T 3 4 0.16 0.14 T [MeV] T [MeV] 0.12 0 150 200 250 300 350 400 130 170 210 250 290 330 370 Hadron resonance gas (HRG): T c = (154 ± 9)MeV Interacting gas of hadrons = non-interacting gas of hadrons and hadron resonances ✏ c ' 300MeV / fm 3 ( virial expansion, Prakash & Venugopalan ) ✏ nucl ' 150MeV / fm 3 ✏ low ' 180MeV / fm 3 HRG agrees with the lattice for T< 145 MeV ✏ high ' 500MeV / fm 3 ✏ proton ' 450MeV / fm 3

How Equation of state changed since 2002 � /T 4 16 ideal gas 14 12 10 8 m q /T=0.4, N � =4 (2000) HISQ (2014) 6 4 2 T [MeV] 0 100 150 200 250 300 350 400 450 • Much smoother transition to QGP • The energy density keeps increasing up to 450 MeV instead of flattening

Equation of State on the lattice and in the weak coupling 6 s/s SB 0.95 stout ( � -3p)/T 4 asqtad, N � =8 0.9 p4, N � =8 5 0.85 p4, N � =6 HISQ, N � =8 0.8 4 HISQ, N � =10 O(g 6 ) EQCD 0.75 p4: N � =8 3 0.7 6 0.65 HISQ 2 stout 0.6 perturbative, NLA O(g 6 ) EQCD 0.55 1 T [MeV] T [MeV] 0.5 250 300 350 400 450 500 250 300 350 400 450 500 550 600 650 The high temperature behavior of the trace anomaly is not inconsistent with weak coupling calculations (EQCD) for T>300 MeV For the entropy density the continuum lattice results are below the weak coupling calculations For T< 500 MeV At what temperature can one see good agreement between the lattice and the weak coupling results ?

QCD thermodynamics at non-zero chemical potential Taylor expansion : hadronic S quark Taylor expansion coefficients give the fluctuations and correlations of conserved charges, e.g. information about carriers of the conserved charges ( hadrons or quarks ) probes of deconfinement

Equation of state at non-zero baryon density Taylor expansion up to 4 th order for net zero strangeness and r = n Q /n B = Z/A = 0 . 4 n S = 0 BNL-Bielefeld-CCNU Moderate effects due to non-zero baryon density µ B /T = 2 ↔ √ s ∼ 20GeV up to Energy density at freeze-out is independent of µ B

Deconfinement : fluctuations of conserved charges 1 h B 2 i � h B i 2 � � baryon number χ B = V T 3 1 � h Q 2 i � h Q i 2 � electric charge χ Q = V T 3 1 h S 2 i � h S i 2 � � strangeness χ S = V T 3 Ideal gas of massless quarks : 1 SB � i / � i 0.8 i=B Q 0.6 χ SB = 1 S S 0.4 conserved charges carried filled : HISQ, N � =6, 8 by light quarks open : stout continuum 0.2 HotQCD: PRD86 (2012) 034509 T [MeV] 0 150 200 250 300 350 BW: JHEP 1201 (2012) 138, conserved charges are carried by massive hadrons

Deconfinement of strangeness Partial pressure of strange hadrons in uncorrelated hadron gas: Strange hadrons are heavy treat them As Boltzmann gas 0.30 non-int. quarks should vanish ! 0.25 • v 1 and v 2 do vanish within errors at low T 0.20 B - χ 4 B • v 1 ¡ and v 2 rapidly increase above χ 2 0.15 v 1 the transition region, eventually 0.10 reaching non-interacting quark v 2 gas values 0.05 uncorr. 0.00 hadrons T [MeV] Bazavov et al, PRL 111 (2013) 082301 140 180 220 260 300 340

Quark number fluctuations at high T At high temperatures quark number fluctuations can be described by weak coupling approach due to asymptotic freedom of QCD quark number fluctuations quark number correlations 0.9 � u 4 / � ideal 0 4 � ud 11 0.85 -0.002 0.8 -0.004 EQCD -0.006 0.75 1.05 1.05 1.05 1.05 1.05 1.05 1.05 EQCD � u � u � u � u � u � u � u 2 / � ideal 2 / � ideal 2 / � ideal 2 / � ideal 2 / � ideal 2 / � ideal 2 / � ideal N � =6 -0.008 2 2 2 2 2 2 2 1 1 1 1 1 1 1 0.7 8 10 -0.01 0.95 0.95 0.95 0.95 0.95 0.95 0.95 12 0.65 EQCD -0.012 cont 0.9 0.9 0.9 0.9 0.9 0.9 0.9 � 4 u (cont) T [MeV] 0.6 T [MeV] T [MeV] T [MeV] T [MeV] T [MeV] T [MeV] T [MeV] -0.014 3-loop HTL 0.85 0.85 0.85 0.85 0.85 0.85 0.85 250 300 350 400 450 500 550 600 650 700 300 300 300 300 300 300 300 500 500 500 500 500 500 500 700 700 700 700 700 700 700 900 900 900 900 900 900 900 0.55 300 350 400 450 500 550 600 650 700 T [MeV] • Lattice results converge as the continuum limit is approached • Good agreement between lattice and the weak coupling approach for 2 nd and 4 th order quark number fluctuations as well as for correlations Bazavov et al, PRD88 (2013) 094021, Ding et at, arXiv:1507.06637