Deconfinement at high temperatures and moderately high baryon densities Péter Petreczky

Transcription

1 Deconfinement at high temperatures and moderately high baryon densities Péter Petreczky What is the limiting temperature on hadronic matter? What is the nature of the deconfined matter? In this talk: Chiral transition in QCD at T>0 Color screening deconfinement Equation of state Fluctuations of conserved charges How does the transition and EoS changes with baryon density LQCD INT Program INT-16-2b, Phases of Dense Matter, Seattle, July 14, 2016

2 The temperature dependence of chiral condensate Renormalized chiral condensate introduced by Budapest-Wuppertal collaboration With choice : Bazavov et al (HotQCD), Phys. Rev. D85 (2012) ; Bazavov, PP, PRD 87(2013)094505, Borsányi et al, JHEP 1009 (2010) 073 Calculations with chiral (Domain Wall) fermions: disc = V T h( ) 2 i h i 2 Bhattacharya et al (HotQCD), PRL 113 (2014) l R HISQ, m l =m s /20 HISQ, m l =m s /27 stout, m l =m s /27 χ MS l,disc. /T , HISQ,m l =0.05 m s,m π =161MeV ,m π =200MeV ,m π =200MeV ,m π =200MeV ,m π =140MeV ,m π =140MeV O(4) scaling analysis and continuum limit: T (MeV) Transition is a crossover (no volume dep.) T c = (155 ± 8 ± 1)MeV

3 Deconfinement and color screening Onset of color screening is described by Polyakov loop (order parameter in SU(N) gauge theory) exp( F Q Q(r, T )/T )= 1 9 htrl(r)trl (0)i F Q Q(r!1,T)=2F Q (T ) 2+1 flavor QCD, continuum extrapolated (work in progress with Bazavov, Weber ) 0.9 L ren (T) T QCD c T PG c free energy of static quark anti-quark pair shows Debye screening SU(N) gauge theory QCD! at high temperatures Similar results with stout action Borsányi et al, JHEP04(2015) stout, cont. HISQ, cont. SU(3) SU(2)

4 The entropy of static quark Bazavov, PP, PRD 87 (2013) Hadron gas (of static-light) vs. LQCD F Q (T) [MeV] HISQ stout Bazavov et al, PRD 93 (2016) S Q S Q = T (N local fit global 1/N 4 fit global 1/N 2 fit HRG N = 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

5 Equation of state in the continuum limit Equation of state has been calculated in the continuum limit up to T=400 MeV using two different discretizations and the results agree well Bazavov et al (HotQCD), PRD 90 (2014) T c HRG 3p/T 4 /T 4 3s/4T 3 non-int. limit Hadron resonance gas (HRG): Interacting gas of hadrons = non-interacting gas of hadrons and hadron resonances ç virial expansion Prakash,Venugopalan, NPA546 (1992) 718 HRG agrees with the lattice for T< 155 MeV Borsányi et al, PLB 730 (2014) 99 c 2 s T c = (154 ± 9)MeV c ' 300MeV/fm 3 low ' 180MeV/fm 3 HISQ/tree stout HRG nucl ' 150MeV/fm 3 high ' 500MeV/fm 3 proton ' 450MeV/fm 3

6 QCD thermodynamics at non-zero chemical potential Taylor expansion : p(t,µ B,µ Q,µ S,µ C ) T 4 = X ijkl 1 i!j!k!l! BQSC ijkl µb i µb j µs k µc T T T T l hadronic p(t,µ u,µ d,µ s,µ c ) T 4 = X ijkl 1 i!j!k!l! udsc ijkl µu i µd j µs k µc T T T T l quark abcd ijkl = T i j i l d ln Z(T,V,µ a,µ b,µ c,µ d ) µa =µ b =µ c =µ d =0 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

7 Deconfinement : fluctuations of conserved charges B = 1 VT 3 hb2 i hbi 2 Q = 1 VT 3 hq2 i hqi 2 S = 1 VT 3 hs2 i hsi 2 i / i SB baryon number electric charge strangeness Ideal gas of massless quarks : i=b Q S filled : HISQ, N =6, 8 open : stout continuum SB S =1 conserved charges carried by light quarks Bazavov et al (HotQCD) PRD86 (2012) Borsányi et al, JHEP 1201 (2012) 138 conserved charges are carried by massive hadrons

8 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 u 4 / ideal 4 quark number fluctuations ud 11 quark number correlations EQCD 4 u (cont) 3-loop HTL u 2 / ideal EQCD 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) , Ding et at, PRD92 (2015) EQCD N = cont

9 Deconfinement of strangeness Partial pressure of strange hadrons in uncorrelated hadron gas: Strange hadrons are heavy è treat them as Boltzmann gas should vanish! 0.30 non-int. quarks v 1 and v 2 do vanish within errors at low T v 1 and v 2 rapidly increase above the transition region, eventually reaching non-interacting quark gas values Bazavov et al, PRL 111 (2013) uncorr. hadrons χ 2 B -χ4 B v 1 v 2

10 Deconfinement of strangeness (cont d) Using the six Taylor expansion coefficients related to strangeness it is possible to construct combinations that give up to terms B 3 (0,0) B 3 (0,1/6) B 3 (1/3,1/6) HRG P S =3,B M(0,0) M(0,-3) M(-6,-3) HRG P S =1,M Hadron resonance gas descriptions breaks down for all strangeness sectors above T c Bazavov et al, PRL 111 (2013)

11 Deconfinement of charm XY C nml = T p(t,µ X,µ Y,µ C )/T n C m c T only C =1 sector contributes In the hadronic phase all BC-correlations are the same! BC BC 13 / 22 BC BC 11 / 13 N : 8 6 non-int. quarks Bazavov et al, PLB 737 (2014) 210 Charm baryon to meson pressure BC C BC 13 /( 4-13 ) BQC QC BQC /( ) QM-HRG-3 QM-HRG PDG-HRG non-int. quarks un-corr. hadrons BSC SC BSC /( ) N : 8 6 Hadronic description breaks down just above T 0.3 c open charn deconfines above T c The charm baryon spectrum is not well known (only few states in PDG), HRG works only if the missing states are included

12 Quasi-particle model for charm degrees of freedom Charm dof are good quasi-particles at all T because M c >>T and Boltzmann approximation holds p C (T,µ B,µ c )=p C q (T ) cosh(ˆµ C +ˆµ B /3) + p C B(T ) cosh(ˆµ C +ˆµ B )+p C M (T ) cosh(ˆµ C ) C 2, BC 13, BC 22 ) p C q (T ),p C M (T ),p C B(T ) Partial meson and baryon pressures described by HRG at T c then drop gradually, charm quark only dominant dof at T>200 MeV or ε > 6 GeV/fm p q C /p C p B C /p C ˆµ X = µ X /T and dominate the charm pressure Partial pressures drop because hadronic excitations become broad at high temperatures (bound state peaks merge with the continuum) p M C /p C Mukherjee, PP, Sharma, PRD 93 (2016) See Jakovác, PRD88 (2013), Biró, Jakovác, PRD(2014) Vice versa for quarks

13 Equation of state at non-zero baryon density At the highest energy heavy ion collisions create a system with almost zero net baryon density. by decreasing the the center of mass energy of the collisions E CM = p s the net baryon number can be increased and the EoS calculated in LQCD using Taylor expansion Taylor expansion up to 4 th order for net zero strangeness n S =0 and r = n Q /n B = Z/A =0.4 Moderate effects due to non-zero baryon density up to µ B /T =2$ p s 20GeV and Taylor expansion works well BNL-Bielefeld-CCNU

14 Freeze-out and transition at non-zero baryon density T c (µ B ) T c (0) =1 apple µb T c apple =0.020(4) Cea et al, PRD 93 (2016) apple =0.0135(20) Bonati et al, PRD 92 (2015) apple =0.0149(21) Bellweid et al, PLB 751 (2015) 559 apple =0.0066(7) Kaczmarek et al, PRD 83 (2011) n S = 0, n Q = 0.4n B O(µ B ) N τ = 8 O(µ B 3 ) O(µ B 5 ) n B [fm -3 ] s 1/2 NN [GeV] BNL-Bielefeld-CCNU

15 Summary The deconfinement transition temperature coincides with the chiral transition temperature T c = 154(9) MeV Equation of state are known in the continuum limit up to T=400 MeV at zero baryon density and the energy density at the transition is small 300 MeV/fm 3 Hadron resonance gas (HRG) can describe various thermodynamic quantities at low temperatures Deconfinement transition can be studied in terms of fluctuations and correlations of conserved charges; deconfinement means an abrupt breakdown of hadronic description that occurs at T c and appearance of quark like excitations Hadronic excitations containing charm quark can exist above T c For T > ( ) MeV weak coupling expansion may work for certain quantities (e.g. quark number susceptibilities) The region of moderately large baryon densities relevant for RHIC can be accessed in LQCD using Taylor expansion. The effects of the baryon densities are not large and consistent with HRG (no hint for critical point?); Much more work is needed to obtain reliable results, e.g. T c (µ B ), energy density at T c.

16 How Equation of state changed since 2002? /T 4 ideal gas m q /T=0.4, N =4 (2000) HISQ (2014) Much smoother transition to QGP The energy density keeps increasing up to 450 MeV instead of flattening

17 Entropy of static quark at high temperature S Q (T) LO NLO, µ=(1-4) T NNLO lattice M. Berwein, N. Brambilla, P. Petreczky and A. Vairo, arxiv: [hep-ph]

18 Does the quasi-particle model makes sense? 4 non-trivial constraints on the model provided by : BC 31, SC 31, BSC 121, BSC 211 Diquark pressure is zero! c 1 /p C c 2 /p C c 3 /p C c 4 /p C p B C,S=2 /p C p C,S=1 B /p C p C,S=1 M /p C