Cumulants ratios of conserved charge fluctuations: A comparison of - PowerPoint PPT Presentation

Cumulants ratios of conserved charge fluctuations: A comparison of lattice QCD and experimental results Christian Schmidt BNL-Bi-CCNU Collaboration: A. Bazavov, H.-T. Ding, P. Hegde, O. Kaczmarek, F. Karsch, E. Laermann, S. Mukherjee, P. Petreczky, C. Schmidt, W. Soeldner, M. Wagner 1 Christian Schmidt Sign2015, Debrecen, Hungary

Motivation: The QCD phase diagram Expected phase diagram of QCD: QCD T [MeV] critical end-point quark-gluon-plasma 154(9) hadron gas vacuum nuclear matter neutron stars 0 chemical potential µ B Critical end-point? 2 Christian Schmidt Sign2015, Debrecen, Hungary

Motivation: The QCD phase diagram Expected phase diagram of QCD: QCD T [MeV] critical end-point quark-gluon-plasma 154(9) hadron gas vacuum nuclear matter neutron stars 0 chemical potential µ B Critical end-point? ⇒ Diverging correlation length and fluctuations. Universal behavior within a scaling region. 2 Christian Schmidt Sign2015, Debrecen, Hungary

Motivation: The QCD phase diagram Expected phase diagram of QCD: QCD T [MeV] what we really know... 154(9) vacuum nuclear matter neutron stars 0 chemical potential µ B Critical end-point? 3 Christian Schmidt Sign2015, Debrecen, Hungary

Motivation: The QCD phase diagram Expected phase diagram of QCD: QCD T [MeV] what we really know... 154(9) vacuum nuclear matter neutron stars 0 chemical potential µ B Critical end-point? ⇒ Diverging correlation length and fluctuations. Universal behavior within a scaling region. 3 Christian Schmidt Sign2015, Debrecen, Hungary

Motivation: The QCD phase diagram Quark mass dependance of the phase diagram: More critical T 2nd order, O(4) points! 2nd order, Z(2) 1st order Lattice crossover Experiment (freeze-out) Is physics on the freeze-out line sensitive to QCD critical behavior? µ tri µ CEP B B µ B m phys u,d m u,d 4 Christian Schmidt Sign2015, Debrecen, Hungary

Experimental efforts: Beam Energy Scan Initial conditions: depend on collision energy , √ s NN hydrodynamic evolution the system size (type of ion), the impact parameter, ... dN/dy s =200 GeV NN 2 10 10 Data 1 STAR PHENIX BRAHMS Chemical freeze-out: defines the moment � 1 10 Model, 2 /N =29.7/11 � from where particle abundance are fixed df 3 T=164 MeV, = 30 MeV, V=1950 fm µ b (up to particle decays), parametrized by + � � + � + K K p p � � � � � d d K* * * � � � � � Andronic, Braun-Munzinger, T f ( √ s ) , µ f ( √ s ) , V f ( √ s ) Stachel, PLB 673 (2009) 142. 5 Christian Schmidt Sign2015, Debrecen, Hungary

Experimental efforts: Beam Energy Scan � κσ 2 = χ 4 / χ 2 √ s X. Luo, CPOD’14 intriguing non-monotonic behavior ⇒ � in the cumulant ratio of net-proton number fluctuations 6 Christian Schmidt Sign2015, Debrecen, Hungary � ��

Experimental efforts: Beam Energy Scan � κσ 2 = χ 4 / χ 2 √ s X. Luo, CPOD’14 Can this data be understood in terms of equilibrium thermodynamics? � 7 Christian Schmidt Sign2015, Debrecen, Hungary � ��

Experimental efforts: Beam Energy Scan � κσ 2 = χ 4 / χ 2 X. Luo, CPOD’14 Can this data be understood in terms of equilibrium thermodynamics? � How far do we get with a low order Taylor expansion? 8 Christian Schmidt Sign2015, Debrecen, Hungary � ��

Motivation: The QCD phase diagram Lattice 2015 -- Curvature of the phase diagram Are the curvature of the Bielefeld-BNL P4, Nt=8, PRD 83 (2011) 014504 crossover temperature and Bielefeld-CCNU HISQ Nt=6 Taylor the freeze-out curve considerably different ? Cea et al HISQ Nt=6,8,10,12 Analytical [1508.07599] Pisa 2stout Nt=6,8,10,12 Analytical [1507.03571] T [MeV] Wuppertal 4stout Nt=10,12,16 Analytical [1507.07510] J. Cleymans et al., PRC 73, 034905 (2006). 154(9) Figure taken from S. Borsanyi, QM2015 (modified) 0.005 0.015 0.025 0.01 0.02 0.03 0 vacuum nuclear matter neutron stars 0 chemical potential µ B 9 Christian Schmidt Sign2015, Debrecen, Hungary

Content 1) Introduction and Motivation 2) Taylor expansion of pressure • definitions, state-of-the-art, convergence estimate 2) Cumulant ratios at nonzero baryon number density µ f • determination of freeze-out parameter, expressing by M B / σ 2 B B • RHIC data vs. QCD equilibrium thermodynamics • constraints: strangeness neutrality, constant baryon number to electric charge ratio 3) Conclusions and Summary 10 Christian Schmidt Sign2015, Debrecen, Hungary

Taylor expansion of the pressure 11 Christian Schmidt 2 nd Heavy Ion Collisions in the LHC era and Beyond

Conserved charge fluctuations Expansion of the pressure: ◆ i ✓ µ Q ◆ j ✓ µ S ◆ k ∞ 1 ✓ µ B p X i ! j ! k ! χ BQS T 4 = ijk, 0 T T T i,j,k =0 X = B, Q, S : conserved charges Lattice Experiment V T 3 χ X ( δ N X ) 2 ↵ ⌦ ∂ n [ p/T 4 ] = � 2 χ X � n = � V T 3 χ X ( δ N X ) 2 ↵ 2 ∂ ( µ X /T ) n ⌦ ( δ N X ) 4 ↵ ⌦ = − 3 � µ X =0 4 V T 3 χ X ( δ N X ) 4 ↵ ⌦ = generalized susceptibilities 6 ( δ N X ) 4 ↵ ⌦ ( δ N X ) 2 ↵ ⌦ − 15 ( δ N X ) 2 ↵ 3 ⌦ only at ! +30 ⇒ µ X = 0 cumulants of net-charge fluctuations δ N X ⌘ N X � h N X i ⇒ only at freeze-out ( )! µ f ( √ s ) , T f ( √ s ) 12 Christian Schmidt Sign2015, Debrecen, Hungary

Conserved charge fluctuations Expansion of the pressure: ◆ i ✓ µ Q ◆ j ✓ µ S ◆ k ∞ 1 ✓ µ B p X i ! j ! k ! χ BQS T 4 = ijk, 0 T T T i,j,k =0 X = B, Q, S : conserved charges consider cumulant ratios to eliminate the freeze-out volume Lattice Experiment χ X 1 ( µ B , T ) M X M := mean = χ X 2 ( µ B , T ) σ 2 variance X σ 2 := χ X 3 ( µ B , T ) skewness S := S X σ X = χ X 2 ( µ B , T ) kurtosis κ := χ X 4 ( µ B , T ) κ X σ 2 = X χ X 2 ( µ B , T ) 13 Christian Schmidt Sign2015, Debrecen, Hungary

State-of-the-art equation of state for (2+1)-flavor pressure , energy density and entropy density , at : µ B = µ Q = µ S = 0 p ε s Bazavov et al. [HotQCD], Phys. Rev. D90 (2014) 094503. • improves over earlier HotQCD • up to the crossover region the QCD calculation Bazavov et al. [HotQCD], EoS agrees well with the HRG EoS, Phys. Rev. D80 (2009) 014504. however, QCD results are systematically above HRG • consistent with results from Budapest-Wuppertal (stout) evidence for additional ⇒ S. Borsanyi et al. [WB] Phys. Lett. hadronic states? B730 (2014) 99 14 Christian Schmidt Sign2015, Debrecen, Hungary

The equation of state at µ B > 0 chemical potential dependent part: ratios are unity in the HRG ∞ χ B = P ( T, µ B ) � P ( T, 0) 2 n ( T ) ⇣ µ B ⌘ 2 n X P/T 4 � � ∆ = T 4 (2 n )! T n =1 χ B χ B ✓ ◆ = 1 1 + 1 4 ( T ) 1 6 ( T ) 2 χ B µ 2 µ 2 µ 4 2 ( T )ˆ 2 ( T ) ˆ B + 2 ( T ) ˆ B + ... B χ B χ B 12 360 LO NLO NNLO with µ B = µ B /T ˆ 0.35 1.2 LO NLO B / χ 2 B B free � 2 χ 4 hadron resonance gas 0.3 1 0.25 0.8 N τ =6 0.2 8 continuum extrap. 0.6 N � =12 0.15 BNL-Bielefeld 8 preliminary 6 0.4 0.1 PDG-HRG 0.2 0.05 free quark gas T [MeV] T [MeV] 0 0 120 140 160 180 200 220 240 260 280 120 140 160 180 200 220 240 260 280 15 Christian Schmidt Sign2015, Debrecen, Hungary

The equation of state at µ B > 0 chemical potential dependent part: ratios are unity in the HRG ∞ χ B = P ( T, µ B ) � P ( T, 0) 2 n ( T ) ⇣ µ B ⌘ 2 n X P/T 4 � � ∆ = T 4 (2 n )! T n =1 χ B χ B ✓ ◆ = 1 1 + 1 4 ( T ) 1 6 ( T ) 2 χ B µ 2 µ 2 µ 4 2 ( T )ˆ 2 ( T ) ˆ B + 2 ( T ) ˆ B + ... B χ B χ B 12 360 LO NLO NNLO with µ B = µ B /T ˆ 16 Christian Schmidt Sign2015, Debrecen, Hungary