Microscopic Model for Chemical Freeze-Out in Heavy-Ion Collisions 1 David Blaschke Institute of Theoretical Physics, University Wroc� law, Poland Bogoliubov Laboratory for Theoretical Physics, JINR Dubna, Russia Joint Seminar HMUEC-HP @ BLTP Dubna, May 18, 2012 1 Collaboration: J. Berdermann, J. Cleymans, D. Prorok, K. Redlich, L.Turko ... David Blaschke Chiral Condensate and Chemical Freezeout
QCD Phase Diagram & Heavy-Ion Collisions Beam energy scan (BES) programs Energy density vs. baryon density at freeze-out for different √ s NN (GeV) in the QCD phase diagram Highest baryon densities at freeze-out shall be reached for √ s NN ∼ 8 GeV − → QGP phase transition ? David Blaschke Chiral Condensate and Chemical Freezeout
Chemical Freeze-out in the QCD Phase Diagram “New” freeze-out data from STAR BES @ RHIC. “Old” freeze-out data from RHIC (red), Centrality dependence! SPS (blue), AG (black), SIS (green). F. Becattini, J. Manninen, M. Gazdzicki, Phys. Rev. C73 (2006) 044905 Lokesh Kumar (STAR Collab.), arxiv:1201.4203 [nucl-ex] David Blaschke Chiral Condensate and Chemical Freezeout
Chemical freeze-out condition τ exp ( T, µ ) = τ coll ( T, µ ) � τ − 1 coll ( T, µ ) = σ ij n j i,j σ ij = λ � r 2 i �� r 2 j � D.B. et al., Few Body Systems (2011) arxiv:1109.5391 [hep-ph] B. Povh, J. H¨ ufner, PRD 46 (1992) 990 David Blaschke Chiral Condensate and Chemical Freezeout
Hadronic radii and chiral condensate 3 r 2 4 π 2 F − 2 π ( T, µ ) = π ( T, µ ) . F 2 qq � T,µ /m 2 π ( T, µ ) = − m 0 � ¯ π . 3 m 2 qq � T,µ | − 1 . π r 2 π ( T, µ ) = |� ¯ 4 π 2 m q r 2 N ( T, µ ) = r 2 0 + r 2 π ( T, µ ) , Expansion time from entropy conservation S = s ( T, µ ) V ( τ exp ) = const τ exp ( T, µ ) = a s − 1 / 3 ( T, µ ) , H.-J. Hippe and S. Klevansky, PRC 52 (1995) 2172 D.B., J. Berdermann, J. Cleymans, K. Redlich, Few Body Systems (2011) [arxiv:1109.5391] David Blaschke Chiral Condensate and Chemical Freezeout
Chiral Condensate in a Hadron Resonance Gas � dp p 2 � ¯ qq � m 0 � m f + � � = 1 − 4 N c Φ + f − Φ � ¯ qq � vac F 2 π m 2 2 π 2 ε p π � dp p 2 m M � + d M (2 − N s ) E M ( p ) f M ( E M ( p )) 2 π 2 M = f 0 ,ω,... � dp p 2 � m B � f + � � + d B (3 − N s ) B ( E B ( p )) + f − B ( E B ( p )) 2 π 2 E B ( p ) B = N, Λ ,... p 2 d G r G � � − dp E G ( p ) f G ( E G ( p )) 4 π 2 F 2 G G = π,K,η,η ′ S. Leupold, J. Phys. G (2006) D.B., J. Berdermann, J. Cleymans, K. Redlich, Few Body Systems (2011) David Blaschke Chiral Condensate and Chemical Freezeout
Chemical Freeze-out and Chiral Condensate Chemical freeze-out vs. Condensate Chemical freeze-out from kinetic condition, schematic model D.B., J. Berdermann, J. Cleymans, K. Redlich, Few Body Systems (2011) David Blaschke Chiral Condensate and Chemical Freezeout
Chemical Freeze-out and Chiral Condensate Chemical freeze-out vs. Condensate Chemical freeze-out from kinetic condition, a ∼ inverse system size D.B., J. Berdermann, J. Cleymans, K. Redlich, in preparation (2012) David Blaschke Chiral Condensate and Chemical Freezeout
Strong T-Dependence of (inelastic) Collision Time See: C. Blume in: NICA White Paper (2012) C. Wetterich, P. Braun-Munzinger, J. Stachel, PLB (2004) D.B., J. Berdermann, J. Cleymans, K. Redlich, in preparation (2012) David Blaschke Chiral Condensate and Chemical Freezeout
Conclusions - part I The model works astonishingly well! Improvements are plenty: Hadron mass formulae, e.g. from holographic QCD ... Spectral functions - generalized Beth-Uhlenbeck Thermodynamics ... hydrodynamics . Beyond freeze-out towards the deconfined phase: Mott-Hagedorn model David Blaschke Chiral Condensate and Chemical Freezeout
Theoretical laboratory of QCD The energy density normalized by The pressure normalized by T 4 T 4 as a function of the temperature as a function of the temperature on N t = 6,8 and 10 lattices. on N t = 6,8 and 10 lattices. S. Borsanyi et al. “The QCD equation of state with dynamical quarks,” JHEP 1011 , 077 (2010) David Blaschke Chiral Condensate and Chemical Freezeout
Hagedorn resonance gas: hadrons with finite widths The energy density per degree of freedom with the mass M � ε ( T, µ B , µ S ) = g i ε i ( T, µ i ; m i ) i : m i <m 0 � ∞ � d ( M 2 ) A ( M, m i ) ε i ( T, µ i ; M ) , + g i m 2 i : m i ≥ m 0 0 Spectral function Γ · m A ( M, m ) = N M ( M 2 − m 2 ) 2 + Γ 2 · m 2 , � m � N m � T � m � N T � Γ( T ) = C Γ exp T H T H T H David Blaschke Chiral Condensate and Chemical Freezeout
Hagedorn resonance gas: hadrons with finite widths � T dT ′ ε ( T ′ ) P ( T ) = T . T ′ 2 0 N m in the range from N m = 2 . 5 (dashed line) to N m = 3 . 0 (solid line). C Γ = 10 − 4 N T = 6 . 5 T H = 165 MeV � m � N m � T � m � N T � Γ( T ) = C Γ exp T H T H T H D. Blaschke & K. Bugaev, Fizika B 13 , 491 (2004); PPNP 53 , 197 (2004) David Blaschke Chiral Condensate and Chemical Freezeout
Mott-Hagedorn resonance gas State-dependent hadron resonance width Γ i · m i A i ( M, m i ) = N M , ( M 2 − m 2 i ) 2 + Γ 2 i · m 2 i Γ i ( T ) = τ − 1 � λ � r 2 i � T � r 2 coll , i ( T ) = j � T n j ( T ) j D. B., J. Berdermann, J. Cleymans, K. Redlich, PPN 8, 811 (2011) [arXiv:1102.2908] For pions (mesons) π ( T, µ ) = 3 M 2 qq � T | − 1 ; π r 2 |� ¯ � ¯ qq � T = 304 . 8 [1 − tanh (0 . 002 T − 1)] 4 π 2 m q For nucleons (baryons) r 2 N ( T, µ ) = r 2 0 + r 2 π ( T, µ ); r 0 = 0 . 45 fm pion cloud . David Blaschke Chiral Condensate and Chemical Freezeout
Mott-Hagedorn resonance gas Mott-Hagedorn resonance gas: Pressure and energy density for three values of the mass threshold m 0 = 1 . 0 GeV (solid lines) m 0 = 0 . 98 GeV (dashed lines) and m 0 = 0 (dash-dotted lines) Quarks and gluons are missing! David Blaschke Chiral Condensate and Chemical Freezeout
Quarks and gluons in the PNJL model Systematic expansion of the pressure as the thermodynamical potential in the grand canonical ensemble for a chiral quark model of the PNJL type beyond its mean field description P PNJL , MF ( T ) by including perturbative corrections P ( T ) = P ∗ HRG ( T ) + P PNJL , MF ( T ) + P 2 ( T ) , P HRG ( T ) P ∗ HRG ( T ) = 1 + ( P HRG ( T ) / ( aT 4 )) α , with a = 2 . 7 and α = 1 . 8 . Quark and gluon contributions P 2 ( T ) = P quark ( T ) + P gluon ( T ) 2 2 David Blaschke Chiral Condensate and Chemical Freezeout
Quark and gluon contributions Total perturbative QCD correction P 2 = − 8 πα s T 4 ( I + Λ + P quark ( T ) 2 3 Λ ) 2 + ( I − π 2 (( I + Λ ) 2 )) Λ /T → 0 − 3 π − → 2 α s T 4 P gluon ( T ) 2 where � ∞ d x x I ± Λ = e x ± 1 Λ /T . Energy corrections ε 2 ( T ) = T dP 2 ( T ) − P 2 ( T ) . dT David Blaschke Chiral Condensate and Chemical Freezeout
Quarks, gluons and hadron resonances P MHRG ( T ) = 1 + δ i e − [ √ d 3 p � p 2 + M 2 − µ i ] /T � � � � i δ i d i dMA i ( M, m i ) T ln , (2 π ) 3 Quark-gluon plasma contributions are described within the improved PNJL model with α s corrections . Heavy hadrons are described within the resonance gas with finite width exhibiting a Mott effect at the coincident chiral and deconfinement transitions. David Blaschke Chiral Condensate and Chemical Freezeout
Quarks, gluons and hadron resonances II Contribution restricted to the region around the chiral/deconfinement transition 170-250 MeV Fit formula for the pressure P = aT 4 + bT 4 . 4 tanh( cT − d ) , a = 1 . 0724 , b = 0 . 2254 , c = 0 . 00943 , d = 1 . 6287 David Blaschke Chiral Condensate and Chemical Freezeout
Conclusions - part II An effective model description of QCD thermodynamics at finite temperatures which properly accounts for the fact that in the QCD transition region it is dominated by a tower of hadronic resonances. A generalization of the Hagedorn resonance gas thermodynamics which includes the finite lifetime of hadronic resonances in a hot and dense medium To do Join hadron resonance gas with quark-gluon model. Calculate kurtosis and compare with lattice QCD. Spectral function for low-lying hadrons from microphysics (PNJL model ...). David Blaschke Chiral Condensate and Chemical Freezeout
Invitation to upcoming events DIAS-TH: Dubna International Advanced School for Theoretical Physics Helmholtz International Summer School Dense Matter in Heavy Ion Collisions and Astrophysics: Theory and Experiment Dubna, Russia, August 28 - September 8, 2012 Organisers H. Stöcker (GSI) A. Sorin (JINR) D. Blaschke (Wroclaw & JINR) Topics Local Organisers • Equation of state & QCD phase transitions V. Zhuravlev (JINR) • Transport properties in dense QCD matter J. Schmelzer (Rostock & JINR) • Hadronization & freeze-out in heavy ion A. Khvorostukhin (JINR) A. Friesen (JINR) collisions (HIC) V. Nesterenko (JINR) • Astrophysics of compact stars (CS) V. Novikova (JINR) • Simulations of dense QCD, HIC and CS Contact • Experiments and observational programs dm12@theor.jinr.ru http://theor.jinr.ru/~dm12 David Blaschke Chiral Condensate and Chemical Freezeout
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