Phases and Fluctuations in QCD Bernd-Jochen Schaefer Austria - PowerPoint PPT Presentation

‣ ‣ Phases and Fluctuations in QCD Bernd-Jochen Schaefer Austria Germany Germany October 10 th 2014


 ‣ ‣ Agenda • Phase transitions and QCD � • QCD-like model studies ➜ chiral and deconfinement aspects � � • Significance of Fluctuations � � 10.10.2014 | B.-J. Schaefer | Giessen University | 2


 ‣ ‣ Experiments: Heavy-Ion Collision QCD under extreme conditions: active field for the next 20 years ➜ see e.g. FAIR construction (2014) One important HIC Experiment: C(ompressed) B(aryonic) M(atter) 
 QCD phase diagram and QCD matter Equation of State Understanding fundamental phenomena: 
 e.g. 
 • confinement • nature of chiral & 
 deconfinement transition • nuclear matter • ... 10.10.2014 | B.-J. Schaefer | Giessen University | 3

‣ ‣ Experiments: Heavy-Ion Collision QCD under extreme conditions: active field for the next 20 years ➜ see e.g. FAIR construction (2014) One important HIC Experiment: C(ompressed) B(aryonic) M(atter) 
 QCD phase diagram and QCD matter Equation of State FAIR construction start 2012 Aug.2014 FAIR now � approved for next 2 years � without limitations 
 10.10.2014 | B.-J. Schaefer | Giessen University | 4

‣ ‣ Quantum Chromodynamics QCD at finite temperatures and densities 
 ➜ “transitions” partial deconfinement & partial chiral symmetry restoration For physical quark masses: smooth phase transitions ➜ deconfinement: analytic change of d.o.f. ➜ associated global QCD symmetries only exact in two mass limits: 1.) infinite quark masses ➜ center symmetry: Order parameter: VEV of traced Polyakov loop 2.) massless quarks ➜ chiral symmetry: Order parameter: chiral condensate � � � � 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 for finite quark masses: 
 2 nd order 2 nd order 2 nd order 2 nd order Z(2) Z(2) Z(2) Z(2) order order order order both symmetries 
 O(4) O(4) O(4) O(4) explicitly broken 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 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 10.10.2014 | B.-J. Schaefer | Giessen University | 5

‣ ‣ Quantum Chromodynamics QCD at finite temperatures and densities 
 ➜ “transitions” partial deconfinement & partial chiral symmetry restoration For physical quark masses: smooth phase transitions ➜ deconfinement: analytic change of d.o.f. ➜ associated global QCD symmetries only exact in two mass limits: 1.) infinite quark masses ➜ center symmetry: Order parameter: VEV of traced Polyakov loop 2.) massless quarks ➜ chiral symmetry: Order parameter: chiral condensate � � � � N f =2 N f =2 N f =2 N f =2 PURE PURE PURE PURE open issue: N f =2: O(4)? 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 for finite quark masses: 
 2 nd order 2 nd order 2 nd order 2 nd order U(2) L × U(2) R /U(2) V ? Z(2) Z(2) Z(2) Z(2) order order order order both symmetries 
 O(4) O(4) O(4) O(4) explicitly broken ➜ crit. exp. similar or even 1 st order? physical point physical point physical point physical point N f =3 N f =3 N f =3 N f =3 dep. on strength of axial anomaly! 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 2 nd order crossover m c m π = 0 m π = ∞ 2 nd order 2 nd order 2 nd order 2 nd order 1 st 1 st 1 st 1 st m π ,c Z(2) Z(2) Z(2) Z(2) order order order order still conflicting lattice results! 1 st order � � � � Z (2) crossover m u,d m u,d m u,d m u,d 10.10.2014 | B.-J. Schaefer | Giessen University | 6

‣ ‣ Conjectured QCD phase diagram early universe quark − gluon plasma LHC QCD lattice simulations: no final answer RHIC SPS 195 < ψψ > ∼ 0 Temperature 190 crossover FAIR/JINR Physical m l /m s T c [MeV] 185 180 HISQ/tree AGS quark matter 175 Asqtad SIS 170 < ψψ > = 0 / 165 160 crossover hadronic fluid 155 superfluid/superconducting Combined continuum extrapolation 150 -2 phases ? HISQ/tree: quadratic in N � 145 -2 Asqtad: quadratic in N � n > 0 n = 0 2SC < ψψ > = 0 / B B CFL 140 -2 N � vacuum nuclear matter 135 neutron star cores 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 µ courtesy of F. Karsch Lattice simulations ➜ can one improve the model calculations? ➜ remove model ambiguities 10.10.2014 | B.-J. Schaefer | Giessen University | 7

‣ ‣ Conjectured QC 3 D phase diagram chiral & deconfinement Theoretical questions: early universe transition quark − gluon plasma LHC • CEP: existence/location/number RHIC • Quarkyonic phase: coincidence of both transitions SPS < ψψ > ∼ 0 �� � = � & � > � ? Temperature crossover FAIR/JINR • relation between chiral & deconfinement? ? AGS chiral CEP/deconfinement CEP? quark matter [Braun, Janot, Herbst 12/14] SIS < ψψ > = 0 / • finite volume e ff ects ? ➜ lattice comparison crossover hadronic fluid • inhomogeneous phases? ➜ more favored? superfluid/superconducting phases ? • role of fluctuations? so far mostly mean-field results 
 n > 0 n = 0 2SC < ψψ > = 0 / ➜ effects of fluctuations are important B B CFL vacuum nuclear matter neutron star cores e.g. size of critical region around CEP µ • axial anomaly restoration around chiral transition ? • good experimental signatures? ➜ higher moments more sensitive to criticality ➜ can one improve the model calculations? deviation from HRG model ➜ remove model ambiguities 10.10.2014 | B.-J. Schaefer | Giessen University | 8

‣ ‣ Conjectured QC 3 D phase diagram chiral & deconfinement Theoretical questions: early universe transition quark − gluon plasma LHC • CEP: existence/location/number RHIC • Quarkyonic phase: coincidence of both transitions SPS < ψψ > ∼ 0 �� � = � & � > � ? Temperature crossover FAIR/JINR • relation between chiral & deconfinement? ? AGS chiral CEP/deconfinement CEP? quark matter [Braun, Janot, Herbst 12/14] SIS < ψψ > = 0 / • finite volume e ff ects ? ➜ lattice comparison crossover hadronic fluid • inhomogeneous phases? ➜ more favored? superfluid/superconducting phases ? • role of fluctuations? so far mostly mean-field results 
 n > 0 n = 0 2SC < ψψ > = 0 / ➜ effects of fluctuations are important B B CFL vacuum nuclear matter neutron star cores e.g. size of critical region around CEP µ • axial anomaly restoration around chiral transition ? • good experimental signatures? ➜ higher moments more sensitive to criticality ➜ can one improve the model calculations? deviation from HRG model ➜ remove model ambiguities non-perturbative continuum functional methods (DSE, FRG, nPI) ➜ complementary to lattice ⇒ no sign problem μ >0 ⇒ chiral symmetry/fermions/small masses/chiral limit 10.10.2014 | B.-J. Schaefer | Giessen University | 9

‣ ‣ Conjectured QC 3 D phase diagram chiral & deconfinement Theoretical questions: early universe transition quark − gluon plasma LHC • CEP: existence/location/number RHIC • Quarkyonic phase: coincidence of both transitions SPS < ψψ > ∼ 0 �� � = � & � > � ? Temperature crossover FAIR/JINR • relation between chiral & deconfinement? ? AGS chiral CEP/deconfinement CEP? quark matter [Braun, Janot, Herbst 12/14] SIS < ψψ > = 0 / • finite volume e ff ects ? ➜ lattice comparison crossover hadronic fluid • inhomogeneous phases? ➜ more favored? superfluid/superconducting phases ? • role of fluctuations? so far mostly mean-field results 
 n > 0 n = 0 2SC < ψψ > = 0 / ➜ effects of fluctuations are important B B CFL vacuum nuclear matter neutron star cores e.g. size of critical region around CEP µ • axial anomaly restoration around chiral transition ? • good experimental signatures? Method of choice: 
 Functional Renormalization Group ➜ higher moments more sensitive to criticality e.g. (Polyakov)-quark-meson model truncation deviation from HRG model • good description for chiral sector � • implementation of gauge dynamics 
 (deconfinement sector) 10.10.2014 | B.-J. Schaefer | Giessen University | 10


 ‣ ‣ Agenda • Phase transitions and QCD � • QCD-like model studies ➜ chiral and deconfinement aspects � � • Significance of Fluctuations � � 10.10.2014 | B.-J. Schaefer | Giessen University | 11