Studying the QCD Phase Diagram via BES Fluctuations and the Critical - PowerPoint PPT Presentation

Studying the QCD Phase Diagram via BES Fluctuations and the Critical Point M. Stephanov U. of Illinois at Chicago M. Stephanov (UIC) QCD Phase Diagram via BES Temple 2014 1 / 15

Outline QCD phase diagram 1 Critical point and fluctuations 2 Higher moments RHIC beam energy scan 3 M. Stephanov (UIC) QCD Phase Diagram via BES Temple 2014 2 / 15

QCD Phase Diagram QGP (liquid) critical point ? Quarkyonic regime hadron gas nuclear CFL+ ? matter Lattice at µ B � 2 T (reviewed by S. Mukherjee) Critical point – a singularity of EOS, anchors the 1st order transition. M. Stephanov (UIC) QCD Phase Diagram via BES Temple 2014 3 / 15

Critical point and fluctuations The key equation: P ( X ) ∼ e S ( X ) (Einstein 1910) At the critical point S ( X ) has a “flat direction” or “soft-mode”. Fluctuation measures diverge: � ∂ 2 S � − 1 � X 2 � = − = V Tχ ∂X 2 CLT? ξ → ∞ M. Stephanov (UIC) QCD Phase Diagram via BES Temple 2014 4 / 15

Fluctuations of order parameter and ξ Fluctuations at CP – conformal field theory. Parameter-free → universality. Near CP ξ = m − 1 < ∞ , σ P [ σ ] ∼ exp {− Ω[ σ ] /T } , 2( ∇ σ ) 2 + m 2 � 1 � � 2 σ 2 + λ 3 3 σ 3 + λ 4 4 σ 4 + . . . σ d 3 x Ω = . d 3 x σ ( x ) : � Moments of order parameter σ V ≡ V � = V T ξ 2 . Each propagator gives ξ 2 . Thus � σ 2 As a result higher moments grow faster with ξ with universal exponents M. Stephanov (UIC) QCD Phase Diagram via BES Temple 2014 5 / 15

Sign Higher moments also depend on which side of the CP we are κ 3 [ σ V ] = 2 V T 3 / 2 ˜ λ 3 ξ 4 . 5 ; κ 4 [ σ V ] = 6 V T 2 [ 2(˜ λ 3 ) 2 − ˜ λ 4 ] ξ 7 . E.g., if symmetry ( ± σ ) constrains λ 3 = 0 then κ 3 = 0 and κ 4 < 0 . 2 relevant directions. Using universal Ising model variables: M. Stephanov (UIC) QCD Phase Diagram via BES Temple 2014 6 / 15

Mapping to QCD In QCD ( t, H ) → ( µ − µ CP , T − T CP ) � 4 κ 4 [ N ] = � N � + κ 4 [ σ V ] × g 4 � + . . . , κ 4 [ σ V ] < 0 means κ 4 [ N ] � N � < 1 Lessons: (Athanasiou-Rajagopal-MS 2010) Sensitivity to g . Even more to µ B [ CP ] (exponential). Ratios of cumulants can be used to reduce these uncertanties. At large µ B protons are as good as net-protons wrt CP search. M. Stephanov (UIC) QCD Phase Diagram via BES Temple 2014 7 / 15

Why ξ is finite System expands and is out of equilibrium Universal scaling law: ξ ∼ τ 1 /z , where 1 /τ is expansion rate and z ≈ 3 (Son-MS) . Berdnikov-Rajagopal estimate ξ ∼ 2 − 3 fm. Hydrodynamics with a model EOS by Asakawa-Nonaka: Significant for higher powers of ξ . Need full critical dynamics to take non-equilibrium into account M. Stephanov (UIC) QCD Phase Diagram via BES Temple 2014 8 / 15

RHIC beam energy scan 200 LTE04 LTE03 LTE08 T , 19 LR04 MeV 11 150 RHIC scan 7.7 100 0 0 200 400 600 µ B , MeV Negative contribution to κ 4 around 19 GeV ( µ B ∼ 200 MeV). O(magnitude) consistent with estimates. Acceptance effects important (Asakawa-Kitazava 2012 Bzdak-Koch 2012) M. Stephanov (UIC) QCD Phase Diagram via BES Temple 2014 9 / 15

A scenario/hypothesis Assuming critical region ∆ µ B ∼ O (100) MeV. Critical region fits in the gap between 19 and 11 GeV. M. Stephanov (UIC) QCD Phase Diagram via BES Temple 2014 10 / 15

A scenario/hypothesis Assuming critical region ∆ µ B ∼ O (100) MeV. Critical region fits in the gap between 19 and 11 GeV. First order transition signatures at 11 and 7.7 GeV? (Soft EOS) M. Stephanov (UIC) QCD Phase Diagram via BES Temple 2014 10 / 15

What have we learned so far Consistent with lattice – no signals of the CP at µ B < 200 MeV. Signal consistent with the scenario µ B [ CP ] ∼ 250 MeV seen in κ 4 [ N protons ] . Inconclusive without κ 4 rising above the baseline. M. Stephanov (UIC) QCD Phase Diagram via BES Temple 2014 11 / 15

Questions and Thoughts Why in 0-5% but not in 70-80%? Bigger system. Cools slower . Larger ξ (Berdnikov-Rajagopal) and κ 4 ∼ ξ 7 . Important to study dynamical evolution of fluctuations. M. Stephanov (UIC) QCD Phase Diagram via BES Temple 2014 12 / 15

What needs to be done: theory Non-equilibrium critical dynamics simulations (H. Petersen’s talk) Determine signal and background (baseline) given EOS. Better knowledge of the EOS near the critical point: Critical region: size and shape, mapping tH → Tµ B (Asakawa,Nonaka;Sasaki,Friman,Redlich;Kapusta,Torres- Rincon;Koch,Randrup. . . ) Coupling g of critical mode to protons, pions, kaons. Prediction of µ B [ CP ] : lattice. (S. Mukherjee’s talk) M. Stephanov (UIC) QCD Phase Diagram via BES Temple 2014 13 / 15

What needs to be done: experiment Data at √ s ∈ [11 − 19] GeV is crucial. ⇒ 14.5 GeV data + BESII. The rise above the baseline? More statistics at 7.7 and 11 GeV. ⇒ BESII. (D. Cebra’s talk) M. Stephanov (UIC) QCD Phase Diagram via BES Temple 2014 14 / 15

Summary: Beam Energy Scan and Fluctuations Lattice and RHIC scan Universality and 4th moment (kurtosis) near CP: 200 LTE04 LTE03 LTE08 T , 19 MeV LR04 11 150 R H I 7.7 C s c a n 100 magnitude and sign strongly depend on √ s : O ( ξ 7 ) . 0 0 200 400 600 Doubly non-monotonous. µ B , MeV Critical region could fit in the gap between 19 and 11 GeV. Data at ∼ 15 GeV is needed. If the scenario above is realized: search for 1st-order transition signatures at 11, 7.7 GeV and lower (+FAIR). M. Stephanov (UIC) QCD Phase Diagram via BES Temple 2014 15 / 15