Critical vs. spurious fluctuations in the search for the QCD critical point Maurício Hippert Eduardo S. Fraga Edivaldo M. Santos Instituto de Física - Universidade Federal do Rio de Janeiro June 16, 2016 Maurício Hippert (IF-UFRJ) Critical vs. spurious fluctuations June 16, 2016 1 / 13
Outline 1 Motivation 2 Effective model 3 Limitations 4 Results 5 Final remarks Maurício Hippert (IF-UFRJ) Critical vs. spurious fluctuations June 16, 2016 2 / 13
Motivation The QCD critical point T, GeV QGP 0.1 crossover critical point hadron gas vacuum nuclear matter quark matter phases CFL 0 1 µ B, GeV Figure: A semiquantitative representation of the QCD phase diagram. Ref.: M. Stephanov (2006). Can heavy ion collisions reach the neighborhood of the critical point? Is it there? What would its signatures be? Maurício Hippert (IF-UFRJ) Critical vs. spurious fluctuations June 16, 2016 3 / 13
Motivation Experimental signatures Theory ξ : long range fluctuations (pions, protons...). Statistical moments of observables (e.g. ( N) 3 ) as signatures in HICs (focus: multiplicity). Reality (HICs) Spurious contributions, finite size/duration: ξ... Do signatures survive, even in a simplified model? Need to test basic realistic ingredients! Mission: Test signatures under the most optimistic scenario Maurício Hippert (IF-UFRJ) Critical vs. spurious fluctuations June 16, 2016 4 / 13
Effective model Critical fluctuations Critical mode Classical treatment with homogeneous approximation a Ω[σ 0 ] = V ( ) Ω[σ0 ] P σ0 [σ 0 ] exp, (1) T ( m 2 σ 2 σ2 0+ λ 3 3 σ3 0 + λ ) 4 4 σ4 0 +, (2) with m σ ξ 1, λ 3 T (T ξ) 3/2, λ 4 (T ξ) 1. a Stephanov, Rajagopal, Shuryak (1999); Stephanov (2009); Tsypin (1996). Distribution changes at the CEP change in cumulants! Maurício Hippert (IF-UFRJ) Critical vs. spurious fluctuations June 16, 2016 5 / 13
Effective model Framework Interaction Mass correction δm 2 π = 2G δσ 0, δm p = g δσ 0 (G 300MeV, g 10). (3) Fluctuations of σ change m, change distribution of particles. Freeze-out near the CEP possible observation. Correlated fluctuations of observables signal. Analytically, expansion in δσ 0 followed by average. Framework for Monte Carlo simulations! Background can be added! Maurício Hippert (IF-UFRJ) Critical vs. spurious fluctuations June 16, 2016 6 / 13
Limitations HICs background contributions In HICs, not everything is under control 1 Gaussian temperature fluctuations (σ T = 5%) 2 Geometrical fluctuations (below) Geometric fluctuations Impact parameter distribution Overlap area. Assumption V(b) = C A(b). R Fix R p = 6.8 fm for 0 5% centrality. b Analytically, expansion of p i = α i R p +δr p. Maurício Hippert (IF-UFRJ) Critical vs. spurious fluctuations June 16, 2016 7 / 13
Limitations HICs inherent limitations Also, no thermodynamic limit or equilibrium. Critical Slowing Down ξ ξ (fm) 3.2 3 2.8 2.6 2.4 2.2 2 1.8 1.6-1 -0.5 0 0.5 1 1.5 2 2.5 t/τ A = 1.9 A = 0.9 A = 0.2 Equilibration is slow near the critical point. ξ does not reach its equilibrium value. Speed-of-light limit Berdnikov, Rajagopal (2000), MH, Fraga, Santos (2015). Maurício Hippert (IF-UFRJ) Critical vs. spurious fluctuations June 16, 2016 8 / 13
Results Signatures of pions Signal in ( N π ) 2 / N π. Excellent agreement with analytic calculations! Signal (%) ξ/ξ 0 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 30 Pure - Analytic 25 Pure - Simulation 20 BG - Analytic (V) BG - Simulation (V+T) 15 10 5 0-5 -10 0 0.5 1 1.5 2 2.5 3 3.5 ξ (fm) MH, Fraga, Santos (2015). Maurício Hippert (IF-UFRJ) Critical vs. spurious fluctuations June 16, 2016 9 / 13
Final remarks Final remarks Conclusions: Theoretical expectations vs. reality! Simplified model + noise visible signatures? Background contributions can be very relevant. Perspectives: Other signatures to be tested (soon, higher-order and proton). More background/limitations. Parameter estimation: τ, V p? Dynamics beyond ξ(t). Resonance decay contributions. Maurício Hippert (IF-UFRJ) Critical vs. spurious fluctuations June 16, 2016 10 / 13
Final remarks In progress: higher-order signatures Our code is ready for higher-order moments (skewness and kurtosis). Should yield stronger signals. Results coming soon. Without spurious contributions: Temperature and volume fluctuations included: ξ ѵ ξ ѵ ¾ ½º ¾º½ ¾º ¾º º º Ë(N) Ã(N) ½º ½º¾ ½ ½º ¾º½ ¾º ¾º º º Ë(N) Ã(N) X X0 X0 ¼ ¹¾ ¹ X X0 X0 ¼º ¼º ¼º ¼º¾ ¼ ¹¼º¾ ¹ ¹¼º ¹¼º ¹ ¼ ½ ¾ (ξ/ξ0) 2 ¹¼º ¼ ½ ¾ (ξ/ξ0) 2 Maurício Hippert (IF-UFRJ) Critical vs. spurious fluctuations June 16, 2016 11 / 13
Final remarks Ë Ò Ð ±µ In progress: acceptance effects Acceptance effects can also be introduced. For now only approximate results. Signal (%) ξ/ξ0 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 20 0-1.3 GeV 15 0-1 GeV 0.3-1.3 GeV 0.3-1 GeV 10 5 0-5 0 0.5 1 1.5 2 2.5 3 3.5 ξ (fm) ξ/ξ0 ¼ ¼º¾ ¼º ¼º ½ ½º¾ ½º ½º ¾ ¾¼ η < 0.1 ½ η < 0.2 η < 0.3 η < 0.5 ½¼ η < 1.0 η < 2.0 ¼ ¹ ¼ ¼º ½ ½º ¾ ¾º º ξ ѵ Preliminary: MH, Fraga, in preparation. Maurício Hippert (IF-UFRJ) Critical vs. spurious fluctuations June 16, 2016 12 / 13
Final remarks Acknowledgements Thanks! Thanks also to FAPERJ and CNPq for financial support. Maurício Hippert (IF-UFRJ) Critical vs. spurious fluctuations June 16, 2016 13 / 13