Observables of the non-equilibrium phase transition Boris Tom a - PowerPoint PPT Presentation

Observables of the non-equilibrium phase transition Boris Tom´ aˇ sik Univerzita Mateja Bela, Bansk´ a Bystrica, Slovakia and ˇ Cesk´ e vysok´ e uˇ cen´ ı technick´ e, FNSPE, Praha, Czech Republic boris.tomasik@umb.sk CBM Physics day, 16.9.2015 sik (UMB & ˇ Boris Tom´ aˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 1 / 28

The phase diagram of strongly interacting matter T sQGP 1 s t crossover o r d e r p h a s e t r a n s i t i o n HG μ sik (UMB & ˇ Boris Tom´ aˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 2 / 28

1st order phase transition 2 phase coexistence for slow transitions P 1 spinodal fragmentation e for fast processes c P V a b d 0 1 2 3 4 V L V G V Spinodal fragmentation in liquid/gas nuclear phase transition P. Chomaz, M. Colonna, J. Randrup, Phys. Rept. 384 (2004) 263-440 sik (UMB & ˇ Boris Tom´ aˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 3 / 28

Size of the fragments the size decreases with expansion rate H � 1 / 3 � 5 γ R = ∆ E H 2 ∆ E is latent heat, H is Hubble constant, γ is surface tension I.N.Mishustin, Phys. Rev. Lett. 82 (1999) 4779 sik (UMB & ˇ Boris Tom´ aˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 4 / 28

Simulations J. Randrup, J. Steinheimer: PRL 109 212301, PRC 87 054903, PRC 89 034901 (with V. Koch) Equation of State is augmented by the surface term Enhancement of the baryon density fluctuations figure: J. Steinheimer, J. Randrup: PoS (CPOD 2013) 016 sik (UMB & ˇ Boris Tom´ aˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 5 / 28

N.B. fluctuations at high energies There is a commonly accepted paradigm, that the azimuthal anisotropies observed at RHIC and LHC are caused only by anisotropies in initial state [H. Niemi et al. , Phys. Rev. C 87 (2013) 054901] sik (UMB & ˇ Boris Tom´ aˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 6 / 28

Fluctuating initial conditions 100 P(v 2 / 〈 v 2 〉 ), P( ε 2 / 〈ε 2 〉 ) 20-25% ε 2 IP-Glasma v 2 IP-Glasma+MUSIC 10 v 2 ATLAS Use the fluctuations of v n ’s to 1 get the access to initial 0.1 p T > 0.5 GeV | η | < 2.5 0.01 conditions. 0 0.5 1 1.5 2 2.5 3 v 2 / 〈 v 2 〉 , ε 2 / 〈ε 2 〉 fluctuations of v n ’s seem to 100 20-25% ε 3 IP-Glasma P(v 3 / 〈 v 3 〉 ), P( ε 3 / 〈ε 3 〉 ) follow those of spatial v 3 IP-Glasma+MUSIC 10 v 3 ATLAS anisotropies ε n ’s 1 p T > 0.5 GeV 0.1 | η | < 2.5 0.01 0 0.5 1 1.5 2 2.5 3 v 3 / 〈 v 3 〉 , ε 3 / 〈ε 3 〉 100 20-25% P(v 4 / 〈 v 4 〉 ), P( ε 4 / 〈ε 4 〉 ) ε 4 IP-Glasma v 4 IP-Glasma+MUSIC 10 v 4 ATLAS [Ch. Gale et al.: 1 Phys. Rev. Lett. 110 (2013) 012302] 0.1 p T > 0.5 GeV | η | < 2.5 0.01 0 0.5 1 1.5 2 2.5 3 v 4 / 〈 v 4 〉 , ε 4 / 〈ε 4 〉 sik (UMB & ˇ Boris Tom´ aˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 7 / 28

Fragmentation (cavitation) due to bulk viscosity rate of energy density decrease with ζ/T 3 bulk viscosity u µ ∂ µ ε = ε + p − ζ∂ ρ u ρ ∂ µ u µ ε ε effective decrease of the pressure due to bulk viscosity T c T fragment size estimate in Bjorken scenario 24 ζ c L 2 = ε c ∂ µ u µ | τ = τ c G. Torrieri, B. Tom´ aˇ sik, I.N. Mishustin, Phys. Rev. C 77 (2008) 034903 sik (UMB & ˇ Boris Tom´ aˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 8 / 28

Rapidity correlations If the fireball fragments, hadrons will be correlated choose protons: heavy (less thermal smearing) and still abundant (good statistics) correlation functions in 3D rapidity differences: � � � y 12 = ln γ 12 + γ 12 − 1 p 1 · p 2 γ 12 = m 1 m 2 J. Randrup, Heavy Ion Physics 22 (2005) 69 sik (UMB & ˇ Boris Tom´ aˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 9 / 28

Rapidity difference correlation function for protons all hadrons emitted from |) 12 0.2 3D correlation C(|y droplets at FAIR/NICA expect 0.15 bigger droplets 0.1 lines color coding: FAIR/NICA, 0.05 RHIC 130, RHIC 130 no resonances 0 LHC 0 0.5 1 1.5 2 2.5 3 3.5 Relative rapidity |y | 12 Signal weaker if only a fraction of all hadrons from droplets here neglected Fermi-Dirac statistics and strong interaction: expect effect at 25 MeV (small relative rapidity) M. Schulc, B. Tom´ aˇ sik, Eur. Phys. J. A 45 (2010) 91 sik (UMB & ˇ Boris Tom´ aˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 10 / 28

Comparison of rapidity distribution If there are fluctuations, each event (from the same centrality class) will have a different rapidity distribution. Spinodal fragmentation will lead to droplets which will emit hadrons. How do we recognise a non-statistical difference between two empirical distributions? sik (UMB & ˇ Boris Tom´ aˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 11 / 28

Are these realisations of the same distribution? 1.4 1.2 x x x x x x x x 1 Entries Entries 400 400 Entries Entries 400 400 Entries Entries 400 400 Mean Mean -0.0133 -0.0133 1.2 Mean Mean 0.1612 0.1612 Mean Mean -0.0612 -0.0612 RMS RMS 0.7154 0.7154 1 x RMS RMS 0.7127 0.7127 RMS RMS 0.7363 0.7363 0.8 1 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 0 0 0 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1.2 1.2 x x x x x x 1 Entries Entries 400 400 x Entries Entries 400 400 x Entries Entries 400 400 x Mean Mean -0.08795 -0.08795 Mean Mean -0.05361 -0.05361 Mean Mean 0.09686 0.09686 1 1 RMS RMS 0.729 0.729 RMS RMS 0.7592 0.7592 RMS RMS 0.7891 0.7891 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 0 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 sik (UMB & ˇ Boris Tom´ aˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 12 / 28

The Kolmogorov-Smirnov test Are two empirical distributions generated by the same probability density? Construct distance D between two emipirical distributions (event rapidity distributions) for all event pairs Take away the effect of multiplicity � n 1 n 2 d = D n 1 + n 2 Use the probability Q ( d ): probability, that randomly selected pair of events generated by the same distribution will have their distance bigger than d . Events from the same distribution will lead to uniform Q -distribution. Non-statistically different events will show a peak at small Q . (There are formulas to calculate Q ( d ).) sik (UMB & ˇ Boris Tom´ aˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 13 / 28

Convolution of droplets which emit pions uniformly distributed Gaussian sources with the width 0.707 always the same total multiplicity 90000 80000 (droplets, multiplicity/droplet) (16,128) 70000 (32,64) number of pairs 60000 (64,32) (128,16) 50000 (256,8) 40000 (512,4) 30000 20000 10000 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Q sik (UMB & ˇ Boris Tom´ aˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 14 / 28

Application to Monte-Carlo-generated data 16000 DRAGON: 20000 hadron s Charged hadron s h 3 h 3 15000 R = 112 Entrie s Entrie s 99992 99992 1 8 000 Mean Mean 0.40 8 7 0.40 8 7 R = 6 3 .5 h 3 h 3 Num b er of p air s RM S RM S 0. 3 0 33 0. 3 0 33 num b er of p air s 14000 Entrie s Entrie s 99992 99992 Blast-wave model R = 10 16000 Mean Mean 0.445 0.445 R = 5.0 1 3 000 RM S RM S 0. 3 001 0. 3 001 R = 2.4 14000 R = 1. 3 12000 with possible droplet 12000 11000 10000 production 10000 9000 8 000 8 000 0 0.1 0.2 0. 3 0.4 0.5 0.6 0.7 0. 8 0.9 1 0 0.1 0.2 0. 3 0.4 0.5 0.6 0.7 0. 8 0.9 1 lines color coding: Q Q 11500 RHIC with droplets, 11500 - + π π h 3 h 3 R = 17.4 11000 Entrie s Entrie s 99992 99992 R = 14.6 h 3 h 3 RHIC no droplets, num b er of p air s Mean Mean 0.4 8 92 0.4 8 92 Entrie s Entrie s 99992 99992 num b er of p air s 11000 RM S RM S R = 1.5 0.2947 0.2947 Mean Mean 0.4 8 97 0.4 8 97 R = - 1.1 RM S RM S 0.29 33 0.29 33 R = 0.6 8 R = - 0.1 8 10500 FAIR no droplets 10500 10000 10000 9500 9500 0 0.1 0.2 0. 3 0.4 0.5 0.6 0.7 0. 8 0.9 1 0 0.1 0.2 0. 3 0.4 0.5 0.6 0.7 0. 8 0.9 1 Q Q 12500 14000 12000 + - π π p and p h 3 h 3 1 3 000 h 3 h 3 R = 41 11500 R = - 0.22 Entrie s Entrie s 99992 99992 Entrie s Entrie s 99992 99992 Mean Mean 0.4646 0.4646 num b er of p air s num b er of p air s Mean Mean R = - 2.1 0.512 3 0.512 3 R = 6. 8 RM S RM S 0.2972 0.2972 11000 RM S RM S 0.2944 0.2944 12000 R = - 2.5 R = 5.6 10500 11000 10000 9500 10000 9000 9000 8 500 0 0.1 0.2 0. 3 0.4 0.5 0.6 0.7 0. 8 0.9 1 0 0.1 0.2 0. 3 0.4 0.5 0.6 0.7 0. 8 0.9 1 Q Q sik (UMB & ˇ Boris Tom´ aˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 15 / 28

Kolmogorov-Smirnov test is a powerful tool to check if there are droplets/clusters observed in the observed events. I. Melo et al. , Phys. Rev. C. 80 (2009) 024904 sik (UMB & ˇ Boris Tom´ aˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 16 / 28