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

SLIDE 1

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

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 1 / 28

SLIDE 2

The phase diagram of strongly interacting matter

T μ sQGP HG

crossover 1

s t

r

d e r p h a s e t r a n s i t i

n

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 2 / 28

SLIDE 3

1st order phase transition

phase coexistence for slow transitions spinodal fragmentation for fast processes

a b c d e

V P

1 2 3 4 PV 1 2 VL VG

Spinodal fragmentation in liquid/gas nuclear phase transition

P. Chomaz, M. Colonna, J. Randrup, Phys. Rept. 384 (2004) 263-440

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 3 / 28

SLIDE 4

Size of the fragments

the size decreases with expansion rate H R =

5γ

∆E H2 1/3 ∆E is latent heat, H is Hubble constant, γ is surface tension

I.N.Mishustin, Phys. Rev. Lett. 82 (1999) 4779

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 4 / 28

SLIDE 5

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

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 5 / 28

SLIDE 6

N.B. fluctuations at high energies

There is a commonly accepted paradigm, that the azimuthal anisotropies

bserved at RHIC and LHC are caused only by anisotropies in initial state

[H. Niemi et al., Phys. Rev. C 87 (2013) 054901]

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 6 / 28

SLIDE 7

Fluctuating initial conditions

Use the fluctuations of vn’s to get the access to initial conditions. fluctuations of vn’s seem to follow those of spatial anisotropies εn’s

[Ch. Gale et al.:

Phys. Rev. Lett. 110 (2013) 012302]

0.01 0.1 1 10 100 0.5 1 1.5 2 2.5 3 P(v2/〈v2〉), P(ε2/〈ε2〉) v2/〈v2〉, ε2/〈ε2〉 pT > 0.5 GeV |η| < 2.5 20-25% ε2 IP-Glasma v2 IP-Glasma+MUSIC v2 ATLAS 0.01 0.1 1 10 100 0.5 1 1.5 2 2.5 3 P(v3/〈v3〉), P(ε3/〈ε3〉) v3/〈v3〉, ε3/〈ε3〉 pT > 0.5 GeV |η| < 2.5 20-25% ε3 IP-Glasma v3 IP-Glasma+MUSIC v3 ATLAS 0.01 0.1 1 10 100 0.5 1 1.5 2 2.5 3 P(v4/〈v4〉), P(ε4/〈ε4〉) v4/〈v4〉, ε4/〈ε4〉 pT > 0.5 GeV |η| < 2.5 20-25% ε4 IP-Glasma v4 IP-Glasma+MUSIC v4 ATLAS

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 7 / 28

SLIDE 8

Fragmentation (cavitation) due to bulk viscosity

rate of energy density decrease with bulk viscosity uµ∂µε ε = ε + p − ζ∂ρuρ ε ∂µuµ effective decrease of the pressure due to bulk viscosity

T Tc ζ/T3

fragment size estimate in Bjorken scenario L2 = 24ζc εc∂µuµ|τ=τc

G. Torrieri, B. Tom´

aˇ sik, I.N. Mishustin, Phys. Rev. C 77 (2008) 034903

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 8 / 28

SLIDE 9

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: y12 = ln

γ12 +
γ12 − 1
γ12

= p1 · p2 m1m2

J. Randrup, Heavy Ion Physics 22 (2005) 69

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 9 / 28

SLIDE 10

Rapidity difference correlation function for protons

all hadrons emitted from droplets at FAIR/NICA expect bigger droplets lines color coding: FAIR/NICA, RHIC 130, RHIC 130 no resonances LHC

|

12

Relative rapidity |y 0.5 1 1.5 2 2.5 3 3.5 |)

12

3D correlation C(|y 0.05 0.1 0.15 0.2

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

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 10 / 28

SLIDE 11

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?

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 11 / 28

SLIDE 12

Are these realisations of the same distribution?

x Entries 400 Mean

0.0133

RMS 0.7154

2
1.5
1
0.5

0.5 1 1.5 2 0.2 0.4 0.6 0.8 1 1.2 1.4 x Entries 400 Mean

0.0133

RMS 0.7154 x x Entries 400 Mean 0.1612 RMS 0.7127

2
1.5
1
0.5

0.5 1 1.5 2 0.2 0.4 0.6 0.8 1 1.2 x Entries 400 Mean 0.1612 RMS 0.7127

x x Entries 400 Mean

0.0612

RMS 0.7363

2
1.5
1
0.5

0.5 1 1.5 2 0.2 0.4 0.6 0.8 1 x Entries 400 Mean

0.0612

RMS 0.7363 x x Entries 400 Mean

0.08795

RMS 0.7592

2
1.5
1
0.5

0.5 1 1.5 2 0.2 0.4 0.6 0.8 1 1.2 x Entries 400 Mean

0.08795

RMS 0.7592 x x Entries 400 Mean

0.05361

RMS 0.7891

2
1.5
1
0.5

0.5 1 1.5 2 0.2 0.4 0.6 0.8 1 x Entries 400 Mean

0.05361

RMS 0.7891 x x Entries 400 Mean 0.09686 RMS 0.729

2
1.5
1
0.5

0.5 1 1.5 2 0.2 0.4 0.6 0.8 1 1.2 x Entries 400 Mean 0.09686 RMS 0.729

x

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 12 / 28

SLIDE 13

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 d = n1n2 n1 + n2 D 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).)

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 13 / 28

SLIDE 14

Convolution of droplets which emit pions

uniformly distributed Gaussian sources with the width 0.707 always the same total multiplicity

Q 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 number of pairs 10000 20000 30000 40000 50000 60000 70000 80000 90000 (droplets, multiplicity/droplet) (16,128) (32,64) (64,32) (128,16) (256,8) (512,4)

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 14 / 28

SLIDE 15

Application to Monte-Carlo-generated data

DRAGON: Blast-wave model with possible droplet production lines color coding: RHIC with droplets, RHIC no droplets, FAIR no droplets

h3 Entries 99992 Mean 0.4087 RMS 0.3033

Q 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Number of pairs 8000 10000 12000 14000 16000 18000 20000

h3 Entries 99992 Mean 0.4087 RMS 0.3033

hadrons R = 112 R = 10 R = 2.4

h3 Entries 99992 Mean 0.445 RMS 0.3001

Q 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 number of pairs 8000 9000 10000 11000 12000 13000 14000 15000 16000

h3 Entries 99992 Mean 0.445 RMS 0.3001

Charged hadrons R = 63.5 R = 5.0 R = 1.3

h3 Entries 99992 Mean 0.4897 RMS 0.2933

Q 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 number of pairs 9500 10000 10500 11000 11500

h3 Entries 99992 Mean 0.4897 RMS 0.2933

π

R = 14.6 R = - 1.1 R = - 0.18

h3 Entries 99992 Mean 0.4646 RMS 0.2972

Q 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 number of pairs 9000 10000 11000 12000 13000 14000

h3 Entries 99992 Mean 0.4646 RMS 0.2972

π

+

π R = 41 R = 6.8 R = 5.6

h3 Entries 99992 Mean 0.4892 RMS 0.2947

Q 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 number of pairs 9500 10000 10500 11000 11500

h3 Entries 99992 Mean 0.4892 RMS 0.2947 +

π R = 17.4 R = 1.5 R = 0.68

h3 Entries 99992 Mean 0.5123 RMS 0.2944

Q 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 number of pairs 8500 9000 9500 10000 10500 11000 11500 12000 12500

h3 Entries 99992 Mean 0.5123 RMS 0.2944

p p and R = - 0.22 R = - 2.1 R = - 2.5

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 15 / 28

SLIDE 16

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

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 16 / 28

SLIDE 17

Event shapes

How to do Event Shape Engineering among these shapes. . . ?

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 17 / 28

SLIDE 18

. . . ordered

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 18 / 28

SLIDE 19

Similar events

in similar events the evolution is likely to be similar analyse samples of similar events! How to select similar events?

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 19 / 28

SLIDE 20

Event Shape Sorting: the algorithm

We will sort events according to their histograms in azimuthal angle.

1 (Rotate the events appropriately) 2 Sort your events as you wish 3 Divide sorted events into quantiles (we’ll do deciles) 4 Determine average histograms in each quantiles 5 For each event i calculate Bayesian probability P(i|µ) that it belongs

to quantile µ

6 For each event calculate average ¯

µ =

µ µP(i|µ)

7 Sort events according to their values of ¯

µ

8 If order of events changed, return to 3. Otherwise sorting converged.

S. Lehmann, A.D. Jackson, B. Lautrup, arXiv:physics/0512238
S. Lehmann, A. D. Jackson and B. E. Lautrup, Scientometrics 76 (2008) 369

[physics/0701311 [physics.soc-ph]]

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 20 / 28

SLIDE 21

Average histograms for random sorting ’before’

Only fluctuating v2

[rad] φ 1 2 3 4 5 6 20 40 60 80 100 120 140 [rad] φ 1 2 3 4 5 6 20 40 60 80 100 120 140 [rad] φ 1 2 3 4 5 6 20 40 60 80 100 120 140 [rad] φ 1 2 3 4 5 6 20 40 60 80 100 120 140 [rad] φ 1 2 3 4 5 6 20 40 60 80 100 120 140 [rad] φ 1 2 3 4 5 6 20 40 60 80 100 120 140 [rad] φ 1 2 3 4 5 6 20 40 60 80 100 120 140 [rad] φ 1 2 3 4 5 6 20 40 60 80 100 120 140 [rad] φ 1 2 3 4 5 6 20 40 60 80 100 120 140 [rad] φ 1 2 3 4 5 6 20 40 60 80 100 120 140

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 21 / 28

SLIDE 22

Average histograms for random sorting ’after’

Only fluctuating v2

[rad] φ 1 2 3 4 5 6 20 40 60 80 100 120 140 [rad] φ 1 2 3 4 5 6 20 40 60 80 100 120 140 [rad] φ 1 2 3 4 5 6 20 40 60 80 100 120 140 [rad] φ 1 2 3 4 5 6 20 40 60 80 100 120 140 [rad] φ 1 2 3 4 5 6 20 40 60 80 100 120 140 [rad] φ 1 2 3 4 5 6 20 40 60 80 100 120 140 [rad] φ 1 2 3 4 5 6 20 40 60 80 100 120 140 [rad] φ 1 2 3 4 5 6 20 40 60 80 100 120 140 [rad] φ 1 2 3 4 5 6 20 40 60 80 100 120 140 [rad] φ 1 2 3 4 5 6 20 40 60 80 100 120 140

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 22 / 28

SLIDE 23

Toy Model: q2 sorting

Generated 5000 events up to v2, v2 = aM2 + bM + c M ∈ (300, 3000) Initial rotation: Ψ2 Sort: q2

1 2 3 4 5 6 7 8 9 10 2 4 6 8 10 12 14 µ Initial sorting variable: q2

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 23 / 28

SLIDE 24

Elliptic flow for q2 sorting

Correlation v2 and µ: 0.959 Obvious linear dependence v2 might be a better measure than q2

1 2 3 4 5 6 7 8 9 10 0.05 0.1 0.15 0.2 0.25 0.3 0.35 ˆµ v2 (event plane method)

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 24 / 28

SLIDE 25

More realistic: all orders of anisotropy

No correlation with any of the conventional measures

1 2 3 4 5 6 7 8 9 10 0.05 0.1 0.15 0.2 0.25 0.3

−

µ v2

(a)

1 2 3 4 5 6 7 8 9 10 0.05 0.1 0.15 0.2

−

µ v3

(b)

1 2 3 4 5 6 7 8 9 10 2 4 6 8 10 12

−

µ q2

(c)

1 2 3 4 5 6 7 8 9 10 300 800 1300 1800 2300 2800

−

µ M

(d) Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 25 / 28

SLIDE 26

More realistic anisotropy: sorting

1 6

2 7 3 8 4 9 5 10

20 40 60 80 100 120 140 20 40 60 80 100 120 140 0 π/2 π 3π/2 0 π/2 π 3π/2 0 π/2 π 3π/2 0 π/2 π 3π/2 0 π/2 π 3π/2

[rad] φ

Number of particles Number of particles

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 26 / 28

SLIDE 27

Event Shape Sorting

The same method can be applied on rapidity distributions or even on 2D histograms Event Shape is determined in more complicated way than single variable can characterize ESS might be useful (necessary?) for building mixed events samples in the construction of correlation functions ESS might be useful for Single Event Femtoscopy

R. Kopeˇ

cn´ a, B. Tom´ aˇ sik: arxiv:1506.06776

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 27 / 28

SLIDE 28

Summary

spinodal fragmentation at the first-order phase transition first-order phase transition would lead to baryon number/density fuctuations ad correlations (correlation function, Kolmogorov-Smirnov test) there could be fragmentation also at higher collision energies due to bulk viscosity peak—what would be the unique signal of critical point Event Shape Sorting - look at events with similar shapes

Boris Tom´ aˇ sik (UMB & ˇ CVUT) Non-equilibrium phase transition CBM Physics day, 16.9.2015 28 / 28