1. Heavy Ion Physics at NICA Simulations G. Musulmanbekov, V
Heavy Ion Physics at NICA Simulations G.Musulmanbekov, V. Toneev and the Physics Group on NICA

2. Search for signals of Phase Transition in Au + Au collisions at √sNN = 3 – 9 GeV
Motivation
The main goal of the NICA experiment is to study the behaviour of nuclear matter in vicinity of the QCD critical endpoint.
To extract information on the equation-of-state of baryonic matter at high densities.
Search for signals of Phase Transition in Au + Au collisions
at √sNN = 3 – 9 GeV

3. Search for signals of Phase Transition in Au + Au collisions at √sNN = 3 – 9 GeV
Signatures of Possibile Phase Transition :
Strange particle enhancement
Hard spectrum of strange mesons
Charmonium suppression
Dielectron mass spectrum enhancement at the range 0.2 – 0.6 GeV/c

4. Search for signals of Phase Transition in Au + Au collisions at √sNN = 3 – 9 GeV
Observables :
Global characteristics of identified hadrons, including strange baryons
Strange to non-strange particles ratio
Transverse momentum spectra
Fluctuations in multiplicity and transverse momenta
Directed and elliptic flows
Particle correlations (femtoscopy, HBT correlations)
Dilepton spectra

5. Search for signals of Phase Transition in Au + Au collisions at √sNN = 3 – 9 GeV
Simulation Tools :
UrQMD 1.3, UrQMD 2.2
104 central events at 3, 3.8, 5, 7, 9 GeV
105 min bias events at 3, 3.8, 5, 7, 9 GeV
FastMC
104 central events at 3, 5, 7, 9 GeV
PLUTO
106 central events at 3, 5, 7, 9 GeV

6. Mean multiplicities in Au-Au collisions Simulated by UrQMD min
Mean multiplicities in Au-Au collisions Simulated by UrQMD min.bias events 
√s GeV
All
Charged
Protons
π -
π + K+ K- 3
279.6
130.5
68.62
17.76
12.63
0.5206
0.0261 5
610.8
296.8
76.20
61.31
50.81
4.548
0.9366 7
876.2
424.5
80.62
95.66
83.06
7.758
2.471 9
1067
515.6
83.27
120.7
107.1
10.03
4.006

7. Mean multiplicities in Au-Au collisions Simulated by UrQMD central collisions (b ≤ 3 fm) 
Part.
3 GeV/n
5 GeV/n
7 GeV/n
9 GeV/n
All
p > GeV/c
p > 100 GeV/c
p > 100 GeV/c
|η|<1
|η|<2
Charg
305.8
196.3
281.5
993.0
406.3
635.3
1058
536.5
882.0
1332
635.7
1076 p
176.5
114.4
167.3
203.7
108.2
177.6
220.7
102.1
176.8
238.1
99.3
176.3 π+
51.9
33.0
46.0
223.6
126.7
193.8
360.2
188.8
303.9
474.4
236.1
391.3 π-
71.7
45.0
62.7
265.6
148.4
227.6
410.8
212.1
343.5
530.2
259.6
433.9 π0
64.5
40.3
56.4
272.5
152.1
233.3
437.6
225.2
365.4
573.9
280.7
469.5 K+
3.32
2.29
3.11
23.3
13.2
21.0
37.9
18.8
32.6
49.3
22.0
40.5 K-
0.170
0.101
0.152
4.45
2.58
3.99
11.62
6.25
10.19
18.9
9.5
16.2 K0
3.47
2.34
3.25
28.4
25.6
49.5
24.9
42.6
68.2
32.0
56.6 Λ
3.75
2.66
3.74
23.5
13.7
22.2
33.3
16.6
29.5
40.0
17.5
32.9 Σ+
0.881
0.616
0.880
5.54
3.26
5.27
7.60
3.77
6.71
9.10
3.95
7.48 Σ-
1.231
0.873
1.230
6.26
3.58
5.90
8.28
4.08
7.36
9.85
4.19
8.00 Σ0
0.621
5.36
5.05
7.46
3.69
6.62
8.72
3.71
7.11 Ξ-
0.009
0.006
0.43
0.27
0.42
0.83
0.44
0.74
1.21
0.56
1.03 Ξ0
0.013
0.010
0.35
0.21
0.34
0.77
0.37
0.67
1.18
0.52
0.99 Ω-
0.003
0.002
0.005
0.030
0.014
0.023
K+/π+
0.064
0.069
0.068
0.104
0.108
0.105
0.100
0.107
0.093
0.103
K-/π-
.0024
.0022
0.017
0.018
0.028
0.029
0.036
0.037
ΛΣ/π0
0.072
0.081
0.082
0.106
0.111
0.117
0.090
0.099
0.085
0.077
The most topic of interest is the ratio of the yield of strange particles to non-strange ones (the last three rows). As discovered in the experiment NA49 the energetic behavior of this ratio indicates the enhanced yield of the strange hyperons and positive kaons at the energy range of √s = 6-10 GeV. This result, called the “horn” effect is not understandable up to now.

8. Mean multiplicities in Au-Au collisions Simulated by UrQMD central collisions (b ≤ 3 fm) 
Part.
3 GeV/n
5 GeV/n
7 GeV/n
9 GeV/n
All
p > GeV/c
p > 100 GeV/c
p > 100 GeV/c
|η|<1
|η|<2
Charg
305.8
196.3
281.5
993.0
406.3
635.3
1058
536.5
882.0
1332
635.7
1076 p
176.5
114.4
167.3
203.7
108.2
177.6
220.7
102.1
176.8
238.1
99.3
176.3 π+
51.9
33.0
46.0
223.6
126.7
193.8
360.2
188.8
303.9
474.4
236.1
391.3 π-
71.7
45.0
62.7
265.6
148.4
227.6
410.8
212.1
343.5
530.2
259.6
433.9 π0
64.5
40.3
56.4
272.5
152.1
233.3
437.6
225.2
365.4
573.9
280.7
469.5 K+
3.32
2.29
3.11
23.3
13.2
21.0
37.9
18.8
32.6
49.3
22.0
40.5 K-
0.170
0.101
0.152
4.45
2.58
3.99
11.62
6.25
10.19
18.9
9.5
16.2 K0
3.47
2.34
3.25
28.4
25.6
49.5
24.9
42.6
68.2
32.0
56.6 Λ
3.75
2.66
3.74
23.5
13.7
22.2
33.3
16.6
29.5
40.0
17.5
32.9 Σ+
0.881
0.616
0.880
5.54
3.26
5.27
7.60
3.77
6.71
9.10
3.95
7.48 Σ-
1.231
0.873
1.230
6.26
3.58
5.90
8.28
4.08
7.36
9.85
4.19
8.00 Σ0
0.621
5.36
5.05
7.46
3.69
6.62
8.72
3.71
7.11 Ξ-
0.009
0.006
0.43
0.27
0.42
0.83
0.44
0.74
1.21
0.56
1.03 Ξ0
0.013
0.010
0.35
0.21
0.34
0.77
0.37
0.67
1.18
0.52
0.99 Ω-
0.003
0.002
0.005
0.030
0.014
0.023
K+/π+
0.064
0.069
0.068
0.104
0.108
0.105
0.100
0.107
0.093
0.103
K-/π-
.0024
.0022
0.017
0.018
0.028
0.029
0.036
0.037
ΛΣ/π0
0.072
0.081
0.082
0.106
0.111
0.117
0.090
0.099
0.085
0.077
The most topic of interest is the ratio of the yield of strange particles to non-strange ones (the last three rows). As discovered in the experiment NA49 the energetic behavior of this ratio indicates the enhanced yield of the strange hyperons and positive kaons at the energy range of √s = 6-10 GeV. This result, called the “horn” effect is not understandable up to now.

9. Mean multiplicities in Au-Au collisions Simulated by UrQMD central collisions (b ≤ 3 fm) 
Part.
3 GeV/n
5 GeV/n
7 GeV/n
9 GeV/n
All
p > GeV/c
p > 100 GeV/c
p > 100 GeV/c
|η|<1
|η|<2
Charg
305.8
196.3
281.5
993.0
406.3
635.3
1058
536.5
882.0
1332
635.7
1076 p
176.5
114.4
167.3
203.7
108.2
177.6
220.7
102.1
176.8
238.1
99.3
176.3 π+
51.9
33.0
46.0
223.6
126.7
193.8
360.2
188.8
303.9
474.4
236.1
391.3 π-
71.7
45.0
62.7
265.6
148.4
227.6
410.8
212.1
343.5
530.2
259.6
433.9 π0
64.5
40.3
56.4
272.5
152.1
233.3
437.6
225.2
365.4
573.9
280.7
469.5 K+
3.32
2.29
3.11
23.3
13.2
21.0
37.9
18.8
32.6
49.3
22.0
40.5 K-
0.170
0.101
0.152
4.45
2.58
3.99
11.62
6.25
10.19
18.9
9.5
16.2 K0
3.47
2.34
3.25
28.4
25.6
49.5
24.9
42.6
68.2
32.0
56.6 Λ
3.75
2.66
3.74
23.5
13.7
22.2
33.3
16.6
29.5
40.0
17.5
32.9 Σ+
0.881
0.616
0.880
5.54
3.26
5.27
7.60
3.77
6.71
9.10
3.95
7.48 Σ-
1.231
0.873
1.230
6.26
3.58
5.90
8.28
4.08
7.36
9.85
4.19
8.00 Σ0
0.621
5.36
5.05
7.46
3.69
6.62
8.72
3.71
7.11 Ξ-
0.009
0.006
0.43
0.27
0.42
0.83
0.44
0.74
1.21
0.56
1.03 Ξ0
0.013
0.010
0.35
0.21
0.34
0.77
0.37
0.67
1.18
0.52
0.99 Ω-
0.003
0.002
0.005
0.030
0.014
0.023
K+/π+
0.064
0.069
0.068
0.104
0.108
0.105
0.100
0.107
0.093
0.103
K-/π-
.0024
.0022
0.017
0.018
0.028
0.029
0.036
0.037
ΛΣ/π0
0.072
0.081
0.082
0.106
0.111
0.117
0.090
0.099
0.085
0.077
The most topic of interest is the ratio of the yield of strange particles to non-strange ones (the last three rows). As discovered in the experiment NA49 the energetic behavior of this ratio indicates the enhanced yield of the strange hyperons and positive kaons at the energy range of √s = 6-10 GeV. This result, called the “horn” effect is not understandable up to now.

10. Simulated charged multiplicity distributions in central collisions (b < 3fm)

11. Simulated charged pseudorapidity distributions in central collisions (b < 3fm)

12. Simulated charged pseudorapidity distributions in central collisions (b < 3fm)
MPD
-2 < η < 2

13. Simulated charged pseudorapidity distributions in central collisions (b < 3fm)
MPD
-1 < η < 1

14. Strange Baryons Yield
Part.
3 GeV/n
5 GeV/n
7 GeV/n
9 GeV/n
All
p > GeV/c
p > 100 GeV/c
p > 100 GeV/c
|η|<1
|η|<2 Λ
3.75
2.66
3.74
23.5
13.7
22.2
33.3
16.6
29.5
40.0
17.5
32.9 Σ+
0.881
0.616
0.880
5.54
3.26
5.27
7.60
3.77
6.71
9.10
3.95
7.48 Σ-
1.231
0.873
1.230
6.26
3.58
5.90
8.28
4.08
7.36
9.85
4.19
8.00 Σ0
0.621
5.36
3.11
5.05
7.46
3.69
6.62
8.72
3.71
7.11 Ξ-
0.009
0.006
0.43
0.27
0.42
0.83
0.44
0.74
1.21
0.56
1.03 Ξ0
0.013
0.010
0.35
0.21
0.34
0.77
0.37
0.67
1.18
0.52
0.99 Ω-
0.003
0.002
0.005
0.030
0.014
0.023
Only those hyperons are measurable which have charged decay verticies.
Table: Marked hyperons are accessible through their decays into charged hadrons

15. Registration efficiency (%)
Accessible Hyperons
Mass(GeV/c2)
Lifetime cτ (cm)
Multiplicity
Decay channel
BR(%)
Registration efficiency (%)
|p| > 0.1 GeV/c
-1 < y < 1 Λ Ξ- Ω-
1.116
1.321
1.672
7.89
4.91
2.46
39.8
1.21
0.03
p + π-
Λ + π-
Λ + K-
63.9
99.9
67.8 16 8 5

16. Accessible Hyperons Λ → pπ- Ξ- → Λπ- → pπ- π- Ω- → ΛK- → pK- π-
The invariant mass spectra for proton – pion pair selected in events are generated by UrQMD. To simulate the efficiency of track reconstruction we applied Gaussian dispersion for each component of particle momenta.

17. Strange to non-Strange ratios in central collisions “Horn” Effect
<π- >/<π+>
Au+Au/Pb+Pb, central
<K+ >/<π+>
Au+Au/Pb+Pb, central
Particle ratio for central Au + Au collisions. The experimental data are from AGS and NA49 for Pb+Pb collisions. Calculations were performed with the usage of UrQMD and HSD codes. There is an effect of the maximal enhancement of K+ yield (“horn” effect) in the energy range Elab/A = 20 – 40 GeV. Transport models HSD (Hadron String Dynamics) and UrQMD contradict with the experimental data.

18. Strange to non-Strange ratios in central collisions “Horn” Effect
Particle ratio for central Au + Au collisions. The experimental data are from AGS and NA49 for Pb+Pb collisions. Calculations were performed with the usage of UrQMD and HSD codes. There is an effect of the maximal enhancement of K+ yield (“horn” effect) in the energy range Elab/A = 20 – 40 GeV. Transport models HSD (Hadron String Dynamics) and UrQMD contradict with the experimental data.

19. Strange to nonStrange ratios in central collisions
Particle ratio for central Au + Au collisions. The experimental data are from AGS
and NA49 for Pb+Pb collisions. Calculations were performed with the usage of UrQMD and HSD codes. There is an effect of the maximal enhancement of K+ yield (“horn” effect) in the energy range Elab/A = 20 – 40 GeV. Transport models HSD (Hadron String Dynamics) and UrQMD contradict with the experimental data.

20. Strange to nonStrange ratios in central collisions
Particle ratio for central Au + Au collisions. The experimental data are from AGS
and NA49 for Pb+Pb collisions. Calculations were performed with the usage of UrQMD and HSD codes. There is an effect of the maximal enhancement of K+ yield (“horn” effect) in the energy range Elab/A = 20 – 40 GeV. Transport models HSD (Hadron String Dynamics) and UrQMD contradict with the experimental data.

21. Strange to nonStrange ratios in central collisions
Particle ratio for central Au + Au collisions. The experimental data are from AGS
and NA49 for Pb+Pb collisions. Calculations were performed with the usage of UrQMD and HSD codes. There is an effect of the maximal enhancement of K+ yield (“horn” effect) in the energy range Elab/A = 20 – 40 GeV. Transport models HSD (Hadron String Dynamics) and UrQMD contradict with the experimental data.

22. Transverse Mass Spectra of Mesons in central collisions
T – inverse slope
Left plot: Comparison of transverse mass spectra for pions and kaons from HSD and UrQMD for central Pb + Pb collisions with experimental data. Right plot: Comparison of inverse slopes for pions and kaons from HSD and UrQMD for central Pb + Pb collisions pp reactions as a function of invariant energy with experimental data. Again, the data demonstrate unusual behavior for kaons in central Pb + Pb collisions at √s = 6-10 GeV.

23. Transverse Mass Spectra of Mesons in central collisions

24. Transverse Mass Spectra of Mesons in central collisions

25. Scaled multiplicity variances
ω (h+)
ω (h-)
Another topic of the study is multiplicity fluctuations. It is believed that at critical point fluctuations could drastically increase.
Left column: Scaled multiplicity
Middle column: Scaled multiplicity variance for Pb+Pb/Au+Au collisions compared with the UrQMD and HSD models.
Right column: UrQMD predictions for NICA/MPD for 4π and geometrical MPD acceptance.
ω (hch)

26. Scaled multiplicity variances NA49 results
Measured scaled variances are close to the Poisson one – close to 1!
No sign of increased fluctuations as expected for a freezeout
near the critical point of strongly interacting matter was observed.

27. Transverse momentum fluctuations
To exclude trivial fluctuations from consideration the following variable is used:
When the system consist of independently emitted particles (no inter-particle correlations) ΦPT assumes a value of zero. On the other hand, if A+A collisions can be treated as an incoherent superposition, of independent N-N interactions (superposition model), then ΦPT has the constant value, the same for A+A and N+N interactions. It also eliminates geometric fluctuations due to the impact parameter variation. Thus, ΦpT is ’deaf’ to the statistical noise and ’blind’ to the collision centrality.
For the system of independently emitted particles (no inter-particle
correlations) Фpt goes to zero.

28. Directed flow v1 & elliptic flow v2x z
Non-central Au+Au collisions:
Interactions between constituents leads to a pressure gradients => spartial asymmetry is converted in asymmetry in momentum space => collective flows
- directed flow
V2>0 indicates in-plane emission of particles
V2<0 corresponds to out-of-plane emission (squeeze-out perpendicular to the reaction plane)
- elliptic flow

29. Direct flow Au + Au collisions at √sNN = 7GeV, b = 5 – 9 fm

30. Direct flow slope Collision Energy Dependence Au + Au, b = 5 – 9 fm

31. Elliptic flow Au + Au collisions at √sNN = 7GeV, b = 5 fm

32. Elliptic flow Collision Energy Dependence Au+Au/Pb+Pb, b = 5 – 9 fm

33. HBT interferometry C (q) q (GeV/c)
Two-particle interferometry: p-space separation  space-time separation
Rside
Rlong
Rout p1 p2 x1 x2
qout
qside
qlong
HBT: Quantum interference between identical particles
q (GeV/c)
C (q) 1 2
Final-state effects (Coulomb, strong) also can cause correlations, need to be accounted for
Gaussian model (3-d):
Sergey Panitkin

34. HBT interferometry

35. HBT interferometry

36. HBT interferometry

37. Dilepton Spectra

38. Dilepton Spectra

39. Dilepton Spectra

40. Dilepton Spectra

41. Dilepton Spectra

42. Conclusions
New simulation codes which take into account phase transitions of deconfinement and/or chiral symmetry restoration are needed.

43. Thank you!