Analyses of pp, Cu–Cu, Au–Au and Pb–Pb Collisions by Tsallis-Pareto Type Function at RHIC and LHC Energies
Abstract
:1. Introduction
2. The Method and Formalism
3. Results and Discussion
4. Conclusions
- (a)
- The transverse momentum spectra of identified and strange particles were analyzed in -, - and – collisions at 62.4 GeV, 200 GeV and 2760 GeV, respectively, by the Tsallis–Pareto type function, and the effective temperature and mean transverse momentum were extracted. We also analyzed the collisions at 62.4 GeV, 200 GeV and 2760 GeV to check the nature of the extracted parameters in the peripheral collisions and collisions at the exact center of mass energy.
- (b)
- The effective temperature (T) was more prominent in a central collision than in a peripheral collision because many hadrons were involved in the reaction, which transferred more energy in the central collision systems. T in peripheral collisions was closer to that of collisions at the exact center of mass energy, which showed that the two systems had similar thermodynamic properties.
- (c)
- The mean transverse momentum was more significant in central collisions than in peripheral collisions due to substantial momentum transfer. In peripheral collisions, it was close to that of the collisions.
- (d)
- Both the effective temperature and mean transverse momentum were mass-dependent and increased with mass. The increase of T with was consistent with the multiple kinetic freeze-out scenarios.
- (e)
- was larger in – collisions than in – and – collisions, and in the latter two cases, the values were close to each other, which showed a weak dependence on the size of the system and comparatively strong dependence on the collision’s energy because it increased with the increase of energy in collisions.
- (f)
- The multiplicity parameter was slightly larger in central collisions than in peripheral collisions. In peripheral collisions, it was close to that in collisions at the exact center of mass energy. In addition, was mass-dependent and was higher for lighter particles. in central collisions depended on the size of the interacting system; larger sizes of the interacting system yielded higher values of the .
- (g)
- The entropy parameter n was larger in a central collision, rendering the system to an equilibrium state more quickly compared to the peripheral collisions.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Compliance with Ethical Standards
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Figure | Collab. | Centrality | Particle | Factor | T (GeV) | n | dof | |||
---|---|---|---|---|---|---|---|---|---|---|
Figure 1a | STAR | 0–5% | 0.000005 | 21,980 ± 14 | 28 | 7 | ||||
0.000001 | 21,980 ± 22 | 25 | 7 | |||||||
62.4 | 0.001 | 1 | 7 | |||||||
0.0005 | 12 | 7 | ||||||||
0.0005 | 165 | 13 | ||||||||
0.05 | 103 | 9 | ||||||||
0.05 | 84 | 9 | ||||||||
5 | 62 | 8 | ||||||||
2 | 39 | 8 | ||||||||
0.005 | 154 | 12 | ||||||||
0–20% | 500 | 1 | 2 | |||||||
200 | 3 | 2 | ||||||||
Figure 1b | STAR | 70–80% | 0.0000005 | 42 | 7 | |||||
0.0000001 | 32 | 7 | ||||||||
0.005 | 10 | 7 | ||||||||
0.001 | 16 | 7 | ||||||||
0.0005 | 14 | 13 | ||||||||
60–80% | 0.2 | 27 | 8 | |||||||
0.1 | 20 | 7 | ||||||||
20 | 4 | 6 | ||||||||
10 | 7 | 6 | ||||||||
0.01 | 46 | 11 | ||||||||
40–60% | 500 | 2 | 1 | |||||||
100 | 10 | 1 | ||||||||
Figure 1c | BRAHMS | 0–10% | 0.01 | 34 | 11 | |||||
- | 0.001 | 34 | 11 | |||||||
200 | 50 | 19 | 8 | |||||||
10 | 27 | 8 | ||||||||
p | 0.5 | 47 | 11 | |||||||
1 | 48 | 10 | ||||||||
STAR | 100 | 186 | 15 | |||||||
10,000 | 118 | 16 | ||||||||
10,000,000 | 11 | 8 | ||||||||
1,000,000 | 17 | 8 | ||||||||
1000 | 54 | 16 | ||||||||
500,000,000 | 27 | 2 | ||||||||
Figure 1d | BRAHMS | 50–70% | 0.01 | 24 | 11 | |||||
0.001 | 11 | 11 | ||||||||
20 | 14 | 7 | ||||||||
5 | 7 | 8 | ||||||||
p | 0.2 | 28 | 11 | |||||||
0.5 | 19 | 8 | ||||||||
STAR | 40–60% | 10 | 40 | 15 | ||||||
1000 | 52 | 16 | ||||||||
100 | 33 | 16 | ||||||||
1,000,000 | 10 | 8 | ||||||||
100,000 | 10 | 8 | ||||||||
50,000,000 | 15 | 2 | ||||||||
Figure 1e | ALICE | 0–5% | 0.00005 | 68,960 | 63 | 38 | ||||
- | 0.00001 | 68,360 ± 33 | 53 | 38 | ||||||
2760 | 1 | 10,900 ± 22 | 35 | 33 | ||||||
0.2 | 10,680 ± 30 | 23 | 33 | |||||||
p | 0.05 | 419 | 39 | |||||||
0.01 | 128 | 39 | ||||||||
1 | 67,800 ± 23 | 20 | 25 | |||||||
50 | 15,100 ± 26 | 122 | 23 | |||||||
0–10% | 30,000 | 136 | 19 | |||||||
2000 | 104 | 19 | ||||||||
1,000,000 | 4 | 8 | ||||||||
10,000,000 | 4 | 8 | ||||||||
Figure 1f | ALICE | 80–90% | 0.00005 | 82 | 38 | |||||
0.00001 | 68 | 38 | ||||||||
1 | 23 | 33 | ||||||||
0.2 | 35 | 33 | ||||||||
p | 0.05 | 14 | 39 | |||||||
0.01 | 26 | 39 | ||||||||
10 | 1 | 25 | ||||||||
50 | 12 | 26 | ||||||||
60–80% | 30,000 | 11 | 16 | |||||||
2000 | 35 | 16 | ||||||||
1,000,000 | 1 | 7 | ||||||||
10,000,000 | 2 | 7 | ||||||||
Figure 2a | PHENIX | 0.1 | 32 | 23 | ||||||
0.01 | 26 | 23 | ||||||||
62.4 | 1 | 14 | 13 | |||||||
1000 | 20 | 13 | ||||||||
p | 100 | 17 | 24 | |||||||
10 | 24 | 24 | ||||||||
Figure 2b | STAR | 0.001 | 72 | 16 | ||||||
0.0001 | 86 | 16 | ||||||||
200 | p | 1 | 31 | 15 | ||||||
0.1 | 56 | 15 | ||||||||
10 | 14 | 19 | ||||||||
10,000 | 82 | 18 | ||||||||
500 | 29 | 18 | ||||||||
5,000,000 | 8 | 8 | ||||||||
1,000,000 | 9 | 8 | ||||||||
500,000,000 | 0 | 0 | ||||||||
Figure 2c | CMS | 0.1 | 40 | 19 | ||||||
0.01 | 43 | 19 | ||||||||
2760 | 5000 | 26 | 14 | |||||||
1000 | 63 | 14 | ||||||||
p | 100 | 56 | 24 | |||||||
10 | 77 | 24 |
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Li, L.-L.; Waqas, M.; Ajaz, M.; Khubrani, A.M.; Yao, H.; Adil Khan, M. Analyses of pp, Cu–Cu, Au–Au and Pb–Pb Collisions by Tsallis-Pareto Type Function at RHIC and LHC Energies. Entropy 2022, 24, 1219. https://doi.org/10.3390/e24091219
Li L-L, Waqas M, Ajaz M, Khubrani AM, Yao H, Adil Khan M. Analyses of pp, Cu–Cu, Au–Au and Pb–Pb Collisions by Tsallis-Pareto Type Function at RHIC and LHC Energies. Entropy. 2022; 24(9):1219. https://doi.org/10.3390/e24091219
Chicago/Turabian StyleLi, Li-Li, Muhammad Waqas, Muhammad Ajaz, Ahmed M. Khubrani, Hui Yao, and Muhammad Adil Khan. 2022. "Analyses of pp, Cu–Cu, Au–Au and Pb–Pb Collisions by Tsallis-Pareto Type Function at RHIC and LHC Energies" Entropy 24, no. 9: 1219. https://doi.org/10.3390/e24091219
APA StyleLi, L.-L., Waqas, M., Ajaz, M., Khubrani, A. M., Yao, H., & Adil Khan, M. (2022). Analyses of pp, Cu–Cu, Au–Au and Pb–Pb Collisions by Tsallis-Pareto Type Function at RHIC and LHC Energies. Entropy, 24(9), 1219. https://doi.org/10.3390/e24091219