Ratios of moments of baryon distributions
These lattice measurements were presented in the paper "Lattice QCD predictions for shapes of event distributions along the freezeout curve in heavy-ion collisions" by R.V. Gavai and Sourendu Gupta [arXiv:1001.3796]. Please cite this paper if you use these measurements.
The ratio m3
√SNN (GeV) | z = μB/T | Tc=160 MeV | Tc=165 MeV | Tc=170 MeV | Tc=175 MeV | Tc=180 MeV | Tc=185 MeV | Tc=190 MeV |
---|---|---|---|---|---|---|---|---|
11.5 | 2.08 ± 0.07 | 0.94 ± 0.01 5.41 1.2 ± 0.6 |
0.92 ± 0.01 5.40 -5 ± 2 |
0.89 ± 0.01 5.39 0± 1 |
0.86 ± 0.01 NA NA |
0.84 ± 0.01 NA NA |
0.82 ± 0.01 NA NA |
0.80 ± 0.01 NA NA |
18.0 | 1.39 ± 0.05 | 1.00 ± 0.01 5.42 2.7 ± 4 |
0.97 ± 0.01 5.415 1.2 ± 0.5 |
0.94 ± 0.01 5.41 -1± 2 |
0.91 ± 0.01 5.40 46±33 |
0.89 ± 0.01 5.39 0± 1 |
0.86 ± 0.01 NA NA |
0.84 ± 0.01 NA NA |
19.6 | 1.29 ± 0.04 | 1.00 ± 0.01 5.42 2.8 ± 0.3 |
0.97 ± 0.01 5.415 1.4 ± 0.6 |
0.94 ± 0.01 5.41 -0.2± 0.6 |
0.91 ± 0.01 5.40 -0.12±0.01 |
0.89 ± 0.01 5.39 0.1 ± 1.3 |
0.86 ± 0.01 NA NA |
0.84 ± 0.01 NA NA |
27.0 | 0.96 ± 0.02 | 1.02 ± 0.01 5.43 0 ± 2 |
0.99 ± 0.01 5.42 2.8 ± 0.3 |
0.96 ± 0.01 5.415 -3± 5 |
0.93 ± 0.01 5.41 0.7±0.5 |
0.91 ± 0.01 5.40 16± 5 |
0.88 ± 0.01 5.39 -1± 2 |
0.86 ± 0.01 NA NA |
39.0 | 0.68 ± 0.02 | 1.03 ± 0.01 5.43 0.8 ± 0.7 |
1.00 ± 0.01 5.42 3.0 ± 0.2 |
0.97 ± 0.01 5.415 1.1± 0.4 |
0.94 ± 0.01 5.41 0±1 |
0.92 ± 0.01 5.40 5.7± 0.8 |
0.89 ± 0.01 5.39 -47± 39 |
0.87 ± 0.01 NA NA |
62.4 | 0.44 ± 0.02 | 1.03 ± 0.01 5.43 1.8 ± 0.1 |
1.00 ± 0.01 5.42 3.36 ± 0.09 |
0.97 ± 0.01 5.415 2.6 ± 0.5 |
0.94 ± 0.01 5.41 2.6 ± 0.3 |
0.92 ± 0.01 5.40 4.5 ± 0.3 |
0.89 ± 0.01 5.39 6.8 ± 0.4 |
0.87 ± 0.01 5.39 6.8 ± 0.4 |
200.0 | 0.142 ± 0.005 | 1.04 ± 0.01 5.43 6.94 ± 0.03 |
1.01 ± 0.01 5.43 6.94 ± 0.03 |
0.98 ± 0.01 5.42 7.43 ± 0.02 |
0.95 ± 0.01 5.41 7.16 ± 0.08 |
0.92 ± 0.01 5.40 7.69 ± 0.06 |
0.90 ± 0.01 5.39 7.89 ± 0.09 |
0.88 ± 0.01 5.39 7.89 ± 0.09 |
For the lattice determination one uses the relation m3(z,T/Tc)=χ(4)(z,T/Tc)/χ(3)(z,T/Tc). This should equal the combination which can be determined in experiment: m3=Kσ/S, where K is the Kurtosis, σ the square root of the variance and S the skewness.
The ratios m1,2,3
Tc=170 MeV
√SNN (GeV) | z = μB/T | β | m1 | m2 | m3 |
---|---|---|---|---|---|
11.5 | 2.08 ± 0.07 | 5.39 | 2 ± 1 | 1.85 ± 0.03 | 0 ± 1 |
18.0 | 1.39 ± 0.05 | 5.41 | 1.5 ± 0.5 | -0.3 ± 0.6 | -1±2 |
19.6 | 1.29 ± 0.04 | 5.41 | 1.4 ± 0.4 | -0.7 ± 0.7 | -0.2±0.6 |
27.0 | 0.96 ± 0.02 | 5.415 | 3 ± 2 | -1.2 ± 0.3 | -3 ± 5 |
39.0 | 0.68 ± 0.02 | 5.415 | 0.58 ± 0.05 | 1.17 ± 0.1 | 1.1±0.4 |
62.4 | 0.44 ± 0.02 | 5.415 | 0.52 ± 0.03 | 1.6 ± 0.5 | 2.6 ± 0.5 |
200.0 | 0.142 ± 0.005 | 5.42 | 0.146 ± 0.005 | 0.92 ± 0.03 | 7.43 ± 0.02 |
Tc=175 MeV
√SNN (GeV) | z = μB/T | β | m1 | m2 | m3 |
---|---|---|---|---|---|
11.5 | 2.08 ± 0.07 | NA | NA | NA | NA |
18.0 | 1.39 ± 0.05 | 5.40 | 0.9 ± 0.8 | -1.4 ± 0.3 | 46±33 |
19.6 | 1.29 ± 0.04 | 5.40 | 1.1 ± 0.7 | -1.4 ± 0.3 | 10.12±12 |
27.0 | 0.96 ± 0.02 | 5.41 | 0.9 ± 0.2 | 1.4 ± 0.5 | 0.7±0.5 |
39.0 | 0.68 ± 0.02 | 5.41 | 0.6 ± 0.1 | 1.7 ± 0.4 | 6±2 |
62.4 | 0.44 ± 0.02 | 5.41 | 0.4 ± 0.1 | 1.2 ± 0.2 | 2.9 ± 0.3 |
200.0 | 0.142 ± 0.005 | 5.41 | 0.14 ± 0.02 | 1.0 ± 0.1 | 7.16 ± 0.08 |
Sourendu Gupta, ILGTI