Figure for m3
One of the panels of figure 2 of arxiv:1001.3796

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
11.52.08 ± 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
18.01.39 ± 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
19.61.29 ± 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
27.00.96 ± 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
39.00.68 ± 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
62.40.44 ± 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
200.00.142 ± 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 each √SNN and Tc, the first line is the value of T/Tc, the second, the lattice parameter β which corresponds to a run at the nearest T/Tc, and the third (in bold), the value of m3. There are no runs corresponding to the fields marked NA.

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
11.52.08 ± 0.07 5.39 2 ± 11.85 ± 0.030 ± 1
18.01.39 ± 0.05 5.41 1.5 ± 0.5-0.3 ± 0.6-1±2
19.61.29 ± 0.04 5.41 1.4 ± 0.4-0.7 ± 0.7-0.2±0.6
27.00.96 ± 0.02 5.4153 ± 2-1.2 ± 0.3-3 ± 5
39.00.68 ± 0.02 5.4150.58 ± 0.051.17 ± 0.11.1±0.4
62.40.44 ± 0.02 5.4150.52 ± 0.031.6 ± 0.52.6 ± 0.5
200.00.142 ± 0.005 5.42 0.146 ± 0.0050.92 ± 0.037.43 ± 0.02
For each √SNN the values of z and the lattice parameter β (corresponding to Tc=170 MeV) are listed along with the values of >m1, m2 and m3. There are no runs corresponding to the fields marked NA. These were the values used in the figures.

Tc=175 MeV

√SNN
(GeV)		z = μB/T β m1 m2 m3
11.52.08 ± 0.07 NANANANA
18.01.39 ± 0.05 5.40 0.9 ± 0.8-1.4 ± 0.346±33
19.61.29 ± 0.04 5.40 1.1 ± 0.7-1.4 ± 0.310.12±12
27.00.96 ± 0.02 5.41 0.9 ± 0.21.4 ± 0.50.7±0.5
39.00.68 ± 0.02 5.41 0.6 ± 0.11.7 ± 0.46±2
62.40.44 ± 0.02 5.410.4 ± 0.11.2 ± 0.22.9 ± 0.3
200.00.142 ± 0.005 5.410.14 ± 0.021.0 ± 0.17.16 ± 0.08
For each √SNN the values of z and the lattice parameter β (corresponding to Tc=175 MeV) are listed along with the values of >m1, m2 and m3. There are no runs corresponding to the fields marked NA.
Sourendu Gupta, ILGTI