To find the average number of participants and cut off points for each centrality bin: Consider the Nevents vs Nch plot. the area under the curve is the total number of events and the rightmost 10% of the area under the curve is the 10% of the events with the highest multiplicity, this is roughly the ten percent most central events. The next 20% of the area under the curve to the left is the 10-30% bin, etc. Thus, the cutoffs Crange for the bins where found by integrating

.1*s=0 to C0-10%(ds/dnp)dnp (ds/dnp)dnp

etc... Where

s=all Np(ds/dnp)dnp

The average number of participants where simultaneously found over these ranges using

Npa=(1/A)Np*(ds/dNp)*dNp

where

A=(ds/dNp)*dNp



For 200 Gev, Sigma NN=5.341 (average of Regge theory and CHC fit)

0-10% 10-30% 30-50% 50-70%
Np average 326.3 202.2 98.3 39.3
Np end 276 141 63 21
Nch/Np 1.54 1.54 1.54 1.54
Nch average 502.5 311.4 151.4 60.5
Nch end 425 217 97 32




For 20 Gev, Sigma NN=3.89 (average of Regge theory and CHC fit)
(The last row is the cutoffs used in the 20 Gev analysis, for comparison)

0-10% 10-30% 30-50% 50-70%
Np average 317.9 192.3 90.8 35.5
Np end 266 132 57 19
Nch/Np 0.87 0.87 0.87 0.87
Nch average 276.6 167.3 79.0 30.9
Nch end 231 115 50 17
Analysis Nch end 237 117 48 14


This method agreed fairly well wih the cutoffs already used.

--------------------------------------------------------------------------
Bigger tables for 20 and 200 GeV

Experimental data:
Np end Nch end Np average Nch average b average
0-5% 332 289 357 311 1.3
5-10% 291 253 311 271 3.1
10-20% 205 178 248 216 4.7
20-30% 140 122 169 147 6.7
30-40% 101 88 119 104 8.0
40-50% 74.7 65 87.3 76.0 8.9
50-60% 54.0 47 63.8 55.5 9.8
60-70% 39.1 34 46.2 40.2 10.4
70-80% 27.6 24 33.0 28.7 11.0
80-100% 4.60 4 16.7 14.5 12.0

Nch end and Nch average are calculated directly from the experimental data, Np end and Np average are obtained by multiplying by the proportionality factor a=0.87 where Nch=a*Np. This value of a was obtained from this eyeball fit. b average is obtained from Glauber generated table Np average vs b.


20 gev Glauber data
Np end Nch end Np average Nch average b average
0-5% 316 275 347 302 1.8
5-10% 267 232 291 253 3.6
10-20% 190 165 226 197 5.3
20-30% 133 115 160 139 6.9
30-40% 90 78.3 110 95.7 8.3
40-50% 58 50.5 73.1 63.6 9.4
50-60% 35 30.5 45.8 39.8 10.5
60-70% 19 16.5 26.3 22.9 11.4
70-80% 10 8.70 14.0 12.2 12.2
80-100% 2 1.74 5.06 4.40 13.2

Np end and Np average are calculated directly from the experimental data, Nch end and Nch average are obtained by multiplying by the proportionality factor a=0.87 where Nch=a*Np. This value of a was obtained from this eyeball fit. b average is obtained from Glauber generated table Np average vs b.


200 gev experiment
Np end Nch end Np average Nch average b average
0-5% 324 499 353 544 1.5
5-10% 276 425 299 460 3.4
10-20% 199 306 236 363 5.0
20-30% 141 217 169 260 6.8
30-40% 97 149 118 181 8.1
40-50% 63 97.0 79.1 122 9.2
50-60% 39 60.0 50.3 77.5 10.2
60-70% 22 33.9 29.9 46.0 11.2
70-80% 12 18.5 16.5 25.4 12.0
80-100% 3 4.62 6.52 10.0 13.1

Nch end and Nch average are calculated directly from the experimental data, Np end and Np average are obtained by multiplying by the proportionality factor a=1.57 where Nch=a*Np. This value of a was obtained from this eyeball fit. b average is obtained from Glauber generated table Np average vs b.


200 gev Glauber data
Np end Nch end Np average Nch average b average
0-5% 327 503 357 550 1.3
5-10% 281 432 303 466 3.3
10-20% 206 317 242 372 4.9
20-30% 148 228 175 270 6.6
30-40% 103 158 124 191 7.9
40-50% 68.2 105 84.4 130 9.1
50-60% 42.9 66 54.8 84.4 10.1
60-70% 24.7 38 33.1 51.0 11.0
70-80% 13.0 20 18.3 28.2 11.9
80-100% 1.3 2 6.2 9.55 13.1
Np end and Np average are calculated directly from the experimental data, Nch end and Nch average are obtained by multiplying by the proportionality factor a=1.57 where Nch=a*Np. This value of a was obtained from this eyeball fit. b average is obtained from Glauber generated table Np average vs b.