Charged-Particle Multiplicity Moments as Described by Shifted Gompertz Distribution in , , and Collisions at High Energies

Table 1

Moments of experimental, shifted Gompertz and modified shifted Gompertz distributions for collisions.

Energy (GeV) ()

Normalized moments (experiment)

Normalized factorial moments (experiment)

L3

91

20.464 ± 0.076

1.093 ± 0.004

1.296 ± 0.008

1.656 ± 0.016

2.268 ± 0.030

1.044 ± 0.003

1.141 ± 0.007

1.304 ± 0.013

1.560 ± 0.021

131

23.301 ± 1.002

1.080 ± 0.044

1.252 ± 0.104

1.546 ± 0.195

2.016 ± 0.343

1.038 ± 0.043

1.117 ± 0.093

1.245 ± 0.157

1.430 ± 0.245

136

24.012 ± 1.116

1.094 ± 0.051

1.295 ± 0.124

1.638 ± 0.237

2.194 ± 0.428

1.052 ± 0.050

1.162 ± 0.111

1.335 ± 0.195

1.586 ± 0.312

172

27.031 ± 1.821

1.095 ± 0.059

1.299 ± 0.142

1.657 ± 0.275

2.245 ± 0.504

1.058 ± 0.057

1.181 ± 0.128

1.384 ± 0.228

1.692 ± 0.378

182

26.795 ± 0.863

1.091 ± 0.030

1.287 ± 0.070

1.626 ± 0.135

2.180 ± 0.245

1.054 ± 0.028

1.168 ± 0.063

1.355 ± 0.112

1.633 ± 0.184

188

26.653 ± 0.609

1.084 ± 0.020

1.260 ± 0.045

1.557 ± 0.085

2.026 ± 0.149

1.046 ± 0.019

1.141 ± 0.041

1.290 ± 0.070

1.502 ± 0.110

194

27.178 ± 0.847

1.093 ± 0.027

1.295 ± 0.064

1.644 ± 0.123

2.216 ± 0.224

1.057 ± 0.026

1.177 ± 0.058

1.375 ± 0.102

1.670 ± 0.168

200

27.575 ± 0.852

1.093 ± 0.027

1.294 ± 0.064

1.644 ± 0.124

2.215 ± 0.227

1.057 ± 0.026

1.178 ± 0.058

1.378 ± 0.103

1.676 ± 0.171

206

27.917 ± 0.720

1.092 ± 0.021

1.290 ± 0.051

1.634 ± 0.098

2.195 ± 0.178

1.056 ± 0.021

1.176 ± 0.046

1.372 ± 0.082

1.665 ± 0.135

OPAL

91

21.394 ± 0.219

1.092 ± 0.011

1.293 ± 0.027

1.648 ± 0.051

2.249 ± 0.095

1.045 ± 0.011

1.144 ± 0.024

1.311 ± 0.041

1.572 ± 0.067

161

24.463 ± 0.859

1.095 ± 0.039

1.304 ± 0.093

1.673 ± 0.180

2.295 ± 0.333

1.054 ± 0.038

1.173 ± 0.084

1.373 ± 0.149

1.684 ± 0.247

183

26.856 ± 0.754

1.097 ± 0.028

1.312 ± 0.068

1.696 ± 0.133

2.348 ± 0.252

1.060 ± 0.027

1.192 ± 0.062

1.419 ± 0.112

1.777 ± 0.195

189

26.886 ± 0.505

1.096 ± 0.018

1.304 ± 0.043

1.669 ± 0.083

2.280 ± 0.153

1.059 ± 0.018

1.184 ± 0.039

1.395 ± 0.070

1.719 ± 0.117

Energy (GeV) ()

Normalized moments (shifted Gompertz)

Normalized factorial moments (shifted Gompertz)

L3

91

20.467 ± 0.029

1.084 ± 0.002

1.278 ± 0.004

1.643 ± 0.008

2.307 ± 0.015

1.035 ± 0.002

1.124 ± 0.004

1.296 ± 0.006

1.604 ± 0.010

131

23.101 ± 0.325

1.084 ± 0.017

1.268 ± 0.039

1.591 ± 0.074

2.126 ± 0.131

1.041 ± 0.016

1.131 ± 0.035

1.284 ± 0.060

1.515 ± 0.094

136

23.530 ± 0.348

1.096 ± 0.018

1.308 ± 0.043

1.684 ± 0.083

2.317 ± 0.152

1.054 ± 0.017

1.172 ± 0.039

1.372 ± 0.068

1.680 ± 0.111

172

26.706 ± 0.359

1.097 ± 0.016

1.309 ± 0.038

1.686 ± 0.073

2.317 ± 0.134

1.059 ± 0.015

1.189 ± 0.035

1.408 ± 0.062

1.747 ± 0.102

182

26.779 ± 0.259

1.096 ± 0.010

1.307 ± 0.025

1.679 ± 0.048

2.303 ± 0.089

1.059 ± 0.010

1.187 ± 0.023

1.403 ± 0.040

1.737 ± 0.067

188

26.624 ± 0.172

1.088 ± 0.007

1.276 ± 0.016

1.599 ± 0.030

2.121 ± 0.053

1.050 ± 0.006

1.156 ± 0.014

1.328 ± 0.025

1.581 ± 0.040

194

27.007 ± 0.232

1.095 ± 0.009

1.305 ± 0.022

1.674 ± 0.043

2.288 ± 0.078

1.058 ± 0.009

1.186 ± 0.020

1.400 ± 0.036

1.729 ± 0.060

200

27.599 ± 0.251

1.095 ± 0.009

1.300 ± 0.022

1.660 ± 0.043

2.253 ± 0.078

1.058 ± 0.009

1.184 ± 0.020

1.392 ± 0.036

1.709 ± 0.060

206

27.940 ± 0.209

1.093 ± 0.007

1.295 ± 0.018

1.646 ± 0.034

2.222 ± 0.062

1.057 ± 0.007

1.180 ± 0.016

1.383 ± 0.029

1.688 ± 0.047

OPAL

91

21.547 ± 0.086

1.093 ± 0.005

1.306 ± 0.012

1.706 ± 0.023

2.425 ± 0.043

1.046 ± 0.005

1.159 ± 0.010

1.368 ± 0.018

1.726 ± 0.031

161

24.322 ± 0.325

1.099 ± 0.017

1.325 ± 0.040

1.742 ± 0.078

2.479 ± 0.148

1.058 ± 0.016

1.193 ± 0.036

1.436 ± 0.065

1.838 ± 0.110

183

26.980 ± 0.244

1.102 ± 0.011

1.333 ± 0.026

1.761 ± 0.051

2.517 ± 0.097

1.065 ± 0.010

1.213 ± 0.023

1.481 ± 0.043

1.926 ± 0.075

189

27.176 ± 0.164

1.103 ± 0.007

1.334 ± 0.017

1.750 ± 0.033

2.466 ± 0.062

1.066 ± 0.007

1.214 ± 0.016

1.471 ± 0.028

1.883 ± 0.048

Energy (GeV) ()

Normalized moments (modified shifted Gompertz)

Normalized factorial moments (modified shifted Gompertz)

L3

91

20.209 ± 0.031

1.092 ± 0.002

1.297 ± 0.005

1.670 ± 0.009

2.329 ± 0.016

1.043 ± 0.002

1.139 ± 0.004

1.313 ± 0.007

1.607 ± 0.011

131

23.293 ± 0.427

1.081 ± 0.022

1.255 ± 0.050

1.555 ± 0.093

2.042 ± 0.164

1.038 ± 0.021

1.120 ± 0.045

1.253 ± 0.076

1.451 ± 0.117

136

23.867 ± 0.499

1.092 ± 0.025

1.291 ± 0.059

1.635 ± 0.113

2.198 ± 0.203

1.050 ± 0.024

1.157 ± 0.054

1.331 ± 0.093

1.589 ± 0.148

172

26.852 ± 0.458

1.092 ± 0.020

1.293 ± 0.048

1.645 ± 0.091

2.229 ± 0.165

1.055 ± 0.019

1.174 ± 0.044

1.372 ± 0.077

1.677 ± 0.125

182

26.771 ± 0.317

1.093 ± 0.013

1.295 ± 0.030

1.650 ± 0.058

2.239 ± 0.106

1.055 ± 0.012

1.175 ± 0.028

1.376 ± 0.049

1.683 ± 0.081

188

26.509 ± 0.212

1.084 ± 0.008

1.264 ± 0.020

1.570 ± 0.036

2.061 ± 0.064

1.047 ± 0.008

1.144 ± 0.018

1.301 ± 0.030

1.528 ± 0.048

194

26.943 ± 0.316

1.092 ± 0.013

1.291 ± 0.030

1.638 ± 0.057

2.210 ± 0.104

1.055 ± 0.012

1.172 ± 0.027

1.367 ± 0.048

1.662 ± 0.079

200

27.548 ± 0.306

1.093 ± 0.011

1.296 ± 0.026

1.651 ± 0.050

2.235 ± 0.092

1.057 ± 0.011

1.180 ± 0.024

1.384 ± 0.042

1.693 ± 0.070

206

27.928 ± 0.259

1.093 ± 0.009

1.295 ± 0.021

1.646 ± 0.040

2.223 ± 0.072

1.057 ± 0.008

1.180 ± 0.019

1.383 ± 0.033

1.689 ± 0.055

OPAL

91

21.461 ± 0.107

1.092 ± 0.006

1.297 ± 0.015

1.670 ± 0.028

2.322 ± 0.051

1.045 ± 0.006

1.149 ± 0.013

1.333 ± 0.022

1.637 ± 0.037

161

24.378 ± 0.396

1.096 ± 0.020

1.310 ± 0.048

1.696 ± 0.093

2.361 ± 0.171

1.055 ± 0.020

1.179 ± 0.044

1.393 ± 0.077

1.739 ± 0.127

183

26.957 ± 0.272

1.101 ± 0.012

1.329 ± 0.028

1.750 ± 0.056

2.492 ± 0.107

1.064 ± 0.011

1.209 ± 0.026

1.470 ± 0.047

1.904 ± 0.082

189

27.007 ± 0.202

1.100 ± 0.009

1.319 ± 0.021

1.710 ± 0.040

2.377 ± 0.075

1.063 ± 0.009

1.199 ± 0.019

1.434 ± 0.034

1.804 ± 0.057