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

Table 2

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

Energy (GeV) ()

Normalized moments (experiment)

Normalized factorial moments (experiment)

200

0.5

2.501 ± 0.074

1.911 ± 0.053

4.895 ± 0.322

15.711 ± 1.876

60.718 ± 11.403

1.511 ± 0.046

2.923 ± 0.238

6.945 ± 1.147

19.796 ± 5.362

1.5

7.940 ± 0.206

1.556 ± 0.037

3.159 ± 0.167

7.792 ± 0.695

22.349 ± 3.004

1.430 ± 0.035

2.603 ± 0.144

5.664 ± 0.548

14.140 ± 2.136

3

15.540 ± 0.294

1.368 ± 0.024

2.329 ± 0.082

4.630 ± 0.249

10.275 ± 0.754

1.304 ± 0.024

2.073 ± 0.075

3.791 ± 0.209

7.615 ± 0.577

5

20.285 ± 0.479

1.278 ± 0.028

1.948 ± 0.087

3.379 ± 0.233

6.442 ± 0.605

1.229 ± 0.027

1.764 ± 0.080

2.836 ± 0.198

4.935 ± 0.470

Full

21.175 ± 0.500

1.244 ± 0.028

1.823 ± 0.082

3.023 ± 0.207

5.496 ± 0.510

1.197 ± 0.027

1.651 ± 0.075

2.536 ± 0.176

4.204 ± 0.395

540

0.5

3.004 ± 0.047

1.915 ± 0.029

5.037 ± 0.175

16.684 ± 1.004

66.035 ± 6.085

1.582 ± 0.026

3.347 ± 0.134

8.737 ± 0.654

26.799 ± 3.240

1.5

9.471 ± 0.137

1.610 ± 0.022

3.480 ± 0.107

9.345 ± 0.482

29.750 ± 2.289

1.504 ± 0.021

2.992 ± 0.096

7.331 ± 0.403

21.149 ± 1.773

3

18.968 ± 0.252

1.474 ± 0.017

2.857 ± 0.073

6.815 ± 0.284

19.083 ± 1.127

1.422 ± 0.017

2.630 ± 0.068

5.955 ± 0.254

15.758 ± 0.956

5

26.330 ± 0.342

1.353 ± 0.016

2.271 ± 0.056

4.480 ± 0.176

10.016 ± 0.556

1.315 ± 0.015

2.120 ± 0.053

3.984 ± 0.159

8.425 ± 0.479

Full

28.375 ± 0.374

1.305 ± 0.016

2.079 ± 0.054

3.868 ± 0.159

8.128 ± 0.465

1.269 ± 0.016

1.943 ± 0.051

3.446 ± 0.143

6.853 ± 0.400

900

0.5

3.614 ± 0.087

1.940 ± 0.046

5.410 ± 0.318

19.789 ± 2.173

89.311 ± 15.604

1.664 ± 0.042

3.952 ± 0.269

12.314 ± 1.648

47.134 ± 10.245

1.5

11.503 ± 0.247

1.582 ± 0.031

3.368 ± 0.144

8.736 ± 0.614

26.012 ± 2.634

1.496 ± 0.029

2.970 ± 0.131

7.107 ± 0.522

19.258 ± 2.066

3

21.925 ± 0.428

1.456 ± 0.027

2.695 ± 0.103

5.828 ± 0.341

13.956 ± 1.108

1.410 ± 0.026

2.500 ± 0.096

5.124 ± 0.303

11.487 ± 0.920

5

32.263 ± 0.642

1.354 ± 0.025

2.278 ± 0.088

4.464 ± 0.266

9.736 ± 0.797

1.323 ± 0.025

2.154 ± 0.083

4.054 ± 0.244

8.427 ± 0.698

Full

35.632 ± 0.686

1.284 ± 0.023

2.003 ± 0.073

3.606 ± 0.203

7.185 ± 0.554

1.256 ± 0.022

1.897 ± 0.069

3.279 ± 0.186

6.227 ± 0.485

Energy (GeV) ()

Normalized moments (shifted Gompertz)

Normalized factorial moments (shifted Gompertz)

0.5

2.475 ± 0.029

1.912 ± 0.024

4.864 ± 0.122

15.015 ± 0.573

53.249 ± 2.762

1.508 ± 0.020

2.873 ± 0.078

6.261 ± 0.264

14.708 ± 0.873

1.5

7.917 ± 0.055

1.536 ± 0.011

3.018 ± 0.045

7.021 ± 0.158

18.455 ± 0.560

1.410 ± 0.011

2.468 ± 0.037

4.992 ± 0.115

11.123 ± 0.349

200

3

15.173 ± 0.061

1.381 ± 0.007

2.348 ± 0.022

4.626 ± 0.063

10.137 ± 0.181

1.315 ± 0.007

2.083 ± 0.020

3.762 ± 0.052

7.425 ± 0.134

5

20.152 ± 0.094

1.297 ± 0.006

2.014 ± 0.020

3.560 ± 0.053

6.915 ± 0.137

1.247 ± 0.006

1.826 ± 0.018

2.995 ± 0.045

5.314 ± 0.106

Full

21.064 ± 0.152

1.245 ± 0.010

1.827 ± 0.028

3.039 ± 0.070

5.560 ± 0.171

1.198 ± 0.009

1.654 ± 0.026

2.549 ± 0.059

4.254 ± 0.132

0.5

2.976 ± 0.016

1.917 ± 0.012

5.082 ± 0.064

17.035 ± 0.324

67.968 ± 1.738

1.581 ± 0.010

3.376 ± 0.045

8.940 ± 0.182

27.480 ± 0.756

1.5

9.428 ± 0.044

1.599 ± 0.008

3.421 ± 0.035

9.095 ± 0.143

28.618 ± 0.611

1.493 ± 0.008

2.935 ± 0.031

7.109 ± 0.115

20.226 ± 0.444

540

3

18.774 ± 0.076

1.448 ± 0.006

2.705 ± 0.023

6.155 ± 0.081

16.359 ± 0.293

1.394 ± 0.006

2.479 ± 0.021

5.335 ± 0.071

13.338 ± 0.243

5

26.154 ± 0.093

1.345 ± 0.005

2.258 ± 0.017

4.523 ± 0.053

10.440 ± 0.166

1.307 ± 0.005

2.107 ± 0.016

4.026 ± 0.048

8.822 ± 0.141

Full

28.112 ± 0.084

1.307 ± 0.004

2.099 ± 0.014

3.982 ± 0.040

8.625 ± 0.115

1.271 ± 0.004

1.962 ± 0.013

3.551 ± 0.036

7.299 ± 0.099

0.5

3.555 ± 0.028

1.894 ± 0.016

4.905 ± 0.087

15.756 ± 0.424

59.066 ± 2.159

1.613 ± 0.015

3.465 ± 0.065

8.991 ± 0.259

26.371 ± 1.043

1.5

11.352 ± 0.054

1.557 ± 0.008

3.187 ± 0.032

7.850 ± 0.121

22.057 ± 0.460

1.469 ± 0.007

2.791 ± 0.029

6.294 ± 0.099

15.956 ± 0.342

900

3

21.835 ± 0.075

1.441 ± 0.005

2.604 ± 0.019

5.486 ± 0.060

12.867 ± 0.189

1.395 ± 0.005

2.410 ± 0.018

4.803 ± 0.053

10.539 ± 0.156

5

32.073 ± 0.101

1.324 ± 0.004

2.134 ± 0.014

3.980 ± 0.040

8.275 ± 0.111

1.293 ± 0.004

2.013 ± 0.013

3.595 ± 0.036

7.105 ± 0.096

Full

35.567 ± 0.157

1.268 ± 0.006

1.935 ± 0.018

3.406 ± 0.048

6.680 ± 0.125

1.240 ± 0.006

1.830 ± 0.017

3.091 ± 0.043

5.774 ± 0.109

Energy (GeV) ()

Normalized moments (modified shifted Gompertz)

Normalized factorial moments (modified shifted Gompertz)

200

0.5

2.477 ± 0.041

1.881 ± 0.033

4.604 ± 0.166

13.493 ± 0.742

45.166 ± 3.376

1.478 ± 0.028

2.651 ± 0.104

5.320 ± 0.326

11.404 ± 0.993

1.5

7.895 ± 0.071

1.547 ± 0.016

3.085 ± 0.063

7.340 ± 0.226

19.818 ± 0.819

1.420 ± 0.015

2.529 ± 0.053

5.257 ± 0.167

12.101 ± 0.520

3

15.537 ± 0.107

1.367 ± 0.010

2.321 ± 0.034

4.593 ± 0.101

10.130 ± 0.300

1.302 ± 0.009

2.065 ± 0.030

3.758 ± 0.084

7.493 ± 0.226

5

20.484 ± 0.134

1.270 ± 0.009

1.923 ± 0.026

3.317 ± 0.068

6.293 ± 0.172

1.221 ± 0.008

1.742 ± 0.024

2.786 ± 0.057

4.827 ± 0.134

Full

21.124 ± 0.185

1.245 ± 0.012

1.830 ± 0.036

3.054 ± 0.089

5.610 ± 0.216

1.197 ± 0.012

1.657 ± 0.033

2.565 ± 0.075

4.301 ± 0.167

540

0.5

2.981 ± 0.022

1.901 ± 0.016

4.929 ± 0.085

15.986 ± 0.419

61.449 ± 2.190

1.566 ± 0.014

3.241 ± 0.059

8.192 ± 0.234

23.951 ± 0.945

1.5

9.463 ± 0.055

1.606 ± 0.011

3.468 ± 0.047

9.313 ± 0.192

29.587 ± 0.828

1.501 ± 0.010

2.981 ± 0.041

7.305 ± 0.154

21.009 ± 0.607

3

18.863 ± 0.092

1.470 ± 0.008

2.836 ± 0.031

6.714 ± 0.112

18.569 ± 0.421

1.417 ± 0.007

2.608 ± 0.028

5.857 ± 0.099

15.278 ± 0.353

5

26.179 ± 0.113

1.352 ± 0.006

2.282 ± 0.022

4.582 ± 0.067

10.568 ± 0.207

1.314 ± 0.006

2.130 ± 0.021

4.080 ± 0.060

8.931 ± 0.177

Full

28.144 ± 0.100

1.306 ± 0.005

2.096 ± 0.017

3.964 ± 0.048

8.553 ± 0.138

1.271 ± 0.005

1.959 ± 0.016

3.535 ± 0.043

7.234 ± 0.118

900

0.5

3.578 ± 0.038

1.907 ± 0.022

5.041 ± 0.120

16.619 ± 0.631

63.995 ± 3.464

1.627 ± 0.019

3.599 ± 0.093

9.671 ± 0.412

29.394 ± 1.868

1.5

11.428 ± 0.071

1.575 ± 0.010

3.303 ± 0.044

8.345 ± 0.172

23.917 ± 0.675

1.487 ± 0.010

2.905 ± 0.039

6.740 ± 0.142

17.448 ± 0.511

3

22.026 ± 0.098

1.449 ± 0.007

2.672 ± 0.026

5.755 ± 0.084

13.741 ± 0.266

1.404 ± 0.007

2.479 ± 0.024

5.060 ± 0.074

11.315 ± 0.221

5

32.341 ± 0.129

1.350 ± 0.006

2.259 ± 0.019

4.393 ± 0.056

9.482 ± 0.163

1.319 ± 0.006

2.136 ± 0.018

3.988 ± 0.052

8.197 ± 0.142

Full

35.734 ± 0.199

1.285 ± 0.008

2.015 ± 0.024

3.653 ± 0.066

7.354 ± 0.177

1.257 ± 0.008

1.908 ± 0.023

3.326 ± 0.060

6.386 ± 0.155