Higher Moments of Net-proton Multiplicity Distributions at RHIC

The STAR Collaboration: M.M. Aggarwal, et al; To appear in Physical Review Letters ; 1004.4959 [nucl-ex]

Figure 1:

0-5%:
------
(X,Y)   Y_error
-12.5,2 +/- 1.41421
-11.5,4 +/- 2
-10.5,9 +/- 3
-9.5,31 +/- 5.56776
-8.5,117 +/- 10.8167
-7.5,379 +/- 19.4679
-6.5,908 +/- 30.133
-5.5,2437 +/- 49.366
-4.5,5085 +/- 71.3092
-3.5,10147 +/- 100.732
-2.5,18671 +/- 136.642
-1.5,30181 +/- 173.727
-0.5,43750 +/- 209.165
0.5,56022 +/- 236.69
1.5,63743 +/- 252.474
2.5,64777 +/- 254.513
3.5,58596 +/- 242.066
4.5,47167 +/- 217.18
5.5,34533 +/- 185.831
6.5,22701 +/- 150.669
7.5,13622 +/- 116.713
8.5,7464 +/- 86.3944
9.5,3736 +/- 61.1228
10.5,1780 +/- 42.19
11.5,741 +/- 27.2213
12.5,271 +/- 16.4621
13.5,114 +/- 10.6771
14.5,47 +/- 6.85565
15.5,20 +/- 4.47214
16.5,4 +/- 2
17.5,1 +/- 1
19.5,1 +/- 1


30-40%:
----------

(X,Y)   Y_error
-8.5,2 +/- 1.41421
-7.5,19 +/- 4.3589
-6.5,95 +/- 9.74679
-5.5,497 +/- 22.2935
-4.5,2383 +/- 48.816
-3.5,9277 +/- 96.3172
-2.5,29810 +/- 172.656
-1.5,76766 +/- 277.067
-0.5,150368 +/- 387.773
0.5,214537 +/- 463.181
1.5,213965 +/- 462.564
2.5,154726 +/- 393.352
3.5,86040 +/- 293.326
4.5,37718 +/- 194.211
5.5,13932 +/- 118.034
6.5,4468 +/- 66.8431
7.5,1252 +/- 35.3836
8.5,290 +/- 17.0294
9.5,56 +/- 7.48331
10.5,13 +/- 3.60555
11.5,3 +/- 1.73205


70-80%:
-----------

(X,Y)   Y_error
-4.5,2 +/- 1.41421
-3.5,49 +/- 7
-2.5,994 +/- 31.5278
-1.5,14290 +/- 119.541
-0.5,137036 +/- 370.184
0.5,626299 +/- 791.391
1.5,186375 +/- 431.712
2.5,26921 +/- 164.076
3.5,2564 +/- 50.636
4.5,162 +/- 12.7279
5.5,7 +/- 2.64575

Figure 2:

AuAu19.6 GeV
//************************************
Npart,mean   stat_err   sys_err

312.1,6.56551 +/- 0.0393149 +/- 1.09087
188.2,3.99049 +/- 0.0246445 +/- 0.650909
85.3,1.80846 +/- 0.0139898 +/- 0.257811
32.1,0.634185 +/- 0.0082474 +/- 0.0862622
8.7,0.226938 +/- 0.00816811 +/- 0.0247104

//**************************************
Npart,St. Deviation   stat_err   sys_err

312.1,2.89815 +/- 0.0415098 +/- 0.215997
188.2,2.35718 +/- 0.0276864 +/- 0.221282
85.3,1.5629 +/- 0.016985 +/- 0.115515
32.1,0.961379 +/- 0.0123387 +/- 0.0685986
8.7,0.562337 +/- 0.016534 +/- 0.0314408

//**************************************
Npart, Skewness   stat_err   sys_err

312.1,0.240298 +/- 0.063188 +/- 0.0317775
188.2,0.491777 +/- 0.0561887 +/- 0.0541871
85.3,0.572904 +/- 0.0548731 +/- 0.0377559
32.1,0.888496 +/- 0.0735821 +/- 0.0411759
8.7,1.21217 +/- 0.193673 +/- 0.0950914

//**************************************
Npart, Kurtosis   stat_err   sys_err

312.1,0.0358484 +/- 0.180364 +/- 0.0880876
188.2,0.359179 +/- 0.220462 +/- 0.155781
85.3,0.556976 +/- 0.210887 +/- 0.101169
32.1,1.40358 +/- 0.363573 +/- 0.157009
8.7,2.98707 +/- 0.976118 +/- 0.256208
//*****************************************



AuAu 62.4 GeV
//************************************
Npart,mean   stat_err   sys_err

347.26,3.47339 +/- 0.00525101 +/- 0.382072
293.26,2.89705 +/- 0.00488789 +/- 0.318676
228.99,2.25322 +/- 0.00308339 +/- 0.247854
162.15,1.59977 +/- 0.00264072 +/- 0.175975
112.03,1.09636 +/- 0.00221669 +/- 0.120599
74.15,0.716577 +/- 0.00187162 +/- 0.0788234
45.79,0.440768 +/- 0.00148661 +/- 0.0484845
25.91,0.241972 +/- 0.00113413 +/- 0.0266169
13.01,0.114118 +/- 0.00079715 +/- 0.0125529

//**************************************
Npart,St. Deviation   stat_err   sys_err

347.26,2.85718 +/- 0.00556291 +/- 0.200003
293.26,2.63626 +/- 0.00521474 +/- 0.184538
228.99,2.3597 +/- 0.00335518 +/- 0.165179
162.15,2.01665 +/- 0.00294523 +/- 0.141166
112.03,1.70323 +/- 0.00256521 +/- 0.119226
74.15,1.40786 +/- 0.00228008 +/- 0.0985501
45.79,1.12933 +/- 0.00196481 +/- 0.0790531
25.91,0.858848 +/- 0.00170871 +/- 0.0601194
13.01,0.608684 +/- 0.00149195 +/- 0.0426079


//**************************************
Npart, Skewness   stat_err   sys_err

347.26,0.147006 +/- 0.00888389 +/- 0.0352815
293.26,0.143007 +/- 0.00906932 +/- 0.0343218
228.99,0.183016 +/- 0.00668659 +/- 0.0439238
162.15,0.198055 +/- 0.00705854 +/- 0.0475331
112.03,0.231532 +/- 0.00753521 +/- 0.0555676
74.15,0.241014 +/- 0.00849293 +/- 0.0578434
45.79,0.298532 +/- 0.00983265 +/- 0.0716477
25.91,0.363636 +/- 0.0121788 +/- 0.0872726
13.01,0.478103 +/- 0.0172715 +/- 0.114745


//**************************************
Npart, Kurtosis   stat_err   sys_err

347.26,0.119988 +/- 0.0236884 +/- 0.0323967
293.26,0.125048 +/- 0.0240959 +/- 0.0337629
228.99,0.1839 +/- 0.0188031 +/- 0.0496529
162.15,0.241599 +/- 0.021017 +/- 0.0652317
112.03,0.339745 +/- 0.0230318 +/- 0.0917312
74.15,0.471526 +/- 0.0272802 +/- 0.127312
45.79,0.754029 +/- 0.0352508 +/- 0.203588
25.91,1.24215 +/- 0.0448156 +/- 0.33538
13.01,2.45751 +/- 0.0720149 +/- 0.663529


AuAu 200 GeV
//************************************
Npart,mean   stat_err   sys_err

352.4,1.71513 +/- 0.00433202 +/- 0.188664
299.3,1.46766 +/- 0.0039544 +/- 0.161443
234.6,1.16116 +/- 0.00252259 +/- 0.127727
166.7,0.841183 +/- 0.00214204 +/- 0.0925301
115.5,0.596715 +/- 0.00186188 +/- 0.0656387
76.6,0.402381 +/- 0.00156811 +/- 0.0442619
47.8,0.256947 +/- 0.00128118 +/- 0.0282642
27.4,0.151421 +/- 0.00101754 +/- 0.0166564
14.1,0.0802132 +/- 0.000736109 +/- 0.00882345

//**************************************
Npart,St. Deviation   stat_err   sys_err

352.4,3.0175 +/- 0.0045628 +/- 0.211225
299.3,2.79673 +/- 0.0041961 +/- 0.195771
234.6,2.51161 +/- 0.00272001 +/- 0.175813
166.7,2.1689 +/- 0.0023602 +/- 0.151823
115.5,1.84982 +/- 0.0021143 +/- 0.129488
76.6,1.54961 +/- 0.00185902 +/- 0.108473
47.8,1.26105 +/- 0.00162198 +/- 0.0882735
27.4,0.986237 +/- 0.00143061 +/- 0.0690366
14.1,0.721274 +/- 0.00123301 +/- 0.0504892


//**************************************
Npart, Skewness   stat_err   sys_err

352.4,0.0603514 +/- 0.00688395 +/- 0.0144843
299.3,0.0614623 +/- 0.00687775 +/- 0.014751
234.6,0.0794329 +/- 0.00507491 +/- 0.0190639
166.7,0.0833079 +/- 0.00523017 +/- 0.0199939
115.5,0.0959312 +/- 0.00565738 +/- 0.0230235
76.6,0.104874 +/- 0.00618755 +/- 0.0251698
47.8,0.118944 +/- 0.00703311 +/- 0.0285466
27.4,0.150615 +/- 0.00859141 +/- 0.0361477
14.1,0.202535 +/- 0.0114016 +/- 0.0486085


//**************************************
Npart, Kurtosis   stat_err   sys_err

352.4,0.109359 +/- 0.0176474 +/- 0.0295271
299.3,0.115535 +/- 0.0179046 +/- 0.0311943
234.6,0.164356 +/- 0.013465 +/- 0.044376
166.7,0.217294 +/- 0.0142558 +/- 0.0586694
115.5,0.284728 +/- 0.0159071 +/- 0.0768765
76.6,0.394606 +/- 0.0181916 +/- 0.106544
47.8,0.584726 +/- 0.0222026 +/- 0.157876
27.4,0.960784 +/- 0.0293266 +/- 0.259412
14.1,1.77824 +/- 0.0425526 +/- 0.480125

Figure 8:




Figure 3:
Au+Au 19.6 GeV (data)
//*************************************
Npart,Skewness*Sigma stat_err sys_err

312.1,0.696418 +/- 0.186847 +/- 0.0848569
188.2,1.1592 +/- 0.138615 +/- 0.0822758
85.3,0.895393 +/- 0.090397 +/- 0.0232277
32.1,0.854181 +/- 0.0757018 +/- 0.0289897
8.7,0.681647 +/- 0.115689 +/- 0.0157184

//*************************************
Npart,Kurtosis*Sigma^2 stat_err sys_err

312.1,0.3011 +/- 1.51624 +/- 0.739477
188.2,1.9957 +/- 1.23698 +/- 0.775608
85.3,1.36051 +/- 0.52535 +/- 0.173403
32.1,1.29726 +/- 0.349643 +/- 0.134296
8.7,0.94458 +/- 0.33315 +/- 0.0360325

Au+Au 62.4 GeV(data)
//*************************************
Npart,Skewness*Sigma stat_err sys_err

347.26,0.420024 +/- 0.0255386 +/- 0.0420024
293.26,0.377004 +/- 0.0240504 +/- 0.0377004
228.99,0.431862 +/- 0.0159072 +/- 0.0431862
162.15,0.399408 +/- 0.0143598 +/- 0.0399408
112.03,0.394353 +/- 0.0129639 +/- 0.0394353
74.15,0.339314 +/- 0.0120732 +/- 0.0339314
45.79,0.337141 +/- 0.0112238 +/- 0.0337141
25.91,0.312308 +/- 0.0105733 +/- 0.0312308
13.01,0.291014 +/- 0.0106172 +/- 0.0291014

//*************************************
Npart,Kurtosis*Sigma^2 stat_err sys_err

347.26,0.97952 +/- 0.193898 +/- 0.137133
293.26,0.869064 +/- 0.16796 +/- 0.121669
228.99,1.02398 +/- 0.105218 +/- 0.143358
162.15,0.982556 +/- 0.0860643 +/- 0.137558
112.03,0.985603 +/- 0.0675465 +/- 0.137984
74.15,0.934595 +/- 0.054931 +/- 0.130843
45.79,0.961678 +/- 0.0460357 +/- 0.134635
25.91,0.916234 +/- 0.0343858 +/- 0.128273
13.01,0.9105 +/- 0.0283351 +/- 0.12747

Au+Au 200 GeV(data)
//*************************************
Npart,Skewness*Sigma stat_err sys_err

352.4,0.182111 +/- 0.0207944 +/- 0.0182111
299.3,0.171893 +/- 0.019257 +/- 0.0171893
234.6,0.199504 +/- 0.0127662 +/- 0.0199504
166.7,0.180687 +/- 0.0113622 +/- 0.0180687
115.5,0.177456 +/- 0.0104855 +/- 0.0177456
76.6,0.162514 +/- 0.00960729 +/- 0.0162514
47.8,0.149995 +/- 0.00888729 +/- 0.0149995
27.4,0.148542 +/- 0.00849242 +/- 0.0148542
14.1,0.146083 +/- 0.00824288 +/- 0.0146083

//*************************************
Npart,Kurtosis*Sigma^2 stat_err sys_err

352.4,0.995754 +/- 0.161029 +/- 0.139406
299.3,0.903675 +/- 0.140384 +/- 0.126515
234.6,1.03678 +/- 0.0852845 +/- 0.14515
166.7,1.02218 +/- 0.0674703 +/- 0.143105
115.5,0.974296 +/- 0.0549185 +/- 0.136401
76.6,0.947569 +/- 0.044269 +/- 0.13266
47.8,0.92986 +/- 0.0360215 +/- 0.13018
27.4,0.934519 +/- 0.0294372 +/- 0.130833
14.1,0.925105 +/- 0.0232938 +/- 0.129515


Lattice QCD Calculation
//******************************************
Energy(GeV) Npart  Skewness*Sigma  stat_err
 19.6        400      1.5            0.6 
 
 62.4        400      0.32           0.04
 
 200         400      0.09           0.01              
//******************************************

Transport Model Calculations
//**************************************
  UrQMD, Au+Au 19.6 GeV, net-proton
//**************************************
 Npart,Skewness*Sigma  stat_err
 
361.34,1.00139 +/- 0.0770523
313.768,0.945305 +/- 0.0718695
250.579,1.02464 +/- 0.0457984
181.673,1.07629 +/- 0.0416792
128.797,0.951931 +/- 0.0364372
87.042,1.00532 +/- 0.0331779
56.514,0.915057 +/- 0.0318081
35.285,0.881171 +/- 0.0313721
19.45,0.843831 +/- 0.032122

//**************************************
  UrQMD, Au+Au 62.4 GeV, net-proton
//**************************************
 Npart,Skewness*Sigma  stat_err
 
361.34,0.658173 +/- 0.0716848
313.768,0.644932 +/- 0.0670201
250.579,0.654408 +/- 0.0423957
181.673,0.638371 +/- 0.0384066
128.797,0.57961 +/- 0.0348726
87.042,0.569402 +/- 0.0320034
56.514,0.463039 +/- 0.0314256
35.285,0.455034 +/- 0.0310813
19.45,0.401757 +/- 0.033272


//**************************************
  UrQMD, Au+Au 200 GeV, net-proton
//**************************************
 Npart,Skewness*Sigma  stat_err

361.34,0.298332 +/- 0.0671317
313.768,0.27045 +/- 0.0632627
250.579,0.28321 +/- 0.0411251
181.673,0.262543 +/- 0.036859
128.797,0.237908 +/- 0.0343306
87.042,0.21406 +/- 0.0306577
56.514,0.174838 +/- 0.0324753
35.285,0.156877 +/- 0.0300118
19.45,0.155744 +/- 0.0310082


//**************************************
  UrQMD, Au+Au 200 GeV, net-proton
//**************************************
 Npart,Kurtosis*Sigma^2  stat_err
 
361.34,1.27184 +/- 0.52481
313.768,0.927365 +/- 0.449994
250.579,1.26189 +/- 0.282054
181.673,1.13718 +/- 0.212249
128.797,1.20392 +/- 0.179189
87.042,1.24166 +/- 0.139207
56.514,1.29062 +/- 0.135814
35.285,1.23661 +/- 0.101862
19.45,1.2808 +/- 0.0918904

//**************************************
  UrQMD, Au+Au 200 GeV, net-baryon
//**************************************
 Npart,Kurtosis*Sigma^2  stat_err
 
361.34,0.969164 +/- 0.510991
313.768,0.905069 +/- 0.462007
250.579,1.23149 +/- 0.274646
181.673,1.4511 +/- 0.240107
128.797,1.27423 +/- 0.187895
87.042,1.29741 +/- 0.142087
56.514,1.31609 +/- 0.136748
35.285,1.19621 +/- 0.0960926
19.45,1.24986 +/- 0.0895199

//**************************************
  UrQMD, Au+Au 200 GeV, net-proton No Decay
//**************************************
 Npart,Kurtosis*Sigma^2  stat_err
 
361.34,0.82428 +/- 0.425665
313.768,1.1098 +/- 0.397707
250.579,1.10532 +/- 0.259158
181.673,1.1434 +/- 0.211777
128.797,1.12418 +/- 0.172618
87.042,1.1538 +/- 0.141537
56.514,1.2821 +/- 0.147814
35.285,1.23798 +/- 0.119013
19.45,1.2604 +/- 0.105421

//**************************************
  AMPT default, Au+Au 200 GeV, net-proton
//**************************************
 Npart,Kurtosis*Sigma^2  stat_err
 
361.34,1.12577 +/- 0.610107
313.768,1.37062 +/- 0.570827
250.579,1.10729 +/- 0.315574
181.673,1.34533 +/- 0.25626
128.797,1.22585 +/- 0.196472
87.0419,1.33982 +/- 0.154935
56.5143,1.36641 +/- 0.136489
35.2851,1.44527 +/- 0.116455
15.8935,1.55221 +/- 0.0875661

//**************************************
  AMPT String Melting, Au+Au 200 GeV, net-proton
//**************************************
 Npart,Kurtosis*Sigma^2  stat_err
 
361.374,1.35858 +/- 0.691533
313.666,1.2795 +/- 0.57346
250.648,1.56418 +/- 0.331769
181.689,1.46799 +/- 0.25806
128.874,1.32144 +/- 0.198422
87.0032,1.37483 +/- 0.14803
56.5274,1.23533 +/- 0.11941
35.241,1.28946 +/- 0.101144
15.9072,1.45715 +/- 0.0858709

//**************************************
  Therminator, Au+Au 200 GeV, net-proton
//**************************************
 Npart,Kurtosis*Sigma^2  stat_err
 
369.994,0.947155 +/- 0.49651
316.404,0.840123 +/- 0.409692
250.974,0.972293 +/- 0.324887
182.049,1.0731 +/- 0.26185
129.748,1.09557 +/- 0.201039
89.6158,0.816559 +/- 0.133243
59.4011,1.02421 +/- 0.107321
37.3316,0.989461 +/- 0.0816468
22.0385,1.0206 +/- 0.0783986

//**************************************
 Hijing, Au+Au 200 GeV, net-proton
//**************************************
 Npart,Kurtosis*Sigma^2  stat_err
 
356.062,1.07111 +/- 0.698471
306.812,1.8615 +/- 0.618178
243.388,2.2504 +/- 0.351577
175.067,1.64995 +/- 0.24366
123.175,1.92499 +/- 0.196061
82.4429,1.71034 +/- 0.137786
53.0044,1.69835 +/- 0.120381
32.7414,1.66723 +/- 0.101656
18.0008,1.58611 +/- 0.0764958

//************************************
Hijing+Geant-Hijing Band, Au+Au 200 GeV net-proton
//************************************
Skewness*Sigma  stat_err

0.113            0.030

Kurtosis*Sigma^2  stat_err

0.359           0.137
//************************************


Figure 4:
STAR Data net-proton
//********************************************
Energy Kurtosis*Sigma^2   stat_err    sys_err

 19.6    1.179           0.4165       0.219
 
 62.4    0.9515          0.03442      0.04445
 
 200     0.9633          0.02836      0.045
 //**********************************************
 
 Model Calculation
 //**********************************************
 UrQMD, net-proton
//********************************************
 Energy(shifted),Kurtosis*Sigma^2  stat_err   

17.6,1.43892 +/- 0.137739
57.4,1.34356 +/- 0.11636
185,1.20577 +/- 0.0918512 
//*******************************************

//**********************************************
 AMPT default, net-proton
//********************************************
 Energy(shifted),Kurtosis*Sigma^2  stat_err 
  
21.6,1.42336 +/- 0.150954
67.4,1.22544 +/- 0.18106
215,1.30318 +/- 0.108849
//*******************************************

//**********************************************
 AMPT String Melting, net-proton
//********************************************
 Energy(shifted),Kurtosis*Sigma^2  stat_err 
  
23.6,1.22405 +/- 0.164789
72.4,1.20373 +/- 0.143339
220,1.35716 +/- 0.114928
//*******************************************

//**********************************************
Therminator, net-proton
//********************************************
Energy(shifted),Kurtosis*Sigma^2  stat_err 
225,0.975453 +/- 0.0910154
//*********************************************

//**********************************************
 Hijing, net-proton
//********************************************
 Energy(shifted),Kurtosis*Sigma^2  stat_err 
  
15.6,1.38545 +/- 0.128683
52.4,1.33965 +/- 0.127959
180,1.71333 +/- 0.11842
 
//*******************************************

 For any questions please contact STAR Physics Analysis Co-ordinator : Bedanga Mohanty - bedanga@rcf.rhic.bnl.gov