Particle correlations in proton-proton collisions

Published

October 7, 2022

Here, I run simulations of proton-proton collisions with Chromo to investigate two-particle correlations in pseudorapidity space. With Chromo, it is very easy to study the output of different event generators.

I generate collisions at 13 TeV center-of-mass energy. For each event, I form all unique pairs of final-state charged particles, these are effectively long-lived prompt charged particles. Prompt here means that they either have no ancestors or that their ancestors are short-lived. I then fill the pseudorapidity pairs into a two-dimensional histogram.

We can see interesting patterns in these plots when different generators are compared. SIBYLL-2.3d shows a stronger concentration around mid-rapidity and has more pairs which are close in rapidity than the other generators.

import impy.models as im
from impy.kinematics import CenterOfMass
from impy.constants import TeV
import boost_histogram as bh
from matplotlib import pyplot as plt
import numba as nb
import numpy as np
ekin = CenterOfMass(13 * TeV, "proton", "proton")

@nb.njit
def pairs(eta, seed):
    r1 = []
    r2 = []
    np.random.seed(seed)
    for i, etai in enumerate(eta):
        for j in range(i):
            etaj = eta[j]
            # avoid structures that arise from implementation-specific
            # ordering of particles in HEPEVT record
            if np.random.uniform(0, 1) < 0.5:
                r1.append(etai)
                r2.append(etaj)
            else:
                r1.append(etaj)
                r2.append(etai)
    return np.array(r1), np.array(r2)

nevent = 1000

histograms = {}
for Model in (im.Sibyll21, im.Sibyll23d, im.QGSJetII04, im.EposLHC, im.Pythia6):
    h = bh.Histogram(bh.axis.Regular(300, -15, 15), bh.axis.Regular(300, -15, 15))
    for i, ev in enumerate(Model(ekin)(nevent)):
        fsc = ev.final_state_charged()
        with np.errstate(invalid="ignore", divide="ignore"):
            eta1, eta2 = pairs(fsc.eta, i)
        h.fill(eta1, eta2)
    histograms[Model] = h
 ====================================================
 |                                                  |
 |                 S I B Y L L  2.1                 |
 |                                                  |
 |         HADRONIC INTERACTION MONTE CARLO         |
 |                        BY                        |
 |                   Ralph ENGEL                    |
 |           R.S. FLETCHER, T.K. GAISSER            |
 |               P. LIPARI, T. STANEV               |
 |                                                  |
 | Publication to be cited when using this program: |
 | R. Engel et al., Proc. 26th ICRC, 1 (1999) 415   |
 |                                                  |
 | last modified:  28. Sept. 2001 by R. Engel       |
 ====================================================


 Table: J, sqs,  PT_cut,  SIG_tot,  SIG_inel,  B_el,  rho,  <n_s>,  <n_h>
 ------------------------------------------------------------------------
    1   1.000E+01    1.45   38.33   30.88   10.83  -0.185   1.964   0.003
    1   1.259E+01    1.49   38.27   31.16   11.10  -0.127   1.949   0.006
    1   1.585E+01    1.54   38.44   31.54   11.36  -0.078   1.934   0.012
    1   1.995E+01    1.59   38.84   32.05   11.63  -0.037   1.918   0.019
    1   2.512E+01    1.64   39.46   32.67   11.89  -0.004   1.901   0.029
    1   3.162E+01    1.69   40.29   33.41   12.16   0.022   1.884   0.043
    1   3.981E+01    1.75   41.28   34.24   12.42   0.044   1.864   0.060
    1   5.012E+01    1.81   42.39   35.13   12.69   0.061   1.844   0.082
    1   6.310E+01    1.87   43.59   36.05   12.95   0.075   1.821   0.109
    1   7.943E+01    1.93   44.92   37.06   13.22   0.085   1.797   0.141
    1   1.000E+02    2.00   46.35   38.14   13.48   0.094   1.771   0.180
    1   1.259E+02    2.07   47.84   39.28   13.73   0.101   1.742   0.226
    1   1.585E+02    2.14   49.39   40.48   13.98   0.106   1.711   0.279
    1   1.995E+02    2.22   51.05   41.74   14.24   0.110   1.677   0.342
    1   2.512E+02    2.30   52.84   43.09   14.50   0.113   1.641   0.413
    1   3.162E+02    2.38   54.79   44.56   14.77   0.116   1.603   0.495
    1   3.981E+02    2.46   56.96   46.16   15.05   0.118   1.563   0.587
    1   5.012E+02    2.55   59.39   47.94   15.33   0.119   1.522   0.691
    1   6.310E+02    2.65   62.15   49.92   15.63   0.120   1.479   0.808
    1   7.943E+02    2.74   65.29   52.14   15.95   0.121   1.435   0.938
    1   1.000E+03    2.84   68.88   54.63   16.28   0.122   1.391   1.081
    1   1.259E+03    2.95   72.53   57.06   16.61   0.123   1.347   1.240
    1   1.585E+03    3.06   76.46   59.64   16.96   0.123   1.303   1.416
    1   1.995E+03    3.17   80.67   62.36   17.32   0.123   1.259   1.609
    1   2.512E+03    3.29   85.17   65.23   17.70   0.124   1.216   1.822
    1   3.162E+03    3.41   89.95   68.24   18.10   0.124   1.175   2.055
    1   3.981E+03    3.54   95.02   71.38   18.51   0.124   1.135   2.312
    1   5.012E+03    3.67  100.35   74.64   18.95   0.124   1.096   2.594
    1   6.310E+03    3.81  105.95   78.03   19.40   0.124   1.059   2.903
    1   7.943E+03    3.95  111.81   81.53   19.88   0.124   1.024   3.244
    1   1.000E+04    4.09  117.90   85.14   20.38   0.125   0.990   3.618
    1   1.259E+04    4.25  124.23   88.85   20.90   0.125   0.959   4.030
    1   1.585E+04    4.40  130.77   92.65   21.44   0.125   0.928   4.481
    1   1.995E+04    4.57  137.51   96.55   22.01   0.125   0.898   4.957
    1   2.512E+04    4.74  144.44  100.54   22.60   0.125   0.865   5.394
    1   3.162E+04    4.91  151.56  104.61   23.21   0.125   0.825   5.707
    1   3.981E+04    5.09  158.85  108.75   23.85   0.125   0.779   5.909
    1   5.012E+04    5.28  166.31  112.98   24.50   0.125   0.733   6.076
    1   6.310E+04    5.47  173.92  117.27   25.17   0.125   0.690   6.243
    1   7.943E+04    5.67  181.69  121.64   25.87   0.125   0.649   6.417
    1   1.000E+05    5.88  189.60  126.07   26.58   0.125   0.611   6.601
    1   1.259E+05    6.10  197.66  130.57   27.31   0.125   0.576   6.799
    1   1.585E+05    6.32  205.84  135.12   28.06   0.125   0.543   7.013
    1   1.995E+05    6.55  214.16  139.74   28.82   0.125   0.512   7.247
    1   2.512E+05    6.78  222.60  144.41   29.60   0.125   0.484   7.501
    1   3.162E+05    7.03  231.15  149.14   30.39   0.125   0.457   7.763
    1   3.981E+05    7.28  239.82  153.93   31.21   0.125   0.432   7.999
    1   5.012E+05    7.54  248.60  158.77   32.03   0.125   0.408   8.168
    1   6.310E+05    7.81  257.49  163.65   32.87   0.125   0.385   8.278
    1   7.943E+05    8.08  266.48  168.59   33.72   0.125   0.364   8.364
    1   1.000E+06    8.37  275.56  173.57   34.59   0.125   0.343   8.442
    1   1.259E+06    8.67  284.75  178.60   35.47   0.125   0.324   8.517
    1   1.585E+06    8.97  294.03  183.68   36.36   0.125   0.307   8.590
    1   1.995E+06    9.28  303.40  188.80   37.27   0.125   0.290   8.663
    1   2.512E+06    9.61  312.87  193.97   38.18   0.125   0.274   8.735
    1   3.162E+06    9.94  322.42  199.18   39.11   0.125   0.259   8.808
    1   3.981E+06   10.29  332.06  204.43   40.05   0.125   0.246   8.882
    1   5.012E+06   10.64  341.79  209.72   41.00   0.125   0.233   8.957
    1   6.310E+06   11.00  351.59  215.05   41.95   0.125   0.220   9.032
    1   7.943E+06   11.38  361.49  220.42   42.92   0.125   0.209   9.101
    1   1.000E+07   11.77  371.46  225.83   43.90   0.125   0.198   9.158

 Table: J, sqs,  PT_cut,  SIG_tot,  SIG_inel,  B_el,  rho,  <n_s>,  <n_h>
 ------------------------------------------------------------------------
    2   1.000E+01    1.45   23.12   19.94   10.12  -0.067   1.845   0.009
    2   1.259E+01    1.49   23.22   20.21   10.27  -0.031   1.827   0.016
    2   1.585E+01    1.54   23.49   20.57   10.42  -0.001   1.807   0.026
    2   1.995E+01    1.59   23.87   21.00   10.56   0.024   1.783   0.040
    2   2.512E+01    1.64   24.33   21.49   10.70   0.045   1.756   0.058
    2   3.162E+01    1.69   24.89   21.95   10.84   0.061   1.727   0.081
    2   3.981E+01    1.75   25.53   22.48   10.97   0.074   1.695   0.110
    2   5.012E+01    1.81   26.25   23.06   11.11   0.085   1.659   0.144
    2   6.310E+01    1.87   27.04   23.69   11.24   0.093   1.621   0.185
    2   7.943E+01    1.93   27.89   24.36   11.37   0.100   1.580   0.233
    2   1.000E+02    2.00   28.80   25.08   11.50   0.105   1.536   0.288
    2   1.259E+02    2.07   29.72   25.72   11.44   0.109   1.490   0.351
    2   1.585E+02    2.14   30.77   26.45   11.39   0.113   1.442   0.423
    2   1.995E+02    2.22   31.96   27.30   11.38   0.115   1.392   0.503
    2   2.512E+02    2.30   33.35   28.30   11.40   0.117   1.340   0.592
    2   3.162E+02    2.38   34.99   29.47   11.45   0.119   1.288   0.690
    2   3.981E+02    2.46   36.93   30.84   11.55   0.120   1.236   0.798
    2   5.012E+02    2.55   39.22   32.47   11.69   0.121   1.184   0.916
    2   6.310E+02    2.65   41.93   34.36   11.88   0.122   1.132   1.044
    2   7.943E+02    2.74   45.10   36.57   12.12   0.123   1.082   1.183
    2   1.000E+03    2.84   48.81   39.13   12.41   0.123   1.033   1.333
    2   1.259E+03    2.95   52.13   41.43   12.78   0.123   0.987   1.497
    2   1.585E+03    3.06   55.69   43.86   13.16   0.124   0.942   1.673
    2   1.995E+03    3.17   59.50   46.43   13.56   0.124   0.899   1.865
    2   2.512E+03    3.29   63.55   49.12   13.97   0.124   0.859   2.072
    2   3.162E+03    3.41   67.83   51.93   14.39   0.124   0.821   2.298
    2   3.981E+03    3.54   72.35   54.85   14.83   0.124   0.785   2.543
    2   5.012E+03    3.67   77.09   57.87   15.28   0.124   0.752   2.809
    2   6.310E+03    3.81   82.06   61.01   15.75   0.124   0.720   3.099
    2   7.943E+03    3.95   87.24   64.23   16.24   0.125   0.691   3.416
    2   1.000E+04    4.09   92.61   67.55   16.74   0.125   0.664   3.761
    2   1.259E+04    4.25   98.18   70.96   17.26   0.125   0.638   4.138
    2   1.585E+04    4.40  103.94   74.44   17.79   0.125   0.614   4.543
    2   1.995E+04    4.57  109.87   78.01   18.34   0.125   0.591   4.953
    2   2.512E+04    4.74  115.96   81.65   18.91   0.125   0.565   5.303
    2   3.162E+04    4.91  122.21   85.36   19.50   0.125   0.535   5.552
    2   3.981E+04    5.09  128.62   89.15   20.10   0.125   0.504   5.737
    2   5.012E+04    5.28  135.18   92.99   20.72   0.125   0.474   5.904
    2   6.310E+04    5.47  141.88   96.91   21.35   0.125   0.446   6.067
    2   7.943E+04    5.67  148.71  100.88   22.00   0.125   0.419   6.233
    2   1.000E+05    5.88  155.68  104.91   22.66   0.125   0.394   6.404
    2   1.259E+05    6.10  162.78  109.01   23.34   0.125   0.371   6.584
    2   1.585E+05    6.32  170.01  113.15   24.03   0.125   0.349   6.776
    2   1.995E+05    6.55  177.35  117.36   24.73   0.125   0.329   6.981
    2   2.512E+05    6.78  184.81  121.61   25.45   0.125   0.311   7.200
    2   3.162E+05    7.03  192.39  125.92   26.18   0.125   0.293   7.426
    2   3.981E+05    7.28  200.08  130.28   26.93   0.125   0.277   7.632
    2   5.012E+05    7.54  207.88  134.69   27.68   0.125   0.261   7.792
    2   6.310E+05    7.81  215.78  139.15   28.45   0.125   0.246   7.909
    2   7.943E+05    8.08  223.78  143.66   29.23   0.125   0.232   8.004
    2   1.000E+06    8.37  231.89  148.21   30.02   0.125   0.219   8.090
    2   1.259E+06    8.67  240.09  152.81   30.83   0.125   0.207   8.172
    2   1.585E+06    8.97  248.39  157.46   31.64   0.125   0.196   8.249
    2   1.995E+06    9.28  256.79  162.15   32.47   0.125   0.185   8.324
    2   2.512E+06    9.61  265.28  166.88   33.30   0.125   0.175   8.398
    2   3.162E+06    9.94  273.86  171.66   34.15   0.125   0.165   8.470
    2   3.981E+06   10.29  282.53  176.48   35.01   0.125   0.156   8.542
    2   5.012E+06   10.64  291.29  181.34   35.88   0.125   0.148   8.615
    2   6.310E+06   11.00  300.14  186.25   36.76   0.125   0.140   8.687
    2   7.943E+06   11.38  309.08  191.19   37.64   0.125   0.133   8.756
    2   1.000E+07   11.77  318.10  196.18   38.54   0.125   0.126   8.819

 Table: J, sqs,  PT_cut,  SIG_tot,  SIG_inel,  B_el,  rho,  <n_s>,  <n_h>
 ------------------------------------------------------------------------
    3   1.000E+01    1.45   18.30   16.13    8.84  -0.025   1.845   0.009
    3   1.259E+01    1.49   18.83   16.69    9.14   0.009   1.827   0.016
    3   1.585E+01    1.54   19.41   17.26    9.40   0.036   1.807   0.026
    3   1.995E+01    1.59   20.02   17.83    9.64   0.056   1.783   0.040
    3   2.512E+01    1.64   20.63   18.41    9.85   0.072   1.756   0.058
    3   3.162E+01    1.69   21.32   18.99   10.05   0.084   1.727   0.081
    3   3.981E+01    1.75   22.04   19.60   10.23   0.093   1.695   0.110
    3   5.012E+01    1.81   22.81   20.23   10.40   0.101   1.659   0.144
    3   6.310E+01    1.87   23.61   20.89   10.56   0.106   1.621   0.185
    3   7.943E+01    1.93   24.46   21.57   10.72   0.111   1.580   0.233
    3   1.000E+02    2.00   25.34   22.28   10.87   0.114   1.536   0.288
    3   1.259E+02    2.07   26.25   23.01   11.06   0.116   1.490   0.351
    3   1.585E+02    2.14   27.21   23.75   11.21   0.118   1.442   0.423
    3   1.995E+02    2.22   28.23   24.53   11.32   0.120   1.392   0.503
    3   2.512E+02    2.30   29.37   25.37   11.42   0.121   1.340   0.592
    3   3.162E+02    2.38   30.68   26.34   11.51   0.122   1.288   0.690
    3   3.981E+02    2.46   32.25   27.48   11.61   0.123   1.236   0.798
    3   5.012E+02    2.55   34.17   28.86   11.73   0.123   1.184   0.916
    3   6.310E+02    2.65   36.58   30.57   11.90   0.123   1.132   1.044
    3   7.943E+02    2.74   39.60   32.72   12.12   0.124   1.082   1.183
    3   1.000E+03    2.84   43.42   35.40   12.41   0.124   1.033   1.333
    3   1.259E+03    2.95   46.38   37.52   12.78   0.124   0.987   1.497
    3   1.585E+03    3.06   49.56   39.77   13.16   0.124   0.942   1.673
    3   1.995E+03    3.17   52.95   42.14   13.56   0.124   0.899   1.865
    3   2.512E+03    3.29   56.56   44.63   13.97   0.124   0.859   2.072
    3   3.162E+03    3.41   60.38   47.23   14.39   0.125   0.821   2.298
    3   3.981E+03    3.54   64.41   49.94   14.83   0.125   0.785   2.543
    3   5.012E+03    3.67   68.64   52.75   15.28   0.125   0.752   2.809
    3   6.310E+03    3.81   73.06   55.67   15.75   0.125   0.720   3.099
    3   7.943E+03    3.95   77.67   58.67   16.24   0.125   0.691   3.416
    3   1.000E+04    4.09   82.46   61.77   16.74   0.125   0.664   3.761
    3   1.259E+04    4.25   87.43   64.95   17.26   0.125   0.638   4.138
    3   1.585E+04    4.40   92.55   68.21   17.79   0.125   0.614   4.543
    3   1.995E+04    4.57   97.83   71.55   18.34   0.125   0.591   4.953
    3   2.512E+04    4.74  103.26   74.97   18.91   0.125   0.565   5.303
    3   3.162E+04    4.91  108.83   78.45   19.50   0.125   0.535   5.552
    3   3.981E+04    5.09  114.54   82.01   20.10   0.125   0.504   5.737
    3   5.012E+04    5.28  120.37   85.63   20.72   0.125   0.474   5.904
    3   6.310E+04    5.47  126.34   89.31   21.35   0.125   0.446   6.067
    3   7.943E+04    5.67  132.43   93.05   22.00   0.125   0.419   6.233
    3   1.000E+05    5.88  138.64   96.85   22.66   0.125   0.394   6.404
    3   1.259E+05    6.10  144.96  100.72   23.34   0.125   0.371   6.584
    3   1.585E+05    6.32  151.39  104.63   24.03   0.125   0.349   6.776
    3   1.995E+05    6.55  157.93  108.61   24.73   0.125   0.329   6.981
    3   2.512E+05    6.78  164.58  112.63   25.45   0.125   0.311   7.200
    3   3.162E+05    7.03  171.33  116.71   26.18   0.125   0.293   7.426
    3   3.981E+05    7.28  178.17  120.84   26.93   0.125   0.277   7.632
    3   5.012E+05    7.54  185.12  125.01   27.68   0.125   0.261   7.792
    3   6.310E+05    7.81  192.15  129.24   28.45   0.125   0.246   7.909
    3   7.943E+05    8.08  199.28  133.52   29.23   0.125   0.232   8.004
    3   1.000E+06    8.37  206.50  137.84   30.02   0.125   0.219   8.090
    3   1.259E+06    8.67  213.80  142.20   30.83   0.125   0.207   8.172
    3   1.585E+06    8.97  221.19  146.62   31.64   0.125   0.196   8.249
    3   1.995E+06    9.28  228.67  151.07   32.47   0.125   0.185   8.324
    3   2.512E+06    9.61  236.23  155.58   33.30   0.125   0.175   8.398
    3   3.162E+06    9.94  243.87  160.12   34.15   0.125   0.165   8.470
    3   3.981E+06   10.29  251.60  164.71   35.01   0.125   0.156   8.542
    3   5.012E+06   10.64  259.40  169.34   35.88   0.125   0.148   8.615
    3   6.310E+06   11.00  267.28  174.01   36.76   0.125   0.140   8.687
    3   7.943E+06   11.38  275.24  178.72   37.64   0.125   0.133   8.756
    3   1.000E+07   11.77  283.28  183.48   38.54   0.125   0.126   8.819
 ====================================================
 |                                                  |
 |                 S I B Y L L  2.3d                |
 |                                                  |
 |         HADRONIC INTERACTION MONTE CARLO         |
 |                        BY                        |
 |            Eun-Joo AHN, Felix RIEHN              |
 |      R. ENGEL, A. FEDYNITCH, R.S. FLETCHER,      |
 |       T.K. GAISSER, P. LIPARI, T. STANEV         |
 |                                                  |
 | Publication to be cited when using this program: |
 | Eun-Joo AHN et al., Phys.Rev. D80 (2009) 094003  |
 | F. RIEHN et al., hep-ph: 1912.03300              |
 | last modifications: F. Riehn (05/20/2020)        |
 ====================================================

 SIG_AIR_INI: initializing target: (i,A)           1           0 air..
 SIG_AIR_INI: initializing target: (i,A)           2          14 nit..
 SIG_AIR_INI: initializing target: (i,A)           3          16 oxy..
 ====================================================
 |                                                  |
 |         QUARK GLUON STRING JET -II MODEL         |
 |                                                  |
 |         HADRONIC INTERACTION MONTE CARLO         |
 |                        BY                        |
 |                 S. OSTAPCHENKO                   |
 |                                                  |
 |             e-mail: sergei@tf.phys.ntnu.no       |
 |                                                  |
 |                   Version II-04                  |
 |                                                  |
 | Publication to be cited when using this program: |
 | S.Ostapchenko, PRD 83 (2011) 014018              |
 |                                                  |
 | last modification:  09.04.2013                   |
 |                                                  |
 | Any modification has to be approved by the author|
 ====================================================

 DATDIR/Users/hdembinski/Extern/impy/src/impy/iamdata/qgsjet/                                                                                                                                                                                                          
  qgaini: cross sections readout from the file: qgsdat-II-04
 done
  qgaini: nuclear cross sections readout from the file sectnu-II-04
impy.models.epos.EposLHC::init_generator(): First initialization
 /Users/hdembinski/Extern/impy/src/impy/iamdata/epos/          52
initializations ...
###################################################################
#        EPOS LHC      K. WERNER, T. PIEROG                       #
#                      Contact: tanguy.pierog@kit.edu             #
###################################################################
#        WARNING: This is a special retuned version !!!           #
#     Do not publish results without contacting the authors.      #
###################################################################
read from /Users/hdembinski/Extern/impy/src/impy/iamdata/epos/epos.iniev ...
read from /Users/hdembinski/Extern/impy/src/impy/iamdata/epos/epos.initl ...
read from /Users/hdembinski/Extern/impy/src/impy/iamdata/epos/epos.inirj.lhc ...
read from /Users/hdembinski/Extern/impy/src/impy/iamdata/epos/epos.inics.lhc ...
 Compute Cross-section (can take a while...)
seedj:   3862463     0.2000000000000000D+01
 EPOS used with FUSION option
1                                                                              
 ******************************************************************************
 ******************************************************************************
 **                                                                          **
 **                                                                          **
 **              *......*                  Welcome to the Lund Monte Carlo!  **
 **         *:::!!:::::::::::*                                               **
 **      *::::::!!::::::::::::::*          PPP  Y   Y TTTTT H   H III   A    **
 **    *::::::::!!::::::::::::::::*        P  P  Y Y    T   H   H  I   A A   **
 **   *:::::::::!!:::::::::::::::::*       PPP    Y     T   HHHHH  I  AAAAA  **
 **   *:::::::::!!:::::::::::::::::*       P      Y     T   H   H  I  A   A  **
 **    *::::::::!!::::::::::::::::*!       P      Y     T   H   H III A   A  **
 **      *::::::!!::::::::::::::* !!                                         **
 **      !! *:::!!:::::::::::*    !!       This is PYTHIA version 6.428      **
 **      !!     !* -><- *         !!       Last date of change:  5 Sep 2013  **
 **      !!     !!                !!                                         **
 **      !!     !!                !!       Now is  0 Jan 2000 at  0:00:00    **
 **      !!                       !!                                         **
 **      !!        lh             !!       Disclaimer: this program comes    **
 **      !!                       !!       without any guarantees. Beware    **
 **      !!                 hh    !!       of errors and use common sense    **
 **      !!    ll                 !!       when interpreting results.        **
 **      !!                       !!                                         **
 **      !!                                Copyright T. Sjostrand (2011)     **
 **                                                                          **
 ** An archive of program versions and documentation is found on the web:    **
 ** http://www.thep.lu.se/~torbjorn/Pythia.html                              **
 **                                                                          **
 ** When you cite this program, the official reference is to the 6.4 manual: **
 ** T. Sjostrand, S. Mrenna and P. Skands, JHEP05 (2006) 026                 **
 ** (LU TP 06-13, FERMILAB-PUB-06-052-CD-T) [hep-ph/0603175].                **
 **                                                                          **
 ** Also remember that the program, to a large extent, represents original   **
 ** physics research. Other publications of special relevance to your        **
 ** studies may therefore deserve separate mention.                          **
 **                                                                          **
 ** Main author: Torbjorn Sjostrand; Department of Theoretical Physics,      **
 **   Lund University, Solvegatan 14A, S-223 62 Lund, Sweden;                **
 **   phone: + 46 - 46 - 222 48 16; e-mail: torbjorn@thep.lu.se              **
 ** Author: Stephen Mrenna; Computing Division, GDS Group,                   **
 **   Fermi National Accelerator Laboratory, MS 234, Batavia, IL 60510, USA; **
 **   phone: + 1 - 630 - 840 - 2556; e-mail: mrenna@fnal.gov                 **
 ** Author: Peter Skands; CERN/PH-TH, CH-1211 Geneva, Switzerland            **
 **   phone: + 41 - 22 - 767 24 47; e-mail: peter.skands@cern.ch             **
 **                                                                          **
 **                                                                          **
 ******************************************************************************
 ******************************************************************************
1****************** PYINIT: initialization of PYTHIA routines *****************

 ==============================================================================
 I                                                                            I
 I             PYTHIA will be initialized for a p+ on p+ collider             I
 I                  at  13000.000 GeV center-of-mass energy                   I
 I                                                                            I
 ==============================================================================

 ******** PYMAXI: summary of differential cross-section maximum search ********

           ==========================================================
           I                                      I                 I
           I  ISUB  Subprocess name               I  Maximum value  I
           I                                      I                 I
           ==========================================================
           I                                      I                 I
           I   92   Single diffractive (XB)       I    7.1189D+00   I
           I   93   Single diffractive (AX)       I    7.1189D+00   I
           I   94   Double  diffractive           I    1.0176D+01   I
           I   95   Low-pT scattering             I    5.4002D+01   I
           I   96   Semihard QCD 2 -> 2           I    1.2350D+04   I
           I                                      I                 I
           ==========================================================

 ****** PYMULT: initialization of multiple interactions for MSTP(82) = 4 ******
        pT0 = 3.28 GeV gives sigma(parton-parton) = 5.65D+02 mb: accepted

 ****** PYMIGN: initialization of multiple interactions for MSTP(82) = 4 ******
        pT0 = 3.28 GeV gives sigma(parton-parton) = 2.38D+02 mb: accepted

 ********************** PYINIT: initialization completed **********************
for Model, h in histograms.items():
    plt.figure()
    h2 = h[bh.loc(-10):bh.loc(10):bh.rebin(5), bh.loc(-10):bh.loc(10):bh.rebin(5)]
    h3 = h2[:, sum]
    nxy = h2.values() / nevent
    nx = ny = h3.values() / nevent
    corr = nxy / np.outer(nx, ny) ** 0.5
    print(Model.__name__, np.mean(corr))
    plt.pcolormesh(*h2.axes.edges.T, np.ma.masked_invalid(corr).T)
    plt.xlabel("eta 1")
    plt.ylabel("eta 2")
    plt.colorbar()
    plt.clim(0, 0.05)
    plt.title(Model.__name__)
Sibyll21 0.020957722916460298
Sibyll23d 0.020768885431597404
QGSJetII04 0.02160297235716634
EposLHC 0.021529706058337213
Pythia6 0.022110986939247387