[12gevmoller_sim] [JeffersonLab/remoll] a76268: MG5: no lower limit on leading and second lepton p...

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  Commit: a762685c1a05c2d9671c777e7e98ceac4b89f102
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  Author: Wouter Deconinck <wdconinc at gmail.com>
  Date:   2019-01-17 (Thu, 17 Jan 2019)

  Changed paths:
    M generators/MG5/ee/template/run_card.dat

  Log Message:
  -----------
  MG5: no lower limit on leading and second lepton pT of 0.025 GeV

The actual pT of the Moller leptons will be 2.8 MeV, much lower
than the 25 MeV limit. This explains why no events were generated
with a meaningful cross section...


  Commit: 2c74ad0b15a9cb5e17f1645a6f78dd708c90e184
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  Author: Wouter Deconinck <wdconinc at gmail.com>
  Date:   2019-01-18 (Fri, 18 Jan 2019)

  Changed paths:
    A generators/MG5/e+e-/proc_card_mg5_ee_mumu_QED.dat
    A generators/MG5/e+e-/template/madanalysis5_hadron_card.dat
    A generators/MG5/e+e-/template/madanalysis5_parton_card.dat
    A generators/MG5/e+e-/template/run_card.dat

  Log Message:
  -----------
  Demonstration of correction operation of MG5 on e+ e- > mu+ mu-

(This is essentially a madgraph5 hello world demo)

With the commands
```
mg5_aMC proc_card_mg5_ee_mumu_QED.dat
cd ee_mumu_QED
bin/generate_events run_01 -f
```
at 5 GeV x 5 GeV and without pT cuts we get 928.1 ± 0.56 pb,
which is correct for pi alpha² / 2s * 8/3 with alpha ~ 1/133 at
s = 4 E1 E2 = 100 GeV² and after conversion with hbarc = 389 GeV⁻² µb.

When adding ptl1min and ptl2min cuts (minimum pt for the leading and
second lepton in pt) in Cards/run_card.dat for the values
pT = p' sin (theta_cm) we get the correct cross section between
theta_cm_min and pi - theta_cm_min, which is after integration of
dsigma/dcos(theta) = pi alpha² / 2s (1 + cos² theta) over dcos(theta),
i.e. pi alpha² / 2s * 1/3 cos(theta_cm_min) ( cos(2 theta_cm_min) + 7 ).

E.g. after generating a bunch of runs we do indeed get the following:
```
ptl12min [GeV]	sigma [pb]	theta_min [deg]
0.001	928.9	0.01
0.002	930.0	0.02
0.003	928.0	0.03
0.004	928.7	0.05
0.005	929.0	0.06
0.05	928.8	0.57
0.5	923.0	5.74
1.0	901.4	11.54
1.5	866.7	17.46
2.5	754.1	30.00
4.0	467.9	53.13
4.5	322.9	64.16
4.8	200.2	73.74
4.9	140.5	78.52
4.95	98.9	81.89
4.99	44.1	86.38
```

So, we now understand that:
- mg5 generates N = 50000 events distributed "as nature would" without any
  need for reweighting and with a total cross section given (e.g. 930 pb),
- it should be possible/appropriate to use the total cross section / N as
  the remoll weight for each event and then use that to determine the rate
  weight in remoll.

We don't understand yet what the effective luminosity is or if we even need
to understand that.


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