= Description of the method
 The method consist to use a sample of events (weighted or unweighted events) and associate to those events a new weight corresponding to a new theoretical hypothesis.
 This weight can be propagate through the all simulation chain in order to avoid to have to perform the full-simulation on a huge number of sample.
 This methods works only if the original hypothesis and the new one are both significant in the same part of the phase-space. 
 the new weight is given by 
 $$W_{new} = |M_{new}|^2 /|M_{old}|^2 * W_{old} $$

= Technical details
 == Limitation
  1. The two theoretical hypothesis should differ ONLY by difference in the model parameters. So this should be the same process, the same model and the same pdf.
  2. The scale choice for the reweighting is done events by events and is given by the value in the LHE file. The same scale is used for both Hypothesis
  3. In presence of decay chain the order of the particle in the events file is important. This is important if you want to use this tools with LHE events not produced by MadGraph/MadEvent.

 == How to get the code
 The code is currently (30/06/13) in beta, and is still expect to be modify before the official release (especially on the interface).
 In order to download the code, you need to have bazaar install on your computer. Then you can download the code via the command
{{{bzr branch lp:~maddevelopers/madgraph5/reweight_module}}}  
After that in order to update your version. You only need to do:
{{{bzr pull}}}
 
 == How to use the code.
 1. go to the process directory. 
 2. launch the '''./bin/madevent''' script
 3. type '''reweight RUN_NAME'''
 4. then you will see the following question:
{{{
Do you want to edit one cards (press enter to bypass editing)?
  1 / reweight  : reweight_card.dat
 you can also
   - enter the path to a valid card.
 [0, done, 1, reweight, enter path][60s to answer]
}}}
    If you didn't define the content of this file already. You need to do it. The syntax is explained inside the file, and you can see example below (validation section). The '''important''' point, is that the first line should be launch, and then you specify which parameter, you want to modify. This is the exact same syntax has for scripting a scan over parameter.
 5. exit the file and you are done (the script will run).

'''If the file Cards/reweight_card.dat is already defined''', you can launch the script with
{{{
./bin/madevent reweight RUN_NAME -f
}}}
The '''-f''' options prevent the question to be asked.

 = Input/Output format

 1. the output format follows the Leshouches agreement (not yet published): http://phystev.in2p3.fr/wiki/2013:groups:tools_lheextension#the_proposal

as an example the header looks like:
 {{{
<initrwgt>
<weightgroup type='mg_reweighting'>
<weight id='mg_reweight_1'>set param_card dim6 1 100.0
</weight>
<weight id='mg_reweight_2'>set param_card dim6 2 100.0
</weight>
<weight id='mg_reweight_3'>set param_card dim6 3 100.0
</weight>
</weightgroup>
</initrwgt>
}}}
and one associated events:
{{{
<event>
 8      0 +7.9887000e-06 1.24664300e+02 7.95774700e-02 1.23856500e-01
        1 -1    0    0  501    0 +0.0000000e+00 +0.0000000e+00 +1.3023196e+03 1.30231957e+03 0.00000000e+00 0.0000e+00 -1.0000e+00
       -2 -1    0    0    0  501 +0.0000000e+00 +0.0000000e+00 -1.4499581e+02 1.44995814e+02 0.00000000e+00 0.0000e+00 1.0000e+00
      -24  2    1    2    0    0 -1.2793809e+01 -8.3954553e+01 -1.1792566e+02 1.65987064e+02 8.02071978e+01 0.0000e+00 0.0000e+00
       23  2    1    2    0    0 +1.2793809e+01 +8.3954553e+01 +1.2752494e+03 1.28132832e+03 9.12640692e+01 0.0000e+00 0.0000e+00
       11  1    3    3    0    0 -1.2462673e+01 +1.3647422e+01 -2.6083861e+01 3.19677669e+01 0.00000000e+00 0.0000e+00 -1.0000e+00
      -12  1    3    3    0    0 -3.3113586e-01 -9.7601975e+01 -9.1841804e+01 1.34019297e+02 0.00000000e+00 0.0000e+00 1.0000e+00
        4  1    4    4  502    0 -1.8321803e+01 +9.0929609e+01 +9.3905973e+02 9.43629724e+02 0.00000000e+00 0.0000e+00 -1.0000e+00
       -4  1    4    4    0  502 +3.1115612e+01 -6.9750557e+00 +3.3618969e+02 3.37698598e+02 0.00000000e+00 0.0000e+00 1.0000e+00
<rwgt>
<wgt id='mg_reweight_1'> 4.55278761371e-06 </wgt>
<wgt id='mg_reweight_2'> 2.65941887458e-06 </wgt>
<wgt id='mg_reweight_3'> 8.68203803896e-06 </wgt>
</rwgt>
</event>
}}}
 2. The reweight_card in that case was:
{{{
launch
   set Dim6 1 100
   set Dim6 2 0
   set Dim6 3 0
   set Dim6 4 0
   set Dim6 5 0
launch
   set Dim6 1 0
   set Dim6 2 100
   set Dim6 3 0
   set Dim6 4 0
   set Dim6 5 0
launch
   set Dim6 1 0
   set Dim6 2 0
   set Dim6 3 100
   set Dim6 4 0
   set Dim6 5 0
}}}
Note:
    a. The production events were in this case made via the SM where all those coefficient were in fact set to zero. Therefore all the line setting the line to zero were superfluous, and this is the reason why they didn't appear in the banner. 
    b. You can also specify a path to a param_card in the reweight_card. The content of the header being computed automatically with the difference of the two param_card.
 
 3. The cross-section of the original file and those associated with the new hyppothesis are printed at the end of the script:
{{{
INFO: Original cross-section: 0.80086112072 +- 0.0025669959099 pb 
INFO: Computed cross-section: 
INFO: 119 : 5.0238030968 
INFO: 120 : 4.46724081967 
INFO: 121 : 0.790019392142 
}}}

 = Validation

  1. The validation of this tools is not yet finish. Use this tools with care. In particular in presence of decay chain, if you have identical particles in the final states coming from different decay. (For example p p > w+ z, w+ > e+ ve, z > e+ e-)

  2. The comparison for the full cross-section are done like this:
{{{ ./bin/madevent ./Cards/reweight_card.dat}}}

 == p p > e+ e- cross-section

 1. The reweight_card is the following:
{{{
launch
 set aewm1 100
launch 
 set aewm1 200
launch 
 set aewm1 300
}}} 
 2. The associated cross-section are 
   1. 1135.25 pb
   2. 1095.28 pb
   3. 1329.52 pb
 3. The cross-section computed with MadEvent are 
   1. 1130 +- 2.815 pb
   2. 1098 +- 2.478 pb
   3. 1336 +- 2.777 pb

 == EWDIM6 Validation
 
 1. The model use for this validation is the EWDIM6 (See: http://arxiv.org/abs/arXiv:1205.4231). 10k events where generated with the standard model (cross-section:  0.8008 ± 0.0026 pb)
 2. The reweight_card was:
{{{
launch
   set Dim6 1 100
   set Dim6 2 0
   set Dim6 3 0
   set Dim6 4 0
   set Dim6 5 0
launch
   set Dim6 1 10
   set Dim6 2 0
   set Dim6 3 0
   set Dim6 4 0
   set Dim6 5 0
launch
   set Dim6 1 1
   set Dim6 2 0
   set Dim6 3 0
   set Dim6 4 0
   set Dim6 5 0
launch
   set Dim6 1 0.1
   set Dim6 2 0
   set Dim6 3 0
   set Dim6 4 0
   set Dim6 5 0
launch
   set Dim6 1 0.01
   set Dim6 2 0
   set Dim6 3 0
   set Dim6 4 0
   set Dim6 5 0
}}} 
The same scan was done for the three first coupling (CWWW, CW, CB)

This is the result:
 1. For CWWW
|| Coupling value (TeV^-2)|| Reweight cross-section (pb) || MadEvent cross-section (pb)|| Status ||
||    0.01                ||  0.800810008029             ||  0.7973 ± 0.0023  || OK ||
||    0.1                 ||  0.800903791291             ||  0.799 ± 0.0026   || OK ||
||    1                   ||  0.802209013071             ||  0.7987 ± 0.0025  || OK ||
||    10                  ||  0.85200014698              ||  0.8584 ± 0.00092 || OK ||
||    100                 ||  5.0238030968               ||  6.09 ± 0.0082    || '''FAIL''' ||
||    100                 ||  5.04763                    ||  6.09 ± 0.0082    || '''FAIL'''  (make with a sample of 100k events) ||

  The last entry fails since the expected distribution for such value of the coupling is too different from the distribution of the Standard Model. Such discrepancy are expected in this case. One hint is that the cross-section is an order of magnitude higher than the original one (Looking at the distribution confirm this).

 2. For CW
|| Coupling value (TeV^-2)|| Reweight cross-section (pb) || MadEvent cross-section (pb)|| Status ||
||    0.01                ||  0.800798262059             ||  0.7953 +- 0.002497  || OK ||
||    0.1                 ||  0.801379445746             ||  0.7988 ± 0.0023   || OK ||
||    1                   ||  0.806872565125             ||  0.8065 ± 0.0023  || OK ||
||    10                  ||  0.889336417677             ||  0.8832 ± 0.003 || OK ||
||    100                 ||  4.46724081967              ||  4.519 ± 0.015    || '''FAIL''' ||
||    100                 ||  4.44273                    ||  4.519 ± 0.015    || '''FAIL'''  (make with a sample of 100k events) ||
  Same comment as for the previous coupling.

 2. For CB
|| Coupling value (TeV^-2)|| Reweight cross-section (pb) || MadEvent cross-section (pb)|| Status ||
||    0.01                ||  0.800798262059             ||  0.7977 ± 0.0027   || OK ||
||    0.1                 ||  0.800782626532             ||  0.7985 ± 0.0024    || OK ||
||    1                   ||  0.800626859275             ||  0.7981 +- 0.002365  || OK ||
||    10                  ||  0.799127987884             ||  0.7971 ± 0.0024 || OK ||
||    100                 ||  0.790019392142             ||  0.7852 ± 0.0026    || OK ||
||    100                 ||  0.786698206995             ||  0.7852 ± 0.0026    || OK  (make with a sample of 100k events) ||
  This operator has less impact on the cross-section/distributions, and therefore even a large value of the coupling is still working fine.

Note:
  1. The cross-section obtained for 100k events sample is 0.7989 ± 0.00087 
  2. The statistical fluctuation of the original sample appears on the reweighing (as expected)