This merge request follows discussion with Powheg experts. The point is that when virtual corrections are added only in the reweighting stage, which is the case when for_reweighting=1, then the "correct" nominal weight is the one in the <rwgt> block, which can be different from the one in the <event> block in the XWGTUP field, which is the one seen by Pythia8.
Comments have been added in the code to explain precisely how this works.
I added a new post-processor, used when for_reweighting is set to 1. It saves the original XWGTUP value (3rd field of the 1st line in the <event> block) into a new weight with id='9001' and name 'XWGTUP_original' in a new weightgroup called 'supplemental', and put the correct nominal weight, i.e. the weight with id='0' in the <rwgt> block as updated XWGTUP value.
I tested this on ttbb(4fs) on which for_reweighting=1 is used by default. I'm actually wondering if we should set this option to 0 by default, as it would solve the problem in the first place (and avoid having weights with weirdly distributed values), even if this would make the integration take longer.
To make this clearer, the postprocessor would replace this header:
<header>
<initrwgt>
<weightgroup name='nominal' combine='None' >
<weight id='0'>nominal</weight>
</weightgroup>
<weightgroup name='scale_variation' combine='envelope' >
<weight id='1001'>MUR0.5_MUF0.5_PDF260400</weight>
<weight id='1002'>MUR2_MUF2_PDF260400</weight>
</weightgroup>
</initrwgt>
</header>by this header:
<header>
<initrwgt>
<weightgroup name='nominal' combine='None' >
<weight id='0'>nominal</weight>
</weightgroup>
<weightgroup name='scale_variation' combine='envelope' >
<weight id='1001'>MUR0.5_MUF0.5_PDF260400</weight>
<weight id='1002'>MUR2_MUF2_PDF260400</weight>
</weightgroup>
<weightgroup name='supplemental' combine='None' >
<weight id='9001'>XWGTUP_original</weight>
</weightgroup>
</initrwgt>
</header>and as an example, the following event:
<event>
7 10000 3.12361E+01 1.16134E+01 -1.00000E+00 1.72973E-01
21 -1 0 0 511 501 0.000000000E+00 0.000000000E+00 1.691171169E+03 1.691171169E+03 0.000000000E+00 0.00000E+00 9.000E+00
21 -1 0 0 503 502 0.000000000E+00 0.000000000E+00 -6.346605967E+01 6.346605967E+01 0.000000000E+00 0.00000E+00 9.000E+00
6 1 1 2 503 0 -7.606837856E+01 8.674122935E+01 3.190628274E+02 3.806149983E+02 1.725000000E+02 0.00000E+00 9.000E+00
-6 1 1 2 0 505 1.506979933E+01 -4.843859098E+01 2.389470862E+02 2.990407262E+02 1.725000000E+02 0.00000E+00 9.000E+00
5 1 1 2 505 0 5.193616324E+01 -2.207973149E+01 3.553083119E+02 3.597936056E+02 4.750000000E+00 0.00000E+00 9.000E+00
-5 1 1 2 0 501 1.135230586E+01 -4.837454490E+00 1.270512428E+02 1.277374519E+02 4.750000000E+00 0.00000E+00 9.000E+00
21 1 1 2 511 502 -2.289889873E+00 -1.138545239E+01 5.873356408E+02 5.874504465E+02 7.629394531E-06 0.00000E+00 9.000E+00
<rwgt>
<wgt id='0'>0.28696E+02</wgt>
<wgt id='1001'>0.26353E+02</wgt>
<wgt id='1002'>0.24219E+02</wgt>
</rwgt>
</event>would be replaced by:
<event>
7 10000 0.28696E+02 1.16134E+01 -1.00000E+00 1.72973E-01
21 -1 0 0 511 501 0.000000000E+00 0.000000000E+00 1.691171169E+03 1.691171169E+03 0.000000000E+00 0.00000E+00 9.000E+00
21 -1 0 0 503 502 0.000000000E+00 0.000000000E+00 -6.346605967E+01 6.346605967E+01 0.000000000E+00 0.00000E+00 9.000E+00
6 1 1 2 503 0 -7.606837856E+01 8.674122935E+01 3.190628274E+02 3.806149983E+02 1.725000000E+02 0.00000E+00 9.000E+00
-6 1 1 2 0 505 1.506979933E+01 -4.843859098E+01 2.389470862E+02 2.990407262E+02 1.725000000E+02 0.00000E+00 9.000E+00
5 1 1 2 505 0 5.193616324E+01 -2.207973149E+01 3.553083119E+02 3.597936056E+02 4.750000000E+00 0.00000E+00 9.000E+00
-5 1 1 2 0 501 1.135230586E+01 -4.837454490E+00 1.270512428E+02 1.277374519E+02 4.750000000E+00 0.00000E+00 9.000E+00
21 1 1 2 511 502 -2.289889873E+00 -1.138545239E+01 5.873356408E+02 5.874504465E+02 7.629394531E-06 0.00000E+00 9.000E+00
<rwgt>
<wgt id='0'>0.28696E+02</wgt>
<wgt id='1001'>0.26353E+02</wgt>
<wgt id='1002'>0.24219E+02</wgt>
<wgt id='9001'>3.12361E+01</wgt>
</rwgt>
</event>