# What is the exact meaning of "PDF variation"?

Hi,

when I'm generating some process in MadGraph5_aMC@NLO, I usually see this in the logs:

22:29:17 INFO: Running Systematics computation
22:29:23 INFO: # events generated with PDF: NNPDF23_lo_as_0130_qed (247000)
22:29:23 INFO: #Will Compute 145 weights per event.
22:29:23 INFO: # currently at event 0 [elapsed time: 0.061 s]
22:29:40 INFO: # currently at event 2500 [elapsed time: 17 s]
22:29:57 INFO: # currently at event 5000 [elapsed time: 34 s]
22:30:15 INFO: # currently at event 7500 [elapsed time: 51 s]
22:30:32 INFO: #***************************************************************************
22:30:32 #
22:30:32 # original cross-section: 2.217067e-05
22:30:32 # scale variation: +11.8% -10.1%
22:30:32 # central scheme variation: +12.9% -9.5e-10%
22:30:32 # PDF variation: +9.86% -9.86%
22:30:32 #
22:30:32 # dynamical scheme # 1 : 2.40165e-05 +12.3% -10.4% # \sum ET
22:30:32 # dynamical scheme # 2 : 2.23752e-05 +11.8% -10.1% # \sum\sqrt{m^2+pt^2}
22:30:32 # dynamical scheme # 3 : 2.50262e-05 +12.5% -10.6% # 0.5 \sum\sqrt{m^2+pt^2}
22:30:32 # dynamical scheme # 4 : 2.21707e-05 +11.8% -10.1% # \sqrt{\hat s}
22:30:32 #***************************************************************************

What is the meaning of the "PDF variation" line? And how can I figure out which PDF variations were actually performed?

Thanks!

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 Yury (letra1947) said on 2021-04-22: #1

Hi,

I didn't see any reply, maybe my question wasn't clear enough: how exactly are the numbers in the line below (taken from my example) are calculated? What is a PDF variation? How is it done exactly?

22:30:32 # PDF variation: +9.86% -9.86%

 Olivier Mattelaer (olivier-mattelaer) said on 2021-04-22: #2

Those are computed by the lhadpf library.
In principle the lhapdf is computing such error in a different way for the various type PDF.
For NNPDF, the various PDF correspond to various replica so I guess this is a standard-deviation computation.

The evaluation of the cross-section for the 100 different PDF needed for computation of the systematics is done by MG5aMC via a re-weighting procedure. ( see 1801.08401 <https://arxiv.org/abs/1801.08401> for more details)

Cheers,

Olivier

> On 22 Apr 2021, at 11:30, Yury <email address hidden> wrote:
>
> Question #696647 on MadGraph5_aMC@NLO changed:
>
> Yury posted a new comment:
> Hi,
>
> I didn't see any reply, maybe my question wasn't clear enough: how
> exactly are the numbers in the line below (taken from my example) are
> calculated? What is a PDF variation? How is it done exactly?
>
> 22:30:32 # PDF variation: +9.86% -9.86%
>
> --