Implementation of correlated PDF and scale error

[tgiani]

In order to implement the theory error on the SM predictions due to the PDFs and scale, for each datapoint we need the theory predictions for each replica and scale variation. We propose the following format to be added in the theory tables:

• for the PDF error we need something like

"pdf_replicas": [
    [1, ..., n_dat,],
    ...,
    [n_rep, ..., n_dat],
 ]

• for the scale error we need all the 7 (or 9, depending on the set up of the monte carlo you are using) variations:

  "(0.5,1)": [
  1, ... , n_dat # (kf=0.5, kr=1)
  ],
  "(1,0.5)" : [
  1, ... , n_dat  # (kf=2, kr=1)
  ],
  ...

  would this work for you? @jacoterh @LucaMantani @moatms

[LucaMantani]

Hi Tommaso, Yes, in general i would say that's doable. I'll think more about it and maybe we can discuss it at the next meeting.

One problem I can foresee, the best_sm is often read from papers where the theory uncertainties are not going to be given in that format. We have the madgraph runs that have the numbers precisely in that shape though.

Is there a specific reason why you would want them in that format? Is it because that way one can infer the correlations?

[tgiani]

Hi Luca, yes indeed, with this kind of format we can build a covmat which takes into account the correlation between different dataset. And indeed I was thinking that the output you have from madgraph should be already in a similar shape