Scale variation grids

[cschwan]

According to the aMCfast paper (first paragraph in section 2.4) it's possible to get the scale-varied results even without the renormalization/factorization-scale grids; they refer to the APPLgrid paper, specifically eq. (14).

Do we want to want to implement this using PineAPPL + EKO? APPLgrid has the same feature, but using HOPPET.

[alecandido]

In principle it should be possible: in the case of DIS we are actually doing it explicitly in yadism.

ker_orders are essentially the separate contributions that we use to fill a PineAPPL grid (indeed they are later assigned to obs.orders, the one consumed to actually fill the PineAPPL grid).

I guess we can do the exact same for hadronic events, we just need the actual formula, the counter-parts of this one:
https://yadism.readthedocs.io/en/latest/theory/scale-variations.html#factorization
and this one:
https://yadism.readthedocs.io/en/latest/theory/scale-variations.html#renormalization

We always need the coefficients of the respective RGE: splitting functions for DGLAP (fact scale), and beta for alphas running (ren scale).
Both are available in EKO.

[alecandido]

Of course we'll need to do two different things for hadronic and DIS (in general for processes with 1 and 2 protons, we do not depend on the specific process).

DIS-like should be strictly simpler, but given that is already available in yadism, I'd do it immediately only if we need a benchmark. Otherwise I would go directly for hadronic, that will be the practical use case.

[alecandido]

Ah, wait a second, maybe we'll need actually yadism: in EKO splitting functions are only present in N-space, but we'll need them in x-space.