Implementation of N3LO k-factors

[giacomomagni]

Here we sketch a TODO list of the major issues
that have to be fixed in order to produce N3LO DIS k-factors
or merge this implementation in Yadism:

• Generalise the code such it can work for any heavy threshold for and generic nf @andreab1997
• Update inputs from ADANI taking advantage from the work done by @niclaurenti writing a new python wrapper for his code.
• Interface ADANI with this code @andreab1997
• Update the x-space N3LO matching conditions (M_QG, M_Qq) using the inverting the N-space Eko implementation @giacomomagni.
• Use the massless N3LO coefficient functions implemented in yadism, to minimise the inputs @giacomomagni
• Implement the actual cross sections (import form yadism)
• Parallelise the integration to make the code faster.
• Decide the output format. There are at least 3 options: integrate the code in yadism, produce k-factors N3LO_heavy/NNLO or produce N3LO_heavy/N3LO
• Eventually propagate the approximation uncertainty to the FK-tables
• extend fonll in F2_M, FL_M
• implement input format (something like pineko) @andreab1997
• Benchmark fonll nlo/nnlo with yadism @giacomomagni
• Benchmark massive coeff funcs against yadism @giacomomagni
• compute all the N3LO grids F2 (tilde funcs) @giacomomagni
• compute all the N3LO grids FL (tilde funcs) @giacomomagni

[giacomomagni]

To summarise, for a first round of fits,
we have agreed that:

• for CC DIS we will use Yadsim at N3LO, which contains ZM-VFNS up to N3LO and FONLL up to NNLO.
• for NC DIS we will produce k-factors of the type N3LO/NNLO both computed with this code and use NNLO Yadism grids
• The above k-factors should not contain any charm mass effect for point Q > m_b
• We will need to implement consistently F_total with this code up to NNLO.
  I wonder if we can delegate Yadism to do this, most likely it will not be consistent...
• The N3LO pieces will be just the sum of F_light + F_heavy.

@andreab1997 please feel free to add more relevant points of the discussion, or amend anything that is not correct.

[giacomomagni]

TODO list:

• Turn off charm effects above m_b and turn on m_b effects. Addition of Ftotal and Flight #14
• Always switch to FO below m_c. Addition of Ftotal and Flight #14
• Add all he relevant NC cross section definition. init k factors runner #12
• Add the possibility to perform operation with different datasets since there is not always the relation one dataset one k-factor file. init k factors runner #12
• Add the F_light and F_total. Can we delegate this to Yadism and remain consistent?? Addition of Ftotal and Flight #14
• Add a dumping to make FONLL transition smoother?

@andreab1997 feel free to put your name close to any of these items if you want to work on it.
Especially the last point seem to be kind of hard to implement again.
But delegating it to Yadism up to NNLO can introduce inconsistencies, for instance in the value of a_s or the treatment of heavy quarks. Any idea?

[giacomomagni]

• Add the F_light and F_total. Can we delegate this to Yadism and remain consistent?? Addition of Ftotal and Flight #14

#14 addressed this except for Fmissing

[andreab1997]

I guess that this is more or less closed. The only points that are still open are:

• Interface ADANI with this code @andreab1997. This I something I should have done but now I think is better to keep the codes separated if you agree @giacomomagni
• Eventually propagate the approximation uncertainty to the FK-tables. I guess this has been done.
• Add a dumping to make FONLL transition smoother? I don't believe we want to do since by default yadism is not doing it.

So if you agree with me I would close this issue.

[giacomomagni]

yes we can close. About the 2 missing items:

• the interface with adani would be really slow with the current status of the code
• the dumping seems to be not needed.